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Abstract In traditional finite element failure analyses of geotechnical structures, the micro grain rotations cannot be modelled and numerical solutions are mesh dependent. In this study, a user element including rotational degree of freedom has been developed based on micropolar theory (Cosserat theory), then an enhanced non-associated sand model is calibrated with laboratory data and used to model the plane strain tests. The simulated results demonstrate the polarized model is able to model reasonably the sand behavior as well as the grain rotations in the localized region. What’s more, with this enhanced model, the mesh independent numerical solutions in terms of mechanical responses, shear bands thickness and orientations have been obtained. Article highlights In failure analysis of geostructures, significant rotations of soil grains have been observed to occur in the strain localized regions, but the current commercial Finite Element tools cannot model the micro rotations. Therefore, a user defined element must be developed to include the rotational degree of freedom. The micropolar approach is proven to be effective to model the grain rations in present paper. More suitable than other classical soil or sand constitutive models, the selected non-associated sand model in present paper is capable of describing well the contraction and shear dilatancy behaviors of sand. Then the model has been enhanced by means of micropolar technique, in this way, the reasonable strain localization phenomena in laboratory tests could be predicted well. There are always the mesh dependent problems for traditional simulations of the strain localization phenomena in finite element analysis. It can be found in present paper that the mesh independent numerical solutions are obtained by means of micropolar technique. Furthermore, the micropolar approach can obviously improve convergence difficulties in finite element analyses.

Deformation behavior of 1Al containing Mg alloy has been investigated in the present study. After annealing, the Mg-1Al alloy shows a typical basal texture. When compared to the pure Mg having a similar texture and grain size, the Mg-1Al alloy shows much higher strength and larger elongation. Slip trace analyses of the tensile strained specimens show that non-basal slips such as pyramidal I and II slips can be easily activated at an early stage of deformation in the Mg-1Al alloy and the grains in the Mg-1Al alloy are seen to accommodate a larger degree of deformation than those in the pure Mg at a given strain. With increasing tensile strain, however, there is a strain localization along the initially formed slip lines of non-basal slips, forming surface steps without activating multiple slip lines.

Extension is a key process controlling the post-orogenic exhumation of metamorphic rocks in subduction and collision zones. Previous studies have largely focused on the mechanics of localized core-complex style post-orogenic extension and the large-scale effects of various internal (e.g. rheology) and external (e.g. plate motions) parameters on the mode of extension. However, many regions on earth underwent rock exhumation during post-orogenic extension, which is characterized by distributed rather than localized deformation. We explore conditions of distributed deformation as illustrated by the Pelagonian unit in the Aegean subduction system. In particular, we explore the influence of structural inheritance related to the pre-extension shortening and mechanical stratigraphy on the localization of extension on the scale of the upper crust through detailed structural analysis on the islands of Skiathos and Skopelos. Additionally, the time frame of deformation has been established by 40Ar/39Ar dating of key shear zones. Shortening on the islands predominantly took place by ductile top-SW thrusting under low-grade metamorphic conditions, localized in weak calcite marble layers within the Upper Cretaceous and Upper Triassic carbonates at ~55 Ma. We show that the presence of shallow decoupling levels in the upper crust resulted in the formation of thin (several 100 m thick) thrust sheets that are defined for the first time on Skiathos. The Early Paleogene accretion of the Pelagonian upper crust to the upper plate (Eurasia/Rhodopia) was followed by the extensional inversion of the nappe stack. Extension was accommodated by opposite-sense, generally top-NE, ductile to brittle shearing, which localized at inherited heterogeneities such as reverse-sense shear zones and stratigraphic contacts at around 35 Ma, as suggested by our 40Ar/39Ar age spectra. The dense network of such northerly-dipping, inherited weakness zones resulted in a highly distributed pattern of extensional deformation dominated by layer-parallel shearing. We argue that the distribution of crustal heterogeneities substantially influences the style of post-orogenic extension.

This paper investigates the deformation and fracture propagation of sandstone specimen under uniaxial compression using the distributed fiber optic strain sensing (DFOSS) technology. It shows that the DFOSS-based circumferential strains are in agreement with the data monitored with the traditional strain gage. The DFOSS successfully scans the full-field view of axial and circumferential strains on the specimen surface. The spatiotemporal strain measurement based on DFOSS manifests crack closure and elastoplastic deformation, detects initialization of microcrack nucleation, and identifies strain localization within the specimen. The DFOSS well observes the effects of rock heterogeneity on rock deformation. The advantage of DFOSS-based strain acquisition includes the high spatiotemporal resolution of signals and the ability of full-surface strain scanning. The introduction to the DFOSS technology yields a better understanding of the rock damage process under uniaxial compression.

The factors controlling the inception of continental-scale transcurrent shear zones are still under debate. In order to a better understanding of the origin and evolution of the 400 km long West Pe...

Deformation microstructures of peak metamorphic conditions in ultrahigh-pressure (UHP) metamorphic rocks constrain the rheological behavior of deeply subducted crustal material within a subduction channel. However, studies of such rocks are limited by the overprinting effects of retrograde metamorphism during exhumation. Here, we present the deformation microstructures and crystallographic-preferred orientation data of minerals in UHP rocks from the Dabie–Shan to study the rheological behavior of deeply subducted continental material under UHP conditions. The studied samples preserve deformation microstructures that formed under UHP conditions and can be distinguished into two types: high-strain mafic–ultramafic samples (eclogite and garnet-clinopyroxenite) and low-strain felsic samples (jadeite quartzite). This distinction suggests that felsic rocks are less strained than mafic–ultramafic rocks under UHP conditions. We argue that the phase transition from quartz to coesite in the felsic rocks may explain the microstructural differences between the studied mafic–ultramafic and felsic rock samples. The presence of coesite, which has a higher strength than quartz, may result in an increase in the bulk strength of felsic rocks, leading to strain localization in nearby mafic–ultramafic rocks. The formation of shear zones associated with strain localization under HP/UHP conditions can induce the detachment of subducted crustal material from subducting lithosphere, which is a prerequisite for the exhumation of UHP rocks. These findings suggest that coesite has an important influence on the rheological behavior of crustal material that is subducted to coesite-stable depths.

Funding Information: Ivan Lomakin and Xavier Sauvage are grateful to the Embassy of France in Russia for supporting their collaboration through Mechnikov’s Scholarship. This work was partially supported by Saint Petersburg State University, Russia via Lot 2017 applied (id: 26130576 ). This work was partially supported by Academy of Finland through grant 317464 . XRD results were obtained by the “Center for X-ray Diffraction Methods” of the Research park of Saint Petersburg University. Anvils for HPT tool were produced in collaboration with center “Applied aerodynamics” of the Research park of Saint Petersburg University. Authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano - Nanomicroscopy Center (Aalto-NMC). Funding Information: Ivan Lomakin and Xavier Sauvage are grateful to the Embassy of France in Russia for supporting their collaboration through Mechnikov's Scholarship. This work was partially supported by Saint Petersburg State University, Russia via Lot 2017 applied (id: 26130576). This work was partially supported by Academy of Finland through grant 317464. XRD results were obtained by the ?Center for X-ray Diffraction Methods? of the Research park of Saint Petersburg University. Anvils for HPT tool were produced in collaboration with center ?Applied aerodynamics? of the Research park of Saint Petersburg University. Authors acknowledge the provision of facilities and technical support by Aalto University at OtaNano - Nanomicroscopy Center (Aalto-NMC). Publisher Copyright: © 2021 The Author(s) The influence of the structural state on deformation mechanisms under large strains was investigated in a Cu – 2 wt.% Be alloy. Torque evolutions during straining exhibit serrations typical of structural relaxations in the precipitation-hardened alloy, but not in the solid solution state. Microstructure characterization revealed that homogeneous deformation of the solid solution led to strong grain size reduction (20 nm), while localization occurred in the precipitated state with numerous shear bands. The role of CuBe precipitates on hindering dislocation glide and the resulting shear localization under large strain is discussed.

Hydrogen repartitioning and the related embrittlement behavior were characterized by studying Al–Zn–Mg–Cu aluminum alloys with different intermetallic particle contents. Using high-resolution X-ray tomography and related microstructural tracking techniques, hydrogen-induced quasi-cleavage cracks and the related strain localization were observed regardless of the content of the intermetallic particles. The area of quasi-cleavage cracks on the fracture surface increased and the strain localization became more intense with a decrease in the content of intermetallic particles, thereby revealing that trapped hydrogen at intermetallic particles increases the resistance to hydrogen embrittlement. In addition, a quantitative assessment of the hydrogen repartitioning taking into account vacancy production and dislocation multiplication during deformation, was applied to characterize the hydrogen embrittlement behavior. Because of the thermal equilibrium among various hydrogen trap sites, internal hydrogen atoms are mainly repartitioned to vacancies and precipitates in the strain localization region during deformation because of their high trap site densities and high hydrogen trap binding energies. Since the concentration of hydrogen trapped at dislocations is extremely limited, it can be assumed that hydrogen repartitioned to precipitates induces decohesion of precipitates along specific crystallographic planes, where quasi-cleavage cracking may originate.

The Pennine Basal Thrust (PBT) is an exhumed megathrust developed during continental collision from late Eocene to Miocene. To trace its evolution, five samples, with indications for up to three microstructurally diachronous white-mica generations, were investigated by laser in-situ and step-heating Ar-40-Ar-39 dating. Three deformation-related crystallization ages can be distinguished: (1) D-1, characterized in the PBT hanging wall by an S-1 foliation defined by white mica + chloritoid, began at or before similar to 38.0 Ma; (2) D-2 formed a pervasive S-2 cleavage and synchronous white-mica rich veins dated at similar to 27 Ma; (3) D(3)produced an S-3 crenulation cleavage and chlorite + white-mica veins dated at similar to 23 Ma. Older ages of similar to 96 Ma (footwall) and similar to 115 Ma (hanging wall) are interpreted as minimum ages for the detrital component. Finally, discrete faulting produced fault gouge, with an illite K-Ar age of similar to 19 Ma. A simplified back-restored reconstruction provides a tectonic context for the dated structures. In this framework, D-1 occurred during middle to late Eocene tectonic accretion. After late Eocene initiation of continental collision, D-2 reflects Oligocene top-to-NW shearing, with both in- and out-of-sequence thrusting. D-3 then developed from 23 to 19 Ma during the progressive deactivation of the PBT.

International audience; The generation of ductile shear zones is essential for the formation of tectonic plate boundaries, such as subduction or strike-slip zones. However, the primary mechanism of ductile strain localization is still contentious. We study here the spontaneous generation of ductile shear zones by thermal softening using thermo-mechanical numerical simulations for linear and power-law viscous flow in one-dimension (1D), 2D and 3D. All models are velocity-driven. The 1D model exhibits bulk simple shear whereas the 2D and 3D models exhibit bulk pure shear. The initial conditions include a small temperature perturbation in otherwise homogeneous material. We use a series of 1D simulations to determine a new analytical formula which predicts the temperature evolution inside the shear zone. This temperature prediction requires knowledge of only the boundary velocity, flow law and thermal parameters, but no a priori information about the shear zone itself, such as thickness, stress and strain rate. The prediction is valid for 1D, 2D and 3D shear zones in bulk pure and simple shear. The results show that shear heating dominates over conductive cooling if the relative temperature increase is >50 °C. The temperature variation induced by the shear zone is nearly one order of magnitude wider than the corresponding finite strain variation so that no significant temperature variation occurs between shear zone and wall rock. Applying typical flow laws for lithospheric rocks shows that shear zone generation by thermal softening occurs for typical plate tectonic velocities of few cm.yr−1 or strain rates between and s−1. Shear stresses larger than 200 MPa can already cause strain localization. The results indicate that thermal softening is a feasible mechanism for spontaneous ductile shear zone generation in the lithosphere and may be one of the primary mechanisms of lithospheric strain localization.

International audience; Granular materials can develop two different failure modes following their initial density and the loading path: a localized mode, generally characterized by shear bands, and a diffuse mode without any macroscopic localized bands. In fact detailed analyses of experiments by tomography, of finite element computations and more recently of discrete element models (DEM) simulations show that two different localized objects co-exist at two different scales: a network of meso-slip lines appearing from the very beginning of deviatoric loading and a few macro-shear bands when approaching limit stress states. This paper aims to compare and analyze these two localized patterns, based on DEM results obtained for a given class of loading paths applied to several 2D numerical granular samples with different initial densities. It is first shown that void ratios and granular meso-structures are the same inside shear bands and for the whole samples in case of diffuse failure. Then slip lines and shear bands are shown to be distinct localized objects. Eventually, the questions of why and how the network of meso-slip lines is sometimes bifurcating into a set of few macro-shear bands are discussed.

In this article, we introduce the Deformation Infrared Calorimetry (DIRC) technique for resolving spatial distributions of heat and work in samples subjected to uniaxial loading under isothermal conditions. Heat and work distributions are computed from synchronized temperature and strain fields obtained by infrared thermography (IRT) and digital image correlation (DIC). The DIRC data acquisition and processing are described in the first part of the article. Then, we show the relevance and usage of DIRC by employing it to characterize the cyclic evolution of the thermomechanical response of a superelastic NiTi wire termed functional fatigue. Particularly, we evaluated the evolution of the heat, work, and internal energy changes upon the repeated propagation of stress-induced martensitic transformations (SIMTs) shear-bands, producing a highly heterogeneous deformation scenario. Further postprocessing of DIRC allowed us to associate the functional fatigue of the material with the evolution of the production/recovery of martensite and the energy storage and dissipation during the propagation of SIMT shear-bands.

The mechanical behavior and the influence of compaction banding on the hydraulic properties in soft porous rocks were studied. The tested rock was Calcarenite Tuffeau de Maastricht. In the frame of experimental investigations, triaxial and oedometric tests were conducted under dry and drained conditions. The results demonstrated that the rock is forming discrete compaction bands under high confining stresses and steep angle shear bands under low confining stresses. Permeability measurements during the oedometric and triaxial compression tests under drained conditions demonstrated that the axial permeability decreases with increasing axial strain. The maximum permeability decrease was three orders of magnitude for 40% of axial strain.

International audience; The impact of the Portevin-Le Chatelier (PLC) effect on plasticity and fracture ahead of a severe notch is investigated by DIC field measurements for C-Mn steel. The PLC effect causes an intermittent activity of highly localized strain rate bands. This first high temperature investigation of the effect of a notch on the PLC localization bands is successfully reproduced numerically in terms of strain localization in 3D FE simulations. This thereby validates quantitatively the McCormick-type model under these complex conditions. It is found that, when the PLC effect is at play at elevated temperature (175 • C), a flat to slant crack transition is observed. In contrast, at room temperature, when only Lüders bands are active, the crack remains mostly flat, i.e. normal to the loading direction of the SENT samples. This behaviour may be related to the early loss of symmetry and intermittency of the plastic zone that is found for PLC even affecting the initial Lüders bands at elevated temperature. During the slant fracture at high temperature, only half the fracture energy is absorbed compared to flat fracture at room temperature. The McCormick-type model simulations predict slant strain rate bands through the sample thickness, that are consistent with the slant fracture found at elevated temperature. Accordingly, no slant bands are found for simulations outside the PLC domain. Both experiments and simulations show PLC strain localization bands that are flip-flopping up and down during crack propagation. By combining the McCormick-type model with a Rousselier porous plasticity model, the flat fracture of the sample at room temperature and the associated macroscopic curve are reproduced successfully, but the toughness at elevated temperature is overestimated.

In this paper the performance of a constitutive model for the description of the hydro mechanical behaviour of soft rock is evaluated with respect to the experimentally observed behaviour of Maastricht Calcarenite under different stress states that is presented in the companion paper. The mechanical model is elasto-plastic and consists of an associated yield surface, internal variables for the description of the hardening and softening behaviour and a non-local extension for the simulation of strain localization in form of shear bands and compaction bands. The model is implemented in the software ABAQUS and the laboratory results from the tests under dry condition with Maastricht Calcarenite are used for the calibration. The good agreement of the numerical results with the laboratory results is shown and the suitability of the model is discussed. To describe the effect of compaction bands on the permeability of soft rocks a simple analytical model based on the Kozeny–Carman equation is proposed and calibrated with the experimental results from drained tests under different stress states for Maastricht Calcarenite rock material. As the results are in good accordance with the experimental results, the model is implemented in the software ABAQUS and the numerical results are presented and discussed. Finally the performance of the model is evaluated and possible improvements are suggested.

International audience; Strain localization zones in the form of shear bands or compaction bands in geomaterials are observed across scales from sub-millimetric (grain size) to kilometric scale (geological structures). Triggering and evolution of such narrow zones of localized deformation depend on many factors. The mechanical behavior of geomaterials is central for the formation of such zones. However, thermal, pore-pressure and chemical effects play a crucial role in shear and compaction banding. Moreover, the inherent heterogeneous microstructure of geomaterials plays a significant role during strain localization. As for faults, compaction bands significantly influence the stress field and fluid transport. In this paper, we shall review some recent advances in experimental testing and numerical modelling on strain localization in geomaterials. The effect of grain crushing as observed in deformation bands under high confinement can be introduced by combining Breakage models and higher order continuum theories leading to a new framework of constitutive models with evolving microstructure. A major difficulty of these models is to establish reliable methods for the calibration of the higher order parameters (such as the internal length) in laboratory experiments. An example of a direct calibration of these parameters based on Digital Image Correlation of images provided by X-Ray tomography is proposed for the study of compaction banding in a carbonate rock.

International audience; To address the question of the initiation and mechanisms involved in the process of subduction zone formation, we explored most of the available evidence for the subduction initiation (SI) during the Cenozoic. For this, we targeted a total of 70 candidate sites for subduction initiation cumulating ~70,000 km of trench, two thirds of which are still active and a majority still immature. Our strategy is to define four stages reached for each subduction initiation site (SIS) from the incipient-diffuse stage through incipient-localized stage and early arc magma production to self-sustained subduction. We have paid special attention to prematurely extinguished, i.e., aborted, subduction attempts in order to better understand the reasons for the termination of the process, and thus to clarify the conditions of success. The failure of SI results from a combination of hindering parameters (e.g., lithosphere cooling, frictional resistance, unfavorable age contrasts for intra-oceanic SISs) and insufficient external forcings (e.g., too low convergence velocity). From this comprehensive study, we find that new subduction zones regularly nucleate, at a mean rate of about once every Myr, and with a success rate of more than 70% to reach subduction maturity, generally in less than ~15 Myr, ~3-8 Myr for the shortest time between the very early stage and the self-sustained stage. A majority forms at the transition between an ocean and a continent, plateau or volcanic arc, demonstrating that large differences in composition, topography and/or lithospheric weaknesses favor the localization of the strain. Lithospheric forces are required to ensure the success of the process in the early (immature) stages, with the help of mantle forces in a third of the cases. Multiple triggers are common. Stress during the SI process is compressive in most, if not all, cases and oriented obliquely to the nascent plate boundary in more than half of the cases. The incipient plate boundary generally reactivates an old lithospheric fault, most often with a change in its kinematics, i.e., conversion of a transform plate boundary, a former normal or a detachment fault, or even a former spreading center. Sometimes, the new lithospheric fault reactivates a former subduction fault. There is no rule concerning the age of the subducting plate which varies from 0 to 140 Ma in the examples studied. In the same vein, the subducting plate is not necessarily older than the overriding plate when it is oceanic. Both situations are equally observed.

International audience; The thin ice covering the polar oceans is a complex geomaterial that is constantly breaking and moving under the action of the wind and ocean currents and that experiences transitions between a brittle solid and a granular fluid state. We have developed a simple continuum mechanical framework in the view of representing accurately its dynamical behavior in regional and global sea ice or coupled climate models. It combines the concepts of elastic memory, progressive damage and viscous-like relaxation of stresses. Here, we present this framework and its ongoing numerical development based on Finite Element, Discontinuous Galerkin methods.

Strain localization in the lithosphere and the formation, evolution, and maintenance of resulting plate boundaries play a crucial role in plate tectonics and thermo‐chemical mantle convection. Previously activated lithospheric deformation zones often appear to maintain a “memory” of weakening, leading to tectonic inheritance within plate reorganizations including the Wilson cycle. Different mechanisms have been proposed to explain such strain localization, but it remains unclear which operates on what spatio‐temporal scales, and how to best incorporate them in large‐scale mantle convection models. Here, we analyze two candidates, (1), grain‐size sensitive rheology and, (2), damage‐style parameterizations of yield, stress which are sometimes used to approximate the former. Grain‐size reduction due to dynamic recrystallization can drive localization in the ductile domain, and grain growth provides a time‐dependent rheological hardening component potentially enabling the preservation of rheological heterogeneities. We compare the dynamic weakening and hardening effects as well as the timescales of strength evolution for a composite rheology including grain‐size dynamics with a pseudo‐plastic rheology including damage‐ (or “strain”‐) dependent weakening. We explore the implications of different proposed grain‐size evolution laws, and test to which extent strain‐dependent rheologies can mimic the weakening and hardening effects of the more complex micro‐physical behavior. Such an analysis helps to better understand the parallels and differences between various strain‐localization modeling approaches used in different tectonics and geodynamics communities. More importantly, our results contribute to efforts to identify the key ingredients of strain‐localization and damage hysteresis within plate tectonics and how to represent those in planetary‐scale modeling., Key Points: Comparative analysis of strain localization and damage memory for grain‐size dependent and strain/damage parameterized rheologies. Identification of key ingredients of strain localization and damage hysteresis and how to represent those in planetary‐scale modeling. Plastic strain softening enables hysteresis with a memory duration similar to grain growth at lithospheric temperature conditions.

The presence of pressurized fluids influences the mechanical behavior of faults. To test the roles of normal stress and fluid pressure on shear strength and localization behavior of calcite gouges, we conducted a series of rotary‐shear experiments with pore fluid pressures up to 10.5 MPa and difference between normal stress and fluid pressure up to 11.2 MPa. Calcite gouges were sheared for displacements of 0.3 m to several meters at slip rates of 1 mm/s and 1 m/s. Drainage conditions in experiments were constrained from estimates of the hydraulic diffusivity. Gouges were found to be drained at 1 mm/s, but possibly partially undrained during sliding at 1 m/s. Shear strength obeys an effective‐stress law with an effective‐stress coefficient close to unity with a friction coefficient of ~0.7 that decreases to 0.19 due to dynamic weakening. The degree of comminution and slip localization constrained from experimental microstructures depends on the effective normal stress. Slip localization in calcite gouges does not occur at low effective normal stress. The presence of pore fluids lowers the shear strength of gouges sheared at 1 mm/s and causes an accelerated weakening at 1 m/s compared to dry gouges, possibly due to enhanced subcritical crack growth and intergranular lubrication. Thermal pressurization occurs only after dynamic weakening when friction is generally low and relatively independent of normal stress and therefore unaffected by thermal pressurization. The experimental results are consistent with the view that the presence of pressurized fluid in carbonate‐bearing faults can facilitate earthquake nucleation., Key Points: Normal stress and fluid pressure equally affect shear strength of calcite gouges at relatively low effective normal stresses (≤11 MPa). The degree of slip localization in calcite gouges sheared at seismic slip rates increases with effective normal stress. Thermal pressurization has small effect on shear stress as it occurs after change from pressure‐ to temperature‐controlled slip behavior., European Research Council http://dx.doi.org/10.13039/501100000781

The Val Malenco peridotite massif is one of the largest exposed ultramafic massifs in Alpine orogen. To better constrain its tectonic history, we have performed a comprehensive petro-structural and geochemical study. Our results show that the Val Malenco serpentinized peridotite recorded both pre-Alpine extension and Alpine convergence events. The pre-Alpine extension is recorded by microstructural and geochemical features preserved in clinopyroxene and olivine porphyroblasts, including partial melting and refertilisation, high-temperature (900&ndash, 1000 &deg, C) deformation and a cooling, and fluid-rock reaction. The following Alpine convergence in a supra-subduction zone setting is documented by subduction-related prograde metamorphism features preserved in the coarse-grained antigorite and olivine grains in the less-strained olivine-rich layers, and later low-temperature (&lt, 350 &deg, C) serpentinization in the fine-grained antigorite in the more strained antigorite-rich layers. The strain shadow structure in the more strained antigorite-rich layer composed of dissolving clinopyroxene porphyroblast and the precipitated oriented diopside and olivine suggest dissolution and precipitation creep, while the consistency between the strain shadow structure and alternating less- and more-strained serpentinized domains highlights the increasing role of strain localization induced by the dissolution-precipitation creep with decreasing temperature during exhumation in Alpine convergence events.

Mechanical behavior of a multifunctional titanium alloy Gum Metal was investigated by conducting tensile tests at various strain rates and applying digital image correlation (DIC) technique. Stress–strain curves confirmed low Young’s modulus and high strength of the alloy. The determined values of yield strength had a tendency to increase, whereas the elongation to the specimen rupture tended to decrease with increasing strain rate. True stress versus strain curves were analyzed using selected lengths of virtual extensometer (VE) placed in the strain localization area. When the initial length of the VE was the same as the gauge length, work hardening was observed macroscopically at lower strain rates, and a softening was seen at higher strain rates. However, the softening effect was not observed at the shorter VE lengths. Evolution of the Hencky strain and rate of deformation tensor component fields were analyzed for various strain rates at selected stages of Gum Metal loading. The DIC analysis demonstrated that for lower strain rates the deformation is macroscopically uniform up to the higher average Hencky strains, whereas for higher strain rates the strain localization occurs at the lower average Hencky strains of the deformation process and takes place in the smaller area. It was also found that for all strain rates applied, the maximal values of Hencky strain immediately before rupture of Gum Metal samples were similar for each of the applied strain rates, and the maximal local values of deformation rate were two orders higher when compared to applied average strain rate values.

This work presents some novel results obtained by using the strain injection techniques for modeling crack propagation in challenging 3D benchmark tests. The techniques were already tested and validated by static and dynamic simulations in 2D ADDIN EN.CITE ADDIN EN.CITE.DATA [ HYPERLINK \l "_ENREF_1" \o "Dias, 2012 #1526" 1-4], so the main goal of this paper is to verify if the most important advantages of the method, low computational cost and independence of the results on the finite element mesh, are kept in 3D. The methodology, implemented in the finite element framework, consists essentially in injecting those elements that are going to capture the cracks with some enhanced strain modes for improving the performance of the elements for modeling propagating material failure.

Unaltered mafic rocks consist of mechanically strong minerals (e.g. pyroxene, plagioclase and garnet) that can be deformed by crystal plastic mechanisms only at high temperatures (>800°C). Yet, many mafic rocks do show extensive deformation by non-brittle mechanisms when they have been subjected to lower temperature conditions. In such cases, the deformation typically is assisted by mineral reactions. Here we show that dissolution-precipitation creep (as a type of diffusion creep) plays a major role in deformation of gabbro lenses at upper amphibolite facies conditions. The Kågen gabbro exposed on south Arnøya is comprised of almost undeformed gabbro lenses with sheared margins wrapping around them. The shearing has taken place at temperatures of 690 ± 25 °C and pressures of 1.0 to 1.1 GPa. This contribution analyses the evolution of the microstructures and fabric of the low strain gabbro to high strain margins. Microstructural and crystallographic preferred orientation (CPO) data indicate that dissolution-precipitation creep is the dominant deformation mechanism, where dissolution of the gabbro took place in reacting phases of clinopyroxene and plagioclase, and precipitation took place in the form of new minerals: new plagioclase and clinopyroxene (with different composition), amphibole, and garnet. Amphibole shows a strong CPO that is primarily controlled by its preferential growth in the stretching direction. Synchronous deformation and mineral reactions of clinopyroxene suggest that mafic rocks can become mechanically weak during a general transformation weakening process, i.e. the interaction of mineral reaction and deformation by diffusion creep. The weakening is directly connected to a fluid-assisted transformation process that facilitates diffusion creep deformation of strong minerals at far lower stresses and temperatures than dislocation creep. Initially strong lithologies can become weak, provided that reactions can proceed during deformation; the transformation process itself is an important weakening mechanism in mafic (and other) rocks, facilitating deformation at low differential stresses and low stress exponents.

International audience; A 3D multi-scale approach is presented to investigate the mechanical behavior of a macroscopic specimen consisting of a granular assembly, as a boundary value problem. The core of this approach is a multi-scale coupling, wherein the finite element method is used to solve a boundary value problem and a micromechanically based model is employed as constitutive relationship used at a representative volume element scale. This approach provides a convenient way to link the macroscopic observations with intrinsic microscopic mechanisms. The plane strain triaxial loading condition is selected to simulate the occurrence of strain localization. A series of tests are performed, wherein distinct failure patterns are observed and analyzed. A system of shear band naturally appears in a homogeneous setting specimen. By defining the shear band area, microstructural mechanisms are separately investigated inside and outside the shear band. The normalized second-order work introduced as an indicator of instability occurrence is analyzed not only on the macroscale but also on the micro scale.

Shear zones play a major role in the deformation of the crust at a variety of scales, as expressions of strain localization during orogeny and rifting, and also as reactivated structures. They influence the geometry and evolution of orogenic belts and rifts, crustal rheology, magma ascent and emplacement, and fluid flow. Consequently, assessing the timing of shear zone activity is crucial to reconstruct the tectonometamorphic evolution of the lithosphere. The interpretation of thermochronologic data from shear zones is, however, not straightforward. In the first place, closure temperatures depend on a number of factors (grain size, cooling rate, mineral composition and pressure, among others). On the other hand, deformation-related processes such as dynamic recrystallization, neocrystallization and fluid circulation seem to be crucial for isotopic systems and, thus, the obtained ages cannot be solely interpreted as a function of temperature in sheared rocks. For this reason, geochronologic data from shear zones might not only record cooling below closure temperature conditions but may also be affected by neo- or recrystallization, fluid-assisted deformation and inheritance of the protolith age(s). In order to robustly reconstruct P-T-ε-t paths of long-term crustal-scale shear zones, structural, microstructural and petrologic data from mylonites need to be integrated with ages from different thermochronometric systems. In addition, geochronologic data from associated intrusions and adjacent blocks can provide further irreplaceable constraints on the timing of deformation and its regional implications. One of the most challenging aspects that future lines of investigation should analyze is the quantitative evaluation of so far poorly explored aspects of isotopic diffusion, particularly the coupling with deformation processes, based on natural, theoretical and experimental data. Future works should also investigate the role of strain partitioning and localization processes in order to constrain the timing of deformation in different parts of a shear zone or in different branches of anastomosing shear zone networks. Fil: Oriolo, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Geociencias Básicas, Aplicadas y Ambientales de Buenos Aires; Argentina Fil: Wemmer, Klaus. Universität Göttingen; Alemania Fil: Oyhantçabal, Pedro. Universidad de la República. Instituto de Ciencias Geológicas; Uruguay Fil: Fossen, Haakon. University of Bergen; Noruega Fil: Schulz, Bernhard. Technische Universitat Bergakademie Freiberg; Alemania Fil: Siegesmund, Siegfried. Universität Göttingen; Alemania

The length, thickness and strain gradients of small-scale (10−3–10−1 m thick) ductile shear zones are pre-determined by the presence of surface precursors (e.g. fractures or compositional layers) and associated fluid-rock interaction. Fractures, with their surrounding host-rock damage zone and concurrent tectonic under-pressure during dilation, provide efficient fluid pathways and networks with diffusive fluid-rock interaction at their margins. The fluid-induced, gradational to zoned compositional haloes that symmetrically surround a fracture control the strain gradients of developing shear zones and result in a diversity of geometric types, including single homogeneous-to-heterogeneous shear zones and paired shear zones. As a consequence, geochemical differences between shear zone and host rock may reflect fluid-rock interaction during the precursor brittle history rather than during slip, especially considering that shear zones with even a small component of stretch may be over-pressured and therefore unable to drain fluids from the surrounding rocks. Support from field observation for this interpretation is given by (1) the lack of correlation between shear zone thickness and accumulated displacement; and (2) the similar thickness of shear zones and locally unexploited alteration haloes surrounding fracture precursors. Most small-scale shear zones in massive rocks (granitoids) are initially neither thickening nor narrowing with increasing strain. This concept may also apply to more foliated rocks, but does not necessarily hold for larger-scale shear zones.

In complex materials there exist different, often independent, mechanisms for the evolution of anelastic phenomena at the micro- and at the macroscale. Consequently, gradient plasticity has been introduced for a large variety of non-local materials. In a similar way, continuum damage has been extended to micromorphic and other non-local models, introducing internal damage variables and their gradient. In the paper is proposed a new continuum damage model for strain gradient materials characterized by two independent damage internal variables, each evolving with its own law. In this way, no additional field equation for the damage variable is needed. The model is intended to be used for metamaterials. Some important characteristics of the model are analysed with numerical analyses of a 1D example. In particular, the ability of the model to prevent strain localization is discussed.

Ultrafine grained austenitic stainless steel, with two different types of grain size distributions, was studied for tensile deformation behavior. Tensile deformed specimens were analyzed by electron backscatter diffraction using scanning electron microscope. It was found from this study that uni-modal grained stainless steel (SS) having a larger fraction of submicron grains exhibited early fracture, which is attributed to the development of extensive strain localization. On the other hand, the microstructure of SS having bimodal grain size distribution showed a good combination of strength and ductility. EBSD analysis of the deformed region of these two samples revealed the presence of a distinct transition zone between undeformed or less deformed and extensively sheared regions. Multiple micro shear bands were found to be associated with the transition zone of unimodal type microstructure. The micro shear bands seen in the transition zone of unimodal SS led to the development of strain-induced martensite (SIM), which, in turn, is helpful in delaying the strain localization. However, in bimodal grained SS, the larger fraction of micron size grains undergoes a shape change, with a rotation towards [112] orientation, which results in the formation of a larger fraction of SIM having [112] orientation. The propensity for development of high SIM was found to prevent strain localization in bimodal grained SS.

Integral Non-Local (INL) formulations are often used to regularize Continuum Damage computations, in the presence of stress softening for instance. The introduction of a characteristic/internal length allows for avoiding pathological mesh dependency. Some questions concerning the identification of the characteristic length, its possible evolution during damage process and the need for special treatments of non-locality operators near boundaries (e.g. edges, cracks) are however still open. A physical request is that material points separated by a crack (or an highly damaged zone) should not interact. Despite what is done in standard Integral Non-Local theories, this can be obtained by allowing non-local interactions to evolve depending on mechanical fields (e.g. damage, strain, stress). The Eikonal Non-Local (ENL) formulation provides a novel interpretation of damage dependent non-local interactions. Based on the Wentzel–Kramers–Brillouin (WKB) approximation for high-frequency wave propagation in a damaged medium, this formulation defines the interaction distances as the solution of a stationary damage dependent Eikonal equation . It allows for the modeling of non-local interactions which gradually vanish in damaged zones, thus ensuring a progressive transition from diffuse damage to fracture in a natural way. The numerical implementation and properties of this regularization technique are investigated and discussed. From a numerical viewpoint, a Fast Marching method is used to compute non-local interaction distances between Gauss integration points. Geodesic distances are then used to define the kernel of weighting function to be used in integral non-local averaging. Several numerical results of quasi-statics simulations of quasi-brittle fracture in isotropic media are presented.

Numerical methods for predicting localized shear failure in elasto-plastic solids have experienced considerable advancements in the last decades. Among these approaches, the so-called “Embedded Strong Discontinuity (ESD)” method is often successfully used to accurately simulate the post-localization response with negligible dependence on the finite element discretization. However, it was observed that the employed discontinuity tracking strategy plays a crucial role in the successful localization analysis. In this contribution, we propose a novel strategy for the global tracking of discontinuity surfaces. It is based on exploiting information obtained from the enhanced parameters employed in Enhanced Assumed Strain (EAS) formulations. It is well known, that enhanced strain element formulations are able to better capture localized shear deformations as compared to standard finite elements. This can be explained as a consequence of the improved performance in bending. We observed, that the approximation of the strain jumps delimiting the shear band is connected with a deformation field characterized by opposite bending curvatures across these two discontinuities. Hence, in view of the relations existing between the kinematics of strong and weak discontinuities, we formulate a proper scalar function of the enhanced parameters to identify potential strong discontinuity surfaces, which are evaluated in each step of the analysis with negligible computational cost. This proposed approach has a global character, as it is based upon evaluating discontinuity surfaces defined in the complete analysis domain that are, by construction, continuous across elements. We demonstrate that the tracking algorithm correctly identifies the potential strong discontinuity surface already in early loading stages, even before a localization condition is fulfilled. In those elements which are crossed by the potential failure surface and which also satisfy the localization condition, the kinematics of embedded strong discontinuities is activated to capture the shear failure surface. The performance of the new tracking algorithm is demonstrated by means of several numerical shear localization analyses using associative and non-associative Drucker–Prager elastoplastic models to simulate 2-D and 3-D benchmarkanalyses.

For progressively deforming multi-phase aggregates, it is unclear to what extent the change in geometry and orientation of the involved phases leads to textural strain weakening and thus may control strain localization. Consequently, the question arises how the ductile flow of multi-phase rocks can be described or determined. To contribute to the understanding of these knowledge gaps, two-dimensional numerical shear experiments of quartz-biotite aggregates were conducted at variable conditions. Textural variations after a shear strain of γ ≈ 10 appear to be dependent on the viscosity contrast between the minerals involved. To estimate whether a numerical experiment is undergoing strain weakening or hardening, the temporal evolution of the mean second invariant of the deviatoric stress tensor was tracked. The results suggest that strain weakening occurs if biotite is distinctly isolated in form of strong or weak inclusions and that it is more effective under conditions with larger viscosity contrasts between matrix and inclusions. However, observed stress drops in experiments purely based on textural strain weakening are low compared to other strain weakening processes. Numerical results from experiments with variable strain rate, temperature and biotite content were combined to determine two-phase flow law parameters for quartz-biotite aggregates, which are in broad agreement with existing analytical mixed-aggregate flow laws., Journal of Structural Geology, 149, ISSN:0191-8141

International audience; The slip localization behavior of the polycrystalline nickel base superalloy Inconel 718 during monotonic tensile loading at room temperature, is investigated for the first time in relation to the 3D microstructure. Multi-modal data merging tools are used to recombine high resolution digital image correlation (HR-DIC) data with 3D electron back-scatter diffraction tomography (3D EBSD), over a wide region of interest. This procedure enables reconstruction of the slip band planes in the 3D microstructure. Statistical analyses conducted over 500 individual slip bands reveal strong correlations between their location and specific microstructure configurations. In particular, over half of the slip bands emanate from triple junction lines (3D lines defined by the junction of three crystals). Moreover, the most intense and longest slip bands, which would become critical fatigue crack nucleation sites during cyclic loading, are located close and parallel to particular annealing twin boundaries and are simultaneously connected to triple junction lines. Crystal plasticity finite elements calculations are performed on the experimental microstructure to identify the slip activity that results in the formation of high intensity slip bands (localized plasticity) or zones of high lattice rotation (non-localized plasticity) in these particular microstructure regions.

This paper investigates the mechanical behavior and strain localization of methane hydrate bearing sediments (MHBS) at different temperatures and water pressures via the distinct element method (DEM). A thermo-hydro-mechanical contact model of MHBS has been employed in the DEM to simulate biaxial tests and mechanical behavior of MHBS is studied with different temperatures and water pressures. Three MHBS specimens are simulated at different temperature-pressure conditions to provide an insight on the evolution of macro and micro variables during strain localization of MHBS, as well as the geometric characteristics of shear band. The results show that MHBS appears to be strain-softening with dilatancy and the existence of MH will increase the cohesion but decrease the friction angle of MHBS. As temperature increases or water pressure decreases, the cohesion and friction angle of MHBS decrease with increasing dilatancy. The strain localization is closely related to bond breakage as well as localization of other micro and macro variables such as contact force chains, principal stress fields, particle velocity fields and average pure rotation rate distributions. As temperature and water pressure change, three different types of shear band can form. The thickness and inclination angle of these shear bands increase as the temperature increases or water pressure decreases.

We present a detailed case study of an exhumed continental strike-slip fault zone, the Ailao Shan-Red River (ASRR) strike-slip fault zone, to investigate how deformation promotes strain localization, and how the weak second phases and fluids trigger rheological weakening during retrogression near the ductile to brittle transition during exhumation. Along the ASRR strike-slip fault zone, in the Diancang Shan (DCS) metamorphic massif, high-temperature ductile deformation (D 1 ) pervasively occurred during shearing and exhumation since late Oligocene. The high-temperature microstructures and textures are in part or entirely altered by subsequent low-temperature shearing (D 2 ) since late Miocene, which is under the conditions of frictional-viscous transition of K-feldspar (ca. 450 °C) during further exhumation to the upper crustal levels. The formation of D 2 microstructures and shear bands overprinted high-temperature intracrystalline plasticity phases (D 1 ) in mylonitic rocks. Depending on the main rock-forming minerals, the results also demonstrate that the brittle–ductile transition involves a combination of different deformation mechanisms and possible rheological paths. In quartz-rich rocks, quartz was deformed in the dislocation creep regime and records transition of microfabrics and slip systems during decreasing temperature, which lasted until retrogression related to exhumation. As a result, grain-size reduction associated with fluids circulating within the ASRR strike-slip fault zone at brittle–ductile transition leads to reaction and texture weakening. Rheological weakening is the consequence of the syntectonic deformation, fluid flow, reaction softening, reaction creep and textural softening. The hydrous fluids resulted in hydration of silicates. Decompression occurred during shearing and as a result of tectonic exhumation. All these results demonstrate that the exhumation through the ductile to ductile-brittle transition involves a combination of different deformation mechanisms, rheological transition features and feedbacks between deformation, decreasing temperature and fluids in the ASRR fault zone.

Depleted oil reservoirs are considered a viable solution to the global challenge of CO2 storage. A key concern is whether the wells can be suitably sealed with cement to hinder the escape of CO2. Under reservoir conditions, CO2 is in its supercritical state, and the high pressures and temperatures involved make real-time microscopic observations of cement degradation experimentally challenging. Here, we present an in situ 3D dynamic X-ray micro computed tomography (μ-CT) study of well cement carbonation at realistic reservoir stress, pore-pressure, and temperature conditions. The high-resolution time-lapse 3D images allow monitoring the progress of reaction fronts in Portland cement, including density changes, sample deformation, and mineral precipitation and dissolution. By switching between flow and nonflow conditions of CO2-saturated water through cement, we were able to delineate regimes dominated by calcium carbonate precipitation and dissolution. For the first time, we demonstrate experimentally the impact of the flow history on CO2 leakage risk for cement plugging. In-situ μ-CT experiments combined with geochemical modeling provide unique insight into the interactions between CO2 and cement, potentially helping in assessing the risks of CO2 storage in geological reservoirs. This is an open access article published under a Creative Commons Attribution (CC-BY) License, which permits unrestricted use, distribution and reproduction in any medium, provided the author and source are cited.

International audience; The recent development of the high resolution and discontinuity-tolerant digital image correlation technique enables the extraction of discontinuities within a displacement field. The technique provides quantitative analysis of discontinuities arising from slip, shear bands, cracks, and grain boundary sliding in a variety of material systems, including polycrystalline metallic materials. The discontinuity-tolerant digital image correlation method can be implemented to retrieve not only quantitative discontinuity analysis but also the local strain and rotation fields that operate near these discontinuities. The present implementation includes high-resolution digital image correlation (HR-DIC) measurements collected in a scanning electron microscope for analysis of both the plastic and elastic fields that develop during deformation of polycrystalline metallic materials. The combination of the discontinuity-tolerant DIC technique with the computation of internal gradients enables extraction of non-localized strain and rotation fields during plastic deformation of a nickel-based superalloy. Therefore the lattice rotation/expansion and plastic localization that occur during deformation can be determined in a single experiment. This method is validated using synthetic images with preset deformation, and experimental measurements using the electron back scatter diffraction (EBSD) technique.

Regional-scale faults typically experience complex, long-lasting histories, commonly recording evidence of multiple reactivation events. Therefore, they contain multiscalar structural domains characterised by varying microstructures, mineralogical compositions and kinematics. These domains result from differential strain partitioning during the recorded faulting stages, and, as a result, can preserve the isotopic and kinematic signature of the different slip periods. Their detailed structural analysis integrated with K-Ar dating of the fault rock assemblage can help to identify these commonly tightly juxtaposed, although not coeval, domains, which we refer herein to as “Brittle Structural Facies” (BSF). BSF analysis is pivotal (i) to understand the structural heterogeneity of fault zones, (ii) the diachronic formation of geometrically and kinematically complex fault cores and (iii) to reconstruct faults' evolution in time and through space. Following this approach, this study relies on meso- and microstructural analysis, chemical characterisation and K-Ar dating to unravel the evolution of the Lærdal-Gjende Fault (LGF, southwestern Norway). The LGF is a multiply reactivated top-to-the-NW extensional fault with a 1 m thick poorly consolidated core. We recognised, sampled and characterised five BSF: I) Indurated dark reddish gouge, (II) Poorly consolidated cataclasite, (III) Weakly foliated greenish gouge, (IV) Clay-rich gouge and (V) A few mm-thick clay smear decorating the principal slip surface. Samples were separated into five grain size fractions (from

International audience; To investigate the mechanism of exhumation of deep crustal rocks in hot orogens, we focus on the southwestern part of the Variscan Canigou gneiss dome (Pyrenees) where the transition between the middle and upper crust can be observed. On the basis of new structural data, geological mapping, cross sections, microstructural analyses, and petrologic observations, we propose that flat-lying foliation within the gneiss dome and steep cleavage developed above it formed coevally. We note the presence of regional-scale shear zones at the boundary between the middle crust (Núria-Canigou Unit) and upper crust (Puigmal unit). At this boundary, the E-W South Canigou Shear Zone is an extensional shear zone showing top-to-the- southwest kinematics. Deformation, which is localized within the andalusite-biotite transition zone, occurred under retrogressive conditions, from high-grade ductile to brittle conditions during the main deformation stage (D2). The tectonic contact was folded during a later stage (D3). We propose that the shape of the Canigou dome resulted from the activation of extensional shear zones at the top of the orthogneiss, leading to partial exhumation of high-grade rocks. The Canigou gneiss dome can be considered an extensional dome that formed during late Variscan (ca. 310-290Ma) transpression.

Structural and microstructural analyses and phase equilibria modeling of migmatitic amphibolite-facies metapelites from the late Carboniferous Calamita Schists, on the Island of Elba, Italy, show how the interplay between partial melting and regional (far-field) deformation assisted deformation at very shallow (P ≤ 0.2 GPa) crustal levels. Partial melting was caused by the heat supplied by an underlying late Miocene intrusion (Porto Azzurro pluton) and occurred by biotite continuous melting. The produced melt remained in situ in patches, likely experienced limited migration in stromatic migmatites, and crystallized as a K-feldspar + plagioclase + quartz assemblage. Deformation in the presence of melt occurred by melt-enhanced grain boundary sliding, producing well-foliated high-strain zones with weak evidence of subsolidus deformation at the microscale where the original melt was present. Melt crystallization caused strain hardening and forced subsolidus deformation into localized mylonitic shear zones. The localized character of retrograde deformation was likely determined by the heterogeneous distribution/ingress of fluids in the aureole that locally assisted strain localization, enhancing dislocation creep and reaction softening.

International audience; We develop a crystal plasticity model to investigate the coupled actions of crystal orientation, grain neighborhood and grain-to-grain elasto-plastic interactions on dynamic strain aging (DSA) and the onset and development of associated plastic strain localization in Al-Li alloys. Considering simple model multilayered microstructures with preferred orientations representative of rolled alloys, the aim is to identify grain orientation couples that can limit dynamic strain aging induced strain localization without compromising the flow stress and strain hardening properties. To this end, a slip system-based formulation of dynamic strain aging is implemented in a crystal plasticity finite element framework. The model validity is first checked with the simulation of a tensile specimen loaded at quasi-static applied strain rate. The introduction of dynamic strain aging allows predicting complex propagation of intense plastic localization bands. We further investigate the influence of crystal orientations on early strain localization in Al-Cu-Li-Mg alloys, by performing simulations representative of the early stage of a Kahn Tear test for single crystals and layered polycrystals. Using experimentally reported crystal orientations for rolled microstructures, the simulation results show that in both single and multilayered crystals, there is a strong influence of dynamic strain aging on localization patterns, as well as a significant orientation dependence. In multilayered crystals, the nature of strain localization can be remarkably modified when stand-alone crystals of a certain orientation are coupled with other orientations: strain localization may intensify or fade away depending on the coupling with neighboring orientations.

International audience; The present paper proposes a new efficient and robust algorithm for evaluating the loss of ellipticity criterion. While commonly used in two-dimensional models for thin metal sheet forming processes, it is rarely evaluated in three-dimensional structures due to the computational cost. The proposed algorithm is based on a Newton-Raphson scheme and a multisampling optimization method based on a discretization method of the half unit sphere. First the new process is compared to the existing methods in the literature and then it is applied to a structural problem, namely tubes in torsion. The evolution of the loss of ellipticity in these structures is analyzed leading to conclusions about the failure of the structure. Meanwhile, the stability of the discretized problem is analyzed in order to better understand the loss of regularity of the finite element method problem. These results are then used to predict the failure of an experimentally tested torsion sample. K E Y W O R D S elastoplasticity, finite deformation, loss of ellipticty, numerical method, strain localization 1 INTRODUCTION Even though strain localization is one of the most critical phenomena leading to the failure of elasto-plastic structures, its emergence is still not fully understood. Indeed, the term "localization" itself is interpreted differently depending on the context. In a loose sense, localization means the development of high strains in a narrow region of the body, like in a shear band with through thickness necking in a thin plate in tension. A more precise definition is the emergence of strain rate discontinuities through surfaces usually associated with loss of ellipticity, and we use this latter definition in the present work. In some situations, both definitions may even coincide, for instance, a one-dimensional bar displaying a softening behavior experiences simultaneously necking and loss of ellipticity, 1,2 or in thin plates modeled under plane stress conditions. 3 However, these definitions do not coincide for three-dimensional (3D) models in general. When localization starts in complex structures and whether it leads to catastrophic failure is still an open problem in many situations , especially when certifying industrial components. The example of tubes loaded in torsion, 1 shows that even an apparently simple structure can lead to difficulties in defining localization and the localization's influence on the safety of the global structure. When dealing with localization, a first distinction needs to be made between types of loss of ellipticity. Strong ellipticity corresponds to definite positiveness of the eigenvalues of the symmetrized acoustic tensor whereas ellipticity refers to the absence of vanishing eigenvalue of the general acoustic tensor. 4,5 Int J Numer Methods Eng. 2019;1-25. wileyonlinelibrary.com/journal/nme

This study examines the combined performance of Portland cement (PC), the binder, and fly ash (FA), the additive, towards improving the mechanical performance of the South Australian copper-gold underground mine cemented paste backfill (CPB) system. A series of unconfined compressive strength (UCS) tests were carried out on various mix designs to evaluate the effects of binder and/or additive contents, as well as curing time, on the CPB&rsquo, s strength, stiffness and toughness. Moreover, the failure patterns of the tested samples were investigated by means of the three-dimensional digital image correlation (DIC) technique. Making use of several virtual extensometers, the state of axial and lateral strain localization was also investigated in the pre- and post-peak regimes. The greater the PC content and/or the longer the curing period, the higher the developed strength, stiffness and toughness. The use of FA alongside PC led to further strength and stiffness improvements by way of inducing secondary pozzolanic reactions. Common strength criteria for CPBs were considered to assess the applicability of the tested mix designs, with regards to stope stability, 4% PC + 3% FA was found to satisfy the minimum 700 kPa threshold, and thus was deemed as the optimum choice. As opposed to external measurement devices, the DIC technique was found to provide strain measurements free from bedding errors. The developed field of axial and lateral strains indicated that strain localization initiates in the pre-peak regime at around 80% of the UCS. The greater the PC (or PC + FA) content, and more importantly the longer the curing period, the closer the axial stress level required to initiate localization to the UCS, thus emulating the failure mechanism of quasi-brittle materials such as rock and concrete. Finally, with an increase in curing time, the difference between strain values at the localized and non-localized zones became less significant in the pre-peak regime and more pronounced in the post-peak regime.

Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. In this work, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier-Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding., Final version. Accepted for publication in Computer Physics Communications

Impurities in polar ice cores have been studied so far mainly for the purpose of reconstructions of past atmospheric aerosol concentrations. However, impurities also critically influence physical properties of the ice matrix itself. To improve the data basis regarding the in-situ form of incorporation and spatial distribution of impurities in ice we used micro-cryo-Raman spectroscopy to identify the location, phase and composition of micrometer-sized inclusions in natural ice samples around the transition from marine isotope stage (MIS) 6 into 5e in the EDML ice core. The combination of Raman results with ice-microsctructure measurements and complementary impurity data provided by the standard analytical methods (IC, CFA, and DEP) allows for a more interdisciplinary approach interconnecting ice core chemistry and ice core physics. While the interglacial samples were dominated by sulfate salts - mainly gypsum, sodium sulfate (possibly thenardite) and iron-potassium sulfate (likely jarosite) - the glacial ice contained high numbers of mineral dust particles - in particular quartz, mica, feldspar, anatase, hematite and carbonaceous particles (black carbon). We cannot confirm cumulation of impurities in the grain boundary network as reported by other studies, neither micro-particles being dragged by migrating grain boundaries nor in form of liquid veins in triple junctions. We argue that mixing of impurities on millimeter scale and chemical reactions are facilitated by the deforming ice matrix. We review possible effects of impurities on physical properties of ice, however the ultimate identification of the deformation agent and the mechanism behind remains challenging.

Strain localization, a cross-scale issue degrading homogeneity and formability during hot working of TA15 titanium alloy, is complicated by lamellar microstructure for hierarchical feature, spatial morphology, and orientation relationship. In this work, by taking advantage of hat-shaped specimens to maintain deformation mode, the effect of heterogeneous lamellar microstructure on strain localization is accessible and visualized by cross-section comparison enlightened by cake cutting. Moreover, the evolution behavior and mechanism are also investigated by the two-scale crystal plasticity model. The mechanism of strain localization during hot working of lamellar microstructure is re-recognized as the structural softening governed by an abrupt phase interface weakening and continuous geometrical softening. The driving force of strain localization is the ‘collapse’ of the stress gradient between constituent phases intensified by the progression of compelled uniformed deformation. The key to microstructure-dependent strain localization is the influence of lamellar orientation on germination and colony interface on intensification. Colonies with lamellar orientation deviated 45 o from the direction of maximum shear stress are endowed with the intrinsic potential of strain localization. Large-size and strongly-orientated colony interfaces intensify strain localization. These findings provide new insights into microstructure-dependent strain localization supporting a more efficient design of processing routing to control localization powerfully.

Bendability is an important property of ultrahigh-strength steels since the typical applications of such materials include structures manufactured by air-bending. Conventional methods to evaluate bendability, such as the bending test according to the standard VDA-238 or the conventional tensile test do not provide sufficient information to evaluate bendability of ultrahigh-strength steels due to the average nature of the material response in these tests. In this study, the mechanical properties were determined using thin tensile specimens cut from the surface of the sheet and the evaluation of bendability was carried out using frictionless bending tests. The results of the experiments and FE-modelling presented in this paper reveal that the mechanical properties of the sheet surface have a significant impact on bendability. Novel ultrahigh-strength steel with better work-hardening capacity at the surface caused by a layer of relatively soft ferrite and lower bainite has good bendability, especially when the bend line is aligned transverse to the rolling direction. Microstructural investigations reveal that in a conventional steel with a relatively hard surface microstructure, the deformation localizes into shear bands that eventually lead to fracture, but similar shear banding was not present in the novel steel surface. This can be attributed to the better work-hardening capacity which delays the onset of shear localization and fracture.

Plastic yielding of amorphous solids occurs by power-law distributed deformation avalanches whose universality is still debated. Experiments and molecular dynamics simulations are hampered by limited statistical samples, and although existing stochastic models give precise exponents, they require strong assumptions about fixed deformation directions, at odds with the statistical isotropy of amorphous materials. Here, we introduce a fully tensorial, stochastic mesoscale model for amorphous plasticity that links the statistical physics of plastic yielding to engineering mechanics. It captures the complex shear patterning observed for a wide variety of deformation modes, as well as the avalanche dynamics of plastic flow. Avalanches are described by universal size exponents and scaling functions, avalanche shapes, and local stability distributions, independent of system dimensionality, boundary and loading conditions, and stress state. Our predictions consistently differ from those of mean-field depinning models, providing evidence that plastic yielding is a distinct type of critical phenomenon., The universality class for plastic yield in amorphous materials remains controversial. Here authors present a tensorial mesoscale model that captures both complex shear patterns and avalanche scaling behaviour, which differs from mean-field models and suggests a distinct type of critical phenomenon.

International audience; We report microstructural evidence for fluid-assisted ductile strain localization in a ≤ 50 m-wide mylonitic–ultramylonitic shear zone in the Ronda Peridotite massif, Southern Spain. Strain localization occurred at relatively low pressure (< 0.8 GPa) and moderate temperature (750–1000 °C). Initial deformation by dislocation creep resulted in formation of mylonites. Focusing of aqueous fluids in the shear zone favored the activation of dissolution–precipitation creep, resulting in further strain localization. This process is recorded by two generations of ultramylonitic bands composed of fine-grained, well-mixed olivine–orthopyroxene aggregates. Microstructural observations in the ultramylonites suggest alternating dissolution and precipitation of olivine and orthopyroxene, which may be explained by local changes in silica molality of the percolating fluid (disequilibrium and mass transfer at scales > mm). In the mylonites, olivine shows a crystal preferred orientation (CPO) coherent with dominant (001)[100] glide, probably due to the presence of interstitial fluids during deformation. In the ultramylonites, olivine CPO is weak to very weak, consistently with a decreasing contribution of dislocation creep to deformation. In contrast, fine-grained orthopyroxene in both mylonites and ultramylonites displays a clear CPO characterized by a [001] maximum normal to the foliation, which is not consistent with dislocation glide in any known slip system for orthopyroxene. We interpret this CPO as formed by oriented crystallization during dissolution–precipitation. In the present study, dissolution–precipitation creep predominates only in small-scale ultramylonite bands due to limited fluid availability and localized dynamic permeability. However, this process may be important in intermediate temperature domains of subduction zones, where it may lead to a feedback between strain localization and fluid transport.

Bubble content influences magma rheology and, thus, styles of volcanic eruption. Increasing magma vesicularity affects the bulk viscosity of the bubble-melt suspension and has the potential to promote non-Newtonian behavior in the form of shear localization or brittle failure. Here, we present a series of high temperature uniaxial deformation experiments designed to investigate the effect of bubbles on the magma bulk viscosity. The starting materials are cores of natural rhyolitic obsidian synthesized to have variable vesicularity ( ϕ = 0 – 66 % ). The foamed cores were deformed isothermally ( T = 750 ° C ) at atmospheric conditions using a high-temperature uniaxial press under constant displacement rates (strain rates between 0.5 – 1 × 10 − 4 s − 1 ) and to total strains of 10–40%. The viscosity of the bubble-free melt ( η 0 ) was measured by micropenetration and parallel plate methods to establish a baseline for experiments on the vesicle rich cores. At the experimental conditions, rising vesicle content produces a marked decrease in bulk viscosity that is best described by a two-parameter empirical equation: log 10 ⁡ η Bulk = log 10 ⁡ η 0 − 1.47 [ ϕ / ( 1 − ϕ ) ] 0.48 . Our parameterization of the bubble-melt rheology is combined with Maxwell relaxation theory to map the potential onset of non-Newtonian behavior (shear localization) in magmas as a function of melt viscosity, vesicularity, and strain rate. For low degrees of strain (i.e. as in our study), the rheological properties of vesicular magmas under different flow types (pure vs. simple shear) are indistinguishable. For high strain or strain rates where simple and pure shear viscosity values may diverge, our model represents a maximum boundary condition. Vesicular magmas can behave as non-Newtonian fluids at lower strain rates than unvesiculated melts, thereby, promoting shear localization and (explosive or non-explosive) magma fragmentation. The extent of shear localization in magma influences outgassing efficiency, thereby, affecting magma ascent and the potential for explosivity.