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This paper deeply couples the exponential-type nonlinear strain softening with the anisotropic method of microstructure tensor combined stress invariants, proposing an effective strength formula that reflects the anisotropy evolution of soil. Furthermore, an expression for the anisotropy ratio k of strength as an equivalent plastic strain-related variable is derived. For natural clay, this evolution of strength anisotropy is incorporated into the Mohr–Coulomb-matched Drucker–Prager (MC-matched DP) yield criterion within the Cosserat continuum framework, resulting in a more refined soil constitutive model. The main strength parameters required for this model can be conveniently obtained based on conventional soil tests, and the model functionality can be degraded through parameter adjustments. The detailed procedure of stress updating algorithm and the elastoplastic tangent modulus matrix are provided for the constitutive integration. Through the finite element implementation, the superiority of the model is demonstrated compared with existing literature. Also, a biaxial compression example is systematically analyzed to prove that the model can effectively reflect the sensitivity of soil to loading direction. Moreover, the evolution of the shear band morphology, particle rotation in the shear band, and the anisotropy degree presented by the model are consistent with previous experimental studies and discrete element method (DEM)-related literature results. Furthermore, the proposed model effectively addresses numerical convergence issues and mesh size dependence usually encountered in classical models during the simulation of strain localization occurred in the soil. [ABSTRACT FROM AUTHOR]

In the last decade, a new multi‐scale FEM×DEM approach has been developed using Finite Element Method (FEM) coupled with Discrete Element Method (DEM) as a constitutive law to account for the specificities of the mechanical behavior of granular materials. In FEM×DEM model, a DEM calculation is performed on a particle assembly (volume element—VE) at each Gauss point. Recent publications have demonstrated that FEM×DEM approach naturally captures the discrete and anisotropic nature of granular materials. Despite its advantages, FEM×DEM with classical FEM, suffers from mesh dependency, especially when material enters softening phase and exhibits strain localization. To overcome this limitation, FEM×DEM model has been enriched by incorporating a local second gradient model. Nevertheless, the existence of multiple possible solutions is observed. In this paper, we study the variability and loss of uniqueness of numerical solutions to a boundary value problem. Different VEs with equivalent mechanical properties are generated and used to model the pressuremeter tests by means of FEM×DEM. The modeling results show a great variability of the numerical results, both in shape of borehole and in different modes of shear bands. For the same VE, the loss of uniqueness of numerical solutions is evidenced by a slight modification of loading history at the level of the internal pressure applied to the borehole. Finally, we show that when a certain heterogeneity is introduced by using different VEs within the same BVP, even if the uniqueness of the solution is not guaranteed, the set of possible solutions seems more restrained. [ABSTRACT FROM AUTHOR]

Strain localization simulation of overconsolidated soils with high overconsolidation ratio (OCR) has been a long‐standing challenge. Some critical state soil models, including the modified Cam‐clay (MCC) model, have been widely applied, but they may not predict the shear dilatancy of overconsolidated soils well in some cases. Hence, the unified hardening (UH) model, which may be viewed as a generalized version of the MCC model, is implemented. It has been recognized, nonetheless, that without resorting to the regularization mechanism, the standard finite element method (FEM) or the second‐order cone programming optimized finite element method (FEM‐SOCP) often experiences instability or interruption of calculating the hardening‐softening responses of overconsolidated soils. To resolve the aforementioned difficulty, the UH model is developed and implemented in the framework of FEM‐SOCP based on the micropolar continuum (mpcFEM‐SOCP) to predict strain localizations of overconsolidated soils. Furthermore, to obviate non‐convexity of mpcFEM‐SOCP induced by material softening, an effective composite update scheme of hardening variable pc, which refers to the implicit variable (IV) scheme for the hardening stage and then refers to the explicit variable (EV) scheme for the softening stage, is proposed. Based on one biaxial compression problem and one rigid strip footing problem, numerical analyses disclose that by applying mpcFEM‐SOCP in conjunction with the composite update scheme of pc, the UH model of micropolar continuum can effectively predict the strain localization behavior of overconsolidated soil during its failure stage, and the stable hardening‐softening responses of overconsolidated soils can be readily attained. [ABSTRACT FROM AUTHOR]

The transition point of the crack length to a microstructurally small crack is necessary for predicting crack extension behavior. The conventional criterion is the crack length smaller than the grain size and is a probabilistic criterion. This criterion does not consider the metal's crystallite plasticity property discrepancy (CPPD). However, CPPD determines crack extension behavior for recently developed advanced materials with complex microstructures. Therefore, the authors propose a deterministic judgment method for microstructurally small cracks considering crystallite plasticity based on a physics‐based crystal plasticity finite element model with strain localization. The proposed method is based on the difference value of the crack tip opening displacement varying with the ratio between the crack length and grain size with the change in the grain orientation ahead of the crack tip. A case study for copper is performed, and the results show that the novel method can be applied to define the microstructurally small crack. [ABSTRACT FROM AUTHOR]

• Fractional gradient direction replaces additional plastic potential. • The FEM implementation of the fractional elastoplastic constitutive model is presented. • The influence of the fractional order on the strain localization is investigated. • Examples are analyzed to demonstrate the effectiveness of the implementation process. The plastic strain localization phenomenon is of critical importance for rock-like materials when undergoing non-homogeneous deformation. This paper presents a fractional plastic framework which is applied to take into account the plastic strain localization of rock-like materials. The novelty of the presented framework lies in the non-coaxial plastic flow that is controlled by the RiemannLiouville (RL) fractional derivative without additional plastic potential. The hardening response is described by a function of the generalized plastic shear strain. The capability of the fractional constitutive model to predict the main mechanical behaviors of rock-like materials is assessed by the conventional triaxial compression test data of Vosges sandstones from the literature. With the help of a MATLAB-based finite element method, several numerical examples (i.e., a plate, a plate with a hole, and a plate with a crack) are implemented, compared and analyzed to demonstrate the effectiveness of the proposed framework and the influence of the fractional order on the strain localization. It can be found from the numerical application of the twin-tunnel that the fractional model is promising to flexibly capture the strain localization zone for rock-like materials. [ABSTRACT FROM AUTHOR]

This paper investigates the mechanical response of coral sand under particle breakage using a hierarchical multiscale model combining the discrete element method (DEM) and the finite element method (FEM). This DEM-FEM model links the microscopic interaction mechanisms to macroscopic phenomena such as strain localization and failure. A cohesive contact model was first utilized to simulate compaction bands in the DEM and construct a cohesive assembly with smaller particles distributed around a larger particle to better simulate the grinding and angular breakage of coral sand. A representative volume element (RVE) that includes particle breakage was then constructed and analyzed under periodic boundary conditions. DEM analysis was performed, and the results were compared with triaxial compression test data obtained from the literature, demonstrating that the constructed RVE effectively represents the mechanical properties of coral sand. The constructed RVE was used for hierarchical multiscale simulations, which showed good agreement with existing triaxial testing of coral sand. Finally, by setting a larger cohesive force, the constructed coral sand particles were prevented from breakage, and comparative analysis revealed that particle breakage weakens the mechanical properties of coral sand. Furthermore, different shapes of coral sand particles were constructed, and RVE and hierarchical multiscale simulations of triaxial tests were performed. The results indicated that the triaxial tests of long strip-shaped coral sand particles exhibit higher peak values compared to spherical coral sand particles. Additionally, a double porosity model of coral sand was constructed to analyze the impact of internal porosity on soil mechanical properties. The results showed that the presence of internal porosity significantly weakened the mechanical properties of coral sand. These findings highlight the significant impact of particle breakage and shape on the mechanical behavior of coral sand, offering important insights for engineering applications. [Display omitted] • A multiscale modeling is used to simulate the breakage of coral sand. • Constructed double porosity model to simulate the breakage of coral sand. • Breakage of coral sand was studied from a microscopic to macroscopic. • Particle breakage weakens the mechanical properties of coral sand. • Different shapes of coral sand particles were constructed and studied. [ABSTRACT FROM AUTHOR]

Capturing realistic deformation behavior in BCC metals at the polycrystal scale is an important aspect of predicting the material's strength and failure. Furthermore, local deformation/strength heterogeneity also influences the lifetime and its assessments in reactor pressure vessel (RPV) steels, especially with accumulating irradiation doses during long-term operational conditions. This work utilizes a micromorphic crystal plasticity (CP) model for BCC materials with the capability to address temperature-dependent stress–strain response and irradiation effects relevant to RPV materials. The microstructure of the investigated material was characterized prior to and during testing using electron microscopy experiments, which are used for finite element model generation and simulation result validation. To analyze the validity of the model to predict strain localization under monotonic tensile loading, micro digital image correlation (DIC) was employed jointly with the CP simulations. Different modeling choices, such as the use Schmid/non-Schmid laws and gradient based CP modeling, greatly affected the capability of the model to represent similar magnitudes in strain localization and grain reorientation. The requirement for experimental measurements, including image based analyses, on a microstructural level as a validation tool for CP modeling is clearly demonstrated. [Display omitted] • BCC crystal plasticity model is validated with μ DIC. • Choice of Schmid and non-Schmid behavior influences polycrystal strain localization. • Micromorphic regularization improves local plasticity prediction. • Temperature and irradiation response of RPV steels is represented by a non-local crystal plasticity model. [ABSTRACT FROM AUTHOR]

A multiscale approach that couples the finite-element method (FEM) and the discrete-element method (DEM) is used to model and analyze the earthquake fault rupture–soil–foundation interaction (FR–SFI) problem. The approach obtains the soil constitutive responses from the DEM solutions of representative volume elements (RVEs) embedded at the FEM integration points, effectively bypassing the phenomenological hypotheses in conventional FEM simulations. The fault rupture surfaces and shear localization patterns under normal and reverse faults with or without foundation atop were adequately captured using the multiscale approach and verified with available centrifuge experimental and numerical results. An examination of the stress-strain responses and the microstructural evolutions of local RVEs revealed that the RVEs located in or immediately outside the shear bands behaved distinctly and might change their stress states from initially at rest to active under normal fault or passive under reverse fault. The micromechanics study also sheds light on the capability of heavy foundations to protect the superstructure due to rupture surface diversion under reverse fault and their possible detriment under normal fault. [ABSTRACT FROM AUTHOR]

Within the framework of second-order cone programming optimized micropolar continuum finite-element method (CosFEM-SOCP), the geotechnical strain localization can be adequately modeled. In most existing literatures, however, the constant internal characteristic length lc has been adopted and less attention has been paid to the evolution of lc. To more accurately predict the strain localization, response, and stability of a geotechnical system, one relationship for evolving lv that relies on the equivalent plastic strain is implemented and investigated. Based on one homogeneous slope example and one rigid strip footing example, it was found that geotechnical stability may not be significantly affected by evolving lv, indicating that constant lc can be simply applied to geotechnical stability analysis. For the rigid strip footing problem, nevertheless, the effects of evolving lv on the pressure–displacement response curves should not be ignored, and the influence range of the shear band predicted by CosFEM-SOCP with evolving lv is generally smaller than that predicted by CosFEM-SOCP with constant lc. Consequently, in order to more accurately predict the pressure–displacement response curves and the failure zone, the evolving lv will be adequately assessed and modeled. [ABSTRACT FROM AUTHOR]

The appearance of strain localization (SL) in front of the crack tip is a factor that promotes transition toward the fatigue crack extension mode. Therefore, to predict fatigue crack extension behavior in case multiple modes occur, it is necessary to evaluate the degree of SL. In this study, the following simulations were performed on a single‐crystal twinning‐induced plasticity (TWIP) steel: (a) SL characterization by crystal plasticity finite element method (CPFEM) analysis of a smooth specimen under tension, (b) strain concentration (SC) characterization by EP‐FEM analysis of a cracked specimen under tension, and (c) characterization of interaction results between SC and SL of a cracked specimen under tension by CPFEM analysis. A comparison of the above results found that the interaction between SC and SL was large for long cracks and a significant strain field, different from the Hutchinson, Rice, Rosengren (HRR) singular field, was formed in front of the crack tip. Therefore, a parameter was proposed to quantify the SL properties in a smooth specimen. Subsequently, a fracture‐mechanics‐like method was proposed in which the results of (b) and the introduced parameters control the results of (c). Highlights: Crystal plasticity finite element model for crack with strain localization.Comparison between crystal plasticity and traditional finite element method.Strain localization affects the strain distribution around the crack tip.Strain localization changes the singularity at the crack tip. [ABSTRACT FROM AUTHOR]

The knowledge of the distribution of local micromechanical fields is crucial in the design of composite materials. Traditionally full-field methods (such as finite element methods) and fast Fourier transformation-based methods are used to obtain the local fields. However, full-field simulations are computationally expensive and time-consuming. Recently, there has been a push toward using the big-data-driven machine learning approaches to estimate the local fields and establish the structure–property linkages. In this work, we use one of the deep learning-based algorithms known as the UNet to predict the local strain fields in a two-phase composite material subjected to uniaxial tensile load. The model is trained and tested on 1200 two-phase microstructures comprising two-volume fraction categories and six different morphological classes. An R2 score of 94% is achieved on the test dataset. A detailed statistical analysis is performed to understand the role of the volume fraction and the ratio of elastic moduli of the phases in the deep learning model's trainability. The insights drawn in this work are then discussed in the context of generating artificial datasets and training a robust predictive deep learning model for localization. [ABSTRACT FROM AUTHOR]

SUMMARY: Finite element analysis of ductile fracture with tetrahedral elements faces two numerical issues: volumetric locking and mesh sensitivity. In this paper, two widely adopted remedies for volumetric locking (F‐bar and mixed field) are evaluated, and the superior performance of the mixed field method is demonstrated. Building on the mixed field formulation, a gradient enhancement is further incorporated to resolve the mesh sensitivity. It is shown that a localizing gradient enhancement can avoid a spurious spreading of damage induced by the conventional gradient approach. A locking‐free, regularized ductile fracture is first presented via a uniformly tapering plate example. Finally, a shear plate test on ferrite‐bainite steel is considered. Numerical results obtained with the proposed approach are shown to capture the rapid strain softening and localized shear fracture phenomenon observed experimentally. [ABSTRACT FROM AUTHOR]

Summary: This study presents a thermo‐hydro‐mechanical (THM) model of unsaturated soils using isogeometric analysis (IGA). The framework employs Bézier extraction to connect IGA to the conventional finite element analysis (FEA), featuring the current study as one of the first attempts to develop an IGA‐FEA framework for solving THM problems in unsaturated soils. IGA offers higher levels of interelement continuity making it an attractive method for solving highly nonlinear problems. The governing equations of linear momentum, mass, and energy balance are coupled based on the averaging procedure within the hybrid mixture theory. The Drucker‐Prager yield surface is used to limit the modified effective stress where the model follows small strain, quasi‐static loading conditions. Temperature dependency of the surface tension is implemented in the soil‐water retention curve. Nonuniform rational B‐splines (NURBS) basis functions are used in the standard Galerkin method and weak formulations of the balance equations. Displacement, capillary pressure, gas pressure, and temperature are four independent quantities that are approximated by NURBS in spatial discretization. The framework is used to simulate strain localization in an undrained dense sand subjected to plane strain biaxial compression under different temperatures and displacement velocities. Results show that an increase in the displacement rate leads to reduction in the equivalent plastic strain while an increase in the temperature leads to an increase in the equivalent plastic strain. The findings suggest that the proposed IGA‐based framework offers a viable alternative for solving THM problems in unsaturated soils. [ABSTRACT FROM AUTHOR]

• Hydride-enhanced strain localization in Zr alloys is studied using the CPFEM. • Simulated features of slip-hydride interaction match experimental observations. • Slip-hydride interaction depends on orientation relation between slip and hydride. • Mechanisms of strain localization in hydrogenated Zr alloys are revealed. • The influences of misfit strain on strain localization should not be neglected. Hydride precipitation in zirconium (Zr) alloys leads to the deterioration of mechanical properties in key components of nuclear reactors. However, the underlying mechanisms governing the failure initiation of hydrogenated Zr alloys remain incompletely understood. This study focuses on investigating the effects of δ-phase hydride precipitation on the local deformation behavior of Zr alloys. A crystal plasticity finite element method is used to simulate micropillar compression tests of single-crystal samples and macroscale tensile tests of polycrystalline samples. Our results reveal that in the case of micropillar B containing δ-hydride (where the hydride is oriented at 45° from the loading direction), the shear along the hydride–matrix interface and the misfit strain induced by hydride precipitation synergistically contribute to strain localization of Zr alloys. However, for micropillar P containing δ-hydride (where the hydride is parallel to the loading direction), the introduction of hydrides does not enhance the strain localization. Instead, it impedes the local prismatic slip. On the other hand, examination of polycrystalline samples through simulations indicates that hydrides enhance the strain localization of Zr alloys. This effect arises from several mechanisms: shear stress along hybrid–matrix interface, promoting plastic slip in the direction close to this interface; hydride-induced hindrance to certain slip bands, leading to non-uniform local deformation; and misfit strains induced by hydride precipitation, contributing to localized deformation around the hydrides. [Display omitted] [ABSTRACT FROM AUTHOR]

Summary: Nonlocal enhancement is widely adopted to resolve the mesh sensitivity issue in standard continuum damage models. Although it regularizes structural response well, the damage profile is reported to exhibit a spurious damage growth. To remedy this problem, a localizing gradient enhancement is adopted in the Rousselier model to simulate a localized rupture. The localizing gradient enhancement, recently developed in the small deformation framework, is extended in this paper to a large deformation framework, motivated by the strain localization phenomenon during a ductile fracture. The regularization property of the current model is verified with a flat grooved plate test, and the superior performance in damage localization is demonstrated with a uniaxial tensile plate test and a compact tension test on aluminum alloy. Results obtained with the localizing gradient enhancement are consistent with experimental observation, without the nonphysical damage growth in conventional gradient enhancement. [ABSTRACT FROM AUTHOR]

Predicting localized failure in granular materials is a problem of great interest from both the scientific and technological perspectives. The initiation and growth of strain localization have been studied using laboratory experiments and particle-based numerical simulations, and their findings have been preliminarily implemented into continuum constitutive models. In this study, we revisit strain localization in granular materials using the spatiotemporal data analysis technique, which has been extensively employed in data mining science and social science for the sake of different applications. A dense packing of granular material subjected to biaxial compression was simulated using the combined finite and discrete element method. The large amount of particle-level kinematical data, including the translational and rotational particle motion, fluctuating velocity, granular temperature, and local strain, are collected for subsequent spatiotemporal data analysis. The spatiotemporal data analysis provides a new perspective on the strain localization in dense granular materials and a rich body of new insights are presented for the first time. The spatial autocorrelation analysis results in Moran's I values close to 1, and positive Z scores and statistically significant p values, which indicate that a dense granular system features clustered patterns during shearing. This finding proves yet again that dense granular materials have an inherent short range order. Eventually, correspondence between localized modes with different particle kinematics and spatial distributions of local Moran statistics and quadrant location map are investigated. By assuming shearing of dense granular materials is a first-order Markov chain process, the convergence and time homogeneity of this process are analyzed. Both the maximum likelihood and Pearson test statistics clearly demonstrate that shearing of dense granular materials is a time-homogenous Markov chain process. [ABSTRACT FROM AUTHOR]

Highlights • Softening laws cause spurious mesh dependence in constitutive modelling. • A remedy for this is the adoption of non-local models, based on averaging procedures. • A non-local damage model is worked in the context of the boundary element method. • A simple technique is used average the equivalent strain in such model. • Regularization of the mechanical response is shown by numerical examples. Abstract The conventional (local) constitutive modelling of materials exhibiting strain softening behaviour is susceptive to a spurious mesh dependence caused by numerically induced strain localization. Also, for refined meshes, numerical instabilities may be verified, mainly if the simulations are performed by the boundary element method. An alternative to overcome such difficulties is the adoption of the so called non-local constitutive models. In these approaches, some internal variables of the constitutive model in a single point are averaged considering its values of the neighbouring points. In this paper, the implicit formulation of the boundary element method for physically non-linear problems in solid mechanics is used with a non-local isotropic damage model and a very simple averaging scheme, over internal cells, is introduced. It is shown that the analysis become more stable in comparison to the case of a local application of the same model and that the results recover the desired objectiveness to mesh refinement. [ABSTRACT FROM AUTHOR]

It is well known that it is necessary to introduce a length scale parameter in a continuum damage mechanics model to correctly simulate strain localization. The second gradient model, a special case of kinematically enriched continua, considers an internal length parameter by taking into account the second-order derivatives of the displacements in the virtual power principle. In this paper, we show that the original second gradient finite element of Chambon and co-workers can present spurious oscillations, especially for mode I crack propagation problems. After providing the plane stress second gradient constitutive law, we propose to add a penalty term in the original formulation in order to improve numerical convergence and to avoid spurious oscillations in the local variables distributions. Two numerical examples using classical damage mechanics laws, a three-point reinforced concrete beam and a trapezoidal notched specimen are used to test the performance of the formulation. Parametrical studies are also shown on the influence of the penalty parameter. The problem of unrealistic damage spreading for damage values close to 1, occurring often in mode I crack propagation problems, is finally discussed. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates two numerical methods for predicting the initiation of ductile failure under moderately and strongly non-proportional loading paths. Two distinct phenomena are considered as indicators for the initiation of ductile failure: (i) the localization of deformation into a narrow band and (ii) the coalescence of microscopic voids. Recent experimental data in the literature from various axisymmetric tension tests on a high-strength steel are used to calibrate and validate the two methods. In the first method, which is based on the imperfection band approach, strain localization analyses are conducted using the deformation history extracted from finite element simulations of the tension tests. In the second method, axisymmetric unit cells are utilized to evaluate the onset of void coalescence using the stress history extracted from the same finite element simulations of the experiments. The various uniaxial tension tests yield different moderately and strongly non-proportional loading paths that are used to evaluate the predictive capabilities of the two methods. The numerical results are further used to discuss the similarities and differences between the two methods. Both the strain localization analyses and the coalescence analyses are found capable of predicting the initiation of failure in the experiments with good accuracy; however, the coalescence analyses are generally in closer agreement to the experiments. Highlights • The effect of non-proportional loading paths on ductile failure is examined. • Unit cell simulations and strain localization analyses are compared to experiments. • Both methods predict failure initiation in the experiments with good accuracy. [ABSTRACT FROM AUTHOR]

Highlights • Force-displacement and strain-displacement curves are presented. • The GTN model accurately predicts the loss of the load carrying capacity. • The GTN model does not predict localization in the strain-displacement curve. Abstract The Gurson–Tvergaard–Needleman (GTN) model includes several parameters of different nature. Some of them have micromechanical roots while others are strictly phenomenological. Hence, a methodology should be developed in order to obtain a robust set of parameters with both numerical and physical meaning. The material parameters of the GTN model are found using an identification methodology based on experimental-numerical results. The method is applied on a DC01 ferritic steel sheet. An extended version of the Gurson model, incorporating plastic anisotropy, mixed isotropic-kinematic hardening, void nucleation, growth, coalescence and shear is used. Material parameters are obtained based on an inverse optimization and a sensitivity analysis on specimens with different geometries. The onset of coalescence, reflected as the loss of load carrying capacity in the force-displacement curve, is correctly predicted by the extended GTN model. The strain distribution, obtained by digital image correlation, is also correctly simulated. Nevertheless, the model does not to predict the increase of strain observed experimentally, because of the decoupling between hardening and the damage variable. In this respect, the article provides experimental evidence of the limitations of a GTN model based on a strain-controlled nucleation law with heuristic extensions of hardening. [ABSTRACT FROM AUTHOR]

Strain localization is ubiquitous in geodynamics and occurs at all scales within the lithosphere. How the lithosphere accommodates deformation controls, for example, the structure of orogenic belts and the architecture of rifted margins. Understanding and predicting strain localization is therefore of major importance in geodynamics. While the deeper parts of the lithosphere effectively deform in a viscous manner, shallower levels are characterized by an elastoplastic rheological behavior. Herein we propose a fast and accurate way of solving problems that involve elastoplastic deformations based on the consistent linearization of the time‐discretized elastoplastic relation and the finite difference method. The models currently account for the pressure‐insensitive Von Mises and the pressure‐dependent Drucker‐Prager yield criteria. Consistent linearization allows for resolving strain localization at kilometer scale while providing optimal, that is, quadratic convergence of the force residual. We have validated our approach by a qualitative and quantitative comparison with results obtained using an independent code based on the finite element method. We also provide a consistent linearization for a viscoelastoplastic framework, and we demonstrate its ability to deliver exact partitioning between the viscous, the elastic, and the plastic strain components. The results of the study are fully reproducible, and the codes are available as a subset of M2Di MATLAB routines. Key Points: Pressure‐dependent plasticity converges with elastoplastic and viscoelastoplastic rheologyWe provide fast and concise MATLAB source codes for full reproducibilityWe combined consistent tangent linearization together with finite difference method [ABSTRACT FROM AUTHOR]

A numerical model for thermo-hydro-mechanical strong couplings in an elasto-plastic Cosserat continuum is developed to explore the influence of frictional heating and thermal pore fluid pressurization on the strain localization phenomenon. This model allows specifically to study the complete stress-strain response of a rock specimen, as well as the size of the strain localization zone for a rock taking into account its microstructure. The numerical implementation in a finite element code is presented, matching adequately analytical solutions or results from other simulations found in the literature. Two different applications of the numerical model are also presented to highlight its capabilities. The first one is a biaxial test on a saturated weak sandstone, for which the influence on the stress-strain response of the characteristic size of the microstructure and of thermal pressurization is investigated. The second one is the rapid shearing of a mature fault zone in the brittle part of the lithosphere. In this example, the evolution of the thickness of the localized zone and the influence of the permeability change on the stress-strain response are studied. [ABSTRACT FROM AUTHOR]

The increasing importance of performance-based earthquake engineering analysis points out the necessity to assess quantitatively the risk of liquefaction of embankment-type structures. In this extreme scenario of soil liquefaction, devastating consequences are observed, e.g., excessive settlements, lateral spreading and slope instability. The present work discusses the global dynamic response and interaction of an earth structure-foundation system, so as to determine quantitatively the collapse mechanism due to foundation’s soil liquefaction. A levee-foundation system is simulated, and the influence of characteristics of input ground motion, as well as of the position of liquefied layer on the liquefaction-induced failure, is evaluated. For the current levee model, its induced damage level (i.e., induced crest settlements) is strongly related to both liquefaction apparition and dissipation of excess pore water pressure on the foundation. The respective role of input ground motion characteristics is a key component for soil liquefaction apparition, as long duration of mainshock can lead to important nonlinearity and extended soil liquefaction. A circular collapse surface is generated inside the liquefied region and extends toward the crest in both sides of the levee. Even so, when the liquefied layer is situated in depth, no significant effect on the levee response is found. This research work provides a reference case study for seismic assessment of embankment-type structures subjected to earthquake and proposes a high-performance computational framework accessible to engineers. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The failure behavior of geological materials depends heavily on confining pressure and strain rate. Under a relatively low confining pressure, these materials tend to fail by brittle, localized fracture, but as the confining pressure increases, they show a growing propensity for ductile, diffuse failure accompanying plastic flow. Furthermore, the rate of deformation often exerts control on the brittleness. Here we develop a theoretical and computational modeling framework that encapsulates this variety of failure modes and their brittle–ductile transition. The framework couples a pressure-sensitive plasticity model with a phase-field approach to fracture which can simulate complex fracture propagation without tracking its geometry. We derive a phase-field formulation for fracture in elastic–plastic materials as a balance law of microforce, in a new way that honors the dissipative nature of the fracturing processes. For physically meaningful and numerically robust incorporation of plasticity into the phase-field model, we introduce several new ideas including the use of phase-field effective stress for plasticity, and the dilative/compactive split and rate-dependent storage of plastic work. We construct a particular class of the framework by employing a Drucker–Prager plasticity model with a compression cap, and demonstrate that the proposed framework can capture brittle fracture, ductile flow, and their transition due to confining pressure and strain rate. [ABSTRACT FROM AUTHOR]

This paper discusses the modeling of cracking in quasi-brittle materials using isotropic and orthotropic damage constitutive laws. A mixed strain/displacement finite element formulation is used, taking advantage of its enhanced precision and its enforced interelemental strain continuity. On the one hand, this formulation avoids the spurious mesh dependency of the computed solution associated to standard elements and does not require the use of tracking techniques. On the other hand, it greatly alleviates the spurious stress locking associated to the use of orthotropic models on standard finite elements. The performance of several isotropic and orthotropic damage constitutive laws is assessed through an extensive comparison with analytical solutions, numerical tests and experimental evidence reported in the literature. The behavior of the different damage models in terms of crack surface, collapse mechanism and force displacement curves is investigated performing 3D analyses in several conditions including Mode I, Mixed Mode and Mode III fracture. When performing the appraisement of planar, bending and twisting cracks, the enhanced accuracy of the mixed formulation allows for a distinct assessment of the several damage models considered. Aspects related to the behavior of damage models, such as the influence of Poisson’s ratio, the shape of the damage surface and the adoption of isotropic and orthotropic models are investigated and noteworthy conclusions are drawn. [ABSTRACT FROM AUTHOR]

Finite element macro-modeling approaches are widely used for the analysis of large-scale masonry structures. Despite their efficiency, they still face two important challenges: the realistic representation of damage and a reasonable independency of the numerical results to the used discretization. In this work, the classical smeared crack approach is enhanced with a crack-tracking algorithm, originating from the analysis of localized cracking in quasi-brittle materials. The proposed algorithm is for the first time applied to a large-scale wall exhibiting multiple shear and flexural cracking. Discussion covers structural aspects, as the response of the structure under different assumptions regarding the floor rigidity, but also numerical issues, commonly overlooked in the simulation of large structures, such the mesh-dependency of the numerical results. [ABSTRACT FROM AUTHOR]

Strain localization bands (SLBs) that appear at early stages of deformation of magnesium alloys have been recently associated with heterogeneous activation of deformation twinning. Experimental evidence has demonstrated that such “Lüders-type” band formations dominate the overall mechanical behavior of these alloys resulting in sigmoidal type stress-strain curves with a distinct plateau followed by pronounced anisotropic hardening. To evaluate the role of SLB formation on the local and global mechanical behavior of magnesium alloys, an integrated experimental/computational approach is presented. The computational part is developed based on custom subroutines implemented in a finite element method that combine a plasticity model with a stiffness degradation approach. Specific inputs from the characterization and testing measurements to the computational approach are discussed while the numerical results are validated against such available experimental information, confirming the existence of load drops and the intensification of strain accumulation at the time of SLB initiation. [ABSTRACT FROM AUTHOR]

We present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. A material stability analysis is used to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems. [ABSTRACT FROM AUTHOR]

This paper presents an investigation on the detection of strain localization in numerical simulation of sheet metal forming. Two methods to determine the onset of localized necking have been compared. The first criterion, newly implemented in this work, is based on the analysis of the through-thickness thinning (through-thickness strain) and its first time derivative in the most strained zone. The limit strain in the second method, studied in the authors’ earlier works, is determined by the maximum of the strain acceleration. The limit strains have been determined for different specimens undergoing deformation at different strain paths covering the whole range of the strain paths typical for sheet forming processes. This has allowed to construct numerical forming limit curves (FLCs). The numerical FLCs have been compared with the experimental one. Mesh sensitivity analysis for these criteria has been performed for the selected specimens. It has been shown that the numerical FLC obtained with the new criterion predicts formability limits close to the experimental results so this method can be used as a potential alternative tool to determine formability in standard finite element simulations of sheet forming processes. [ABSTRACT FROM AUTHOR]

An inappropriate numerical approach adopted for modeling the strain localization of geomaterials often leads to ill-posed boundary value problems (BVP). In this article, we apply spectral analysis to study the regularization mechanism of Cosserat finite element method (CFEM) and strong discontinuity-Cosserat FEM (SD-CFEM). The 1D shear layer model and 2D plane strain tests are modeled to conduct the diagnostic spectral analysis. A 2D slope problem is simulated to demonstrate the effectiveness of SD-CFEM in simulating the characteristics of progressive deformation in geomaterials. The numerical results show that CFEM and SD-CFEM not only maintain the eigenvalues as positive, but also make the dominant eigenvectors for different mesh densities possess the identical evolution pattern which is the fundemental regularization mechanism of both methods. The deformation patterns reflected by dominant eigenvectors indicate that SD-CFEM is more robust in modeling strain localization/shear band than CFEM and SD-FEM do because the former can reflect the energy dissipation both in the shear band with a constant width and on the slip line in the shear band. It can be concluded from the displacement evolution process in the shear band that SD-CFEM inheriting the merits of CFEM and SD-FEM can physically and mathematically better simulate the whole deformation process of geomaterials from weak discontinuity (strain localization) to strong discontinuity (slip). [ABSTRACT FROM AUTHOR]

Finite element (FE) results might suffer from significant mesh dependency, especially when modeling shear bands in strain-softening soils. On the other hand, the shear bands in the field are generally thin. The computational costs might dramatically increase when modeling such thin shear bands, especially for large-scale problems, such as progressive landslides. To overcome these issues, FE analyses are generally performed with larger shear band thicknesses by adopting 'softening scaling' rules based on local and nonlocal (averaged) strains at the shear bands. The present study compares the performances of local and nonlocal approaches, with a specific focus on softening scaling and large deformation. Analyses are performed using a Eulerian-based FE program, which can model large strains in the shear band without numerical issues related to mesh distortion. Implementing strain-softening behavior in local and nonlocal methods, two idealized cases are simulated: (i) biaxial compression test, (ii) slope failure due to upslope surface loading. FE simulations show that the macroscopic response (i.e., load–displacement behavior) can be modeled using both local and nonlocal regularization techniques. Shear band thickness increases with the progress of shearing. In local analysis, mesh orientation has a considerable effect on shear band thickness. The existence of neighboring shear bands could affect nonlocal strain calculation and the simulation results. [ABSTRACT FROM AUTHOR]

• A CPFEM multiscale tool, based on the periodic homogenization scheme, is developed. • The multiscale tool is coupled with the Rice bifurcation approach and a coalescence criterion. • The effect of the matrix heterogeneity on strain localization and void coalescence is investigated. • The effect of texture on the competition between strain localization and void coalescence is studied. • Bifurcation is predicted at realistic strain levels even for non-porous polycrystalline aggregates. The ductility of polycrystalline aggregates is usually limited by two main phenomena: plastic strain localization and void coalescence. The goal of this contribution is to develop a new multiscale framework, based on the crystal plasticity finite element method (CPFEM), for the prediction of ductility limits set by these two phenomena for porous and non-porous polycrystalline aggregates. This numerical framework is based on the combination of crystal plasticity constitutive modeling with the periodic homogenization scheme. Within this strategy, the single crystal constitutive modeling follows a finite strain rate-independent approach, where the plastic flow is governed by the classical Schmid law. Thereby, the competition between the two aforementioned phenomena, which limit ductility, is thoroughly analyzed using the bifurcation theory and a strain-based coalescence criterion. To cover a wide range of mechanical states in this analysis, two types of loadings are applied to the studied aggregates: proportional triaxial stress paths and proportional in-plane strain paths. The developed CPFEM-based framework is well suited to account for essential microstructural features: pre-existence of spherical voids, crystallographic and morphological anisotropy, matrix polycrystallinity and interactions between grains and their surrounding medium. Extensive sensitivity studies are performed to analyze the impact of these microstructural features on the ductility limit predictions. The main trends obtained by classical phenomenological frameworks are extended here within the framework of crystal plasticity constitutive modeling. [ABSTRACT FROM AUTHOR]

This paper presents a novel smoothing gradient damage model, which goes beyond certain limitations of conventional methods, for accurate prediction of localized failure in quasi-brittle materials. The proposed method is particularly tailored to low-order finite elements such as 4-node quadrilateral or 3-node triangular elements. The low-order elements are preferable in practice as they can automatically be generated for problems even with complex geometries at low computational cost. In order to eliminate spurious damage growth and correct wrong prediction of shear band induced by using the constant gradient parameter in terms of conventional models, we thus introduce a novel modified evolving anisotropic nonlocal gradient parameter, which aims to control the behavior of nonlocal interactions of damage microprocess during the entire loading history in a more appropriate manner. Unlike conventional approaches, the novel modified evolving gradient parameter heavily depends on the principal stress and equivalent strain states, which serves to reduce the impact of localized deformation. The stress fields thus play a crucial role in the present formulation as they greatly affect the orientation and intensity of nonlocal interactions. The quality of raw stresses becomes critical (e.g., stress oscillation) once two unknowns (i.e., displacements and nonlocal equivalent strain) are approximated simultaneously using the same orders of interpolation functions (e.g., linear–linear). A smoothing technique is thus adopted to smooth out the raw stresses. The stresses after smoothing are shown adequately in the estimation of the new gradient parameter, providing much better solutions. In addition, to precisely capture the softening in quasi-brittle materials, the original energy norm is decomposed into tensile and compressive parts to form a new bi-energy norm. The scalar equivalent strain is thus estimated through this new bi-energy norm, which is obviously able to distinguish tensile and compressive conditions. To further enhance the capability of the present damage model, the material softening process is also determined through fracture energy in terms of fracture mechanics. Comparison of the present results with reference solutions derived from experimental data and other numerical methods for benchmark applications, regarding the nonlocal equivalent strain, damage profile, structural force–displacement curves, etc., confirms the accuracy and superior performance of the proposed approach for characterizing localized failure in quasi-brittle materials. [ABSTRACT FROM AUTHOR]

Unsaturated soils are solid-water-air systems that include a solid skeleton, pore water, and pore air. Heterogeneities in porosity or degree of saturation are salient features of unsaturated soils. These heterogeneities may trigger localized deformation (eg, shear banding) in such materials as demonstrated by numerical simulations via a pseudo three-phase model. In this article, we formulate a true three-phase mathematical framework implemented via stabilized low-order mixed finite elements. With this mathematical framework, we study the evolution of pore air pressure and its role in the inception of strain localization triggered by initial heterogeneity either in porosity or suction. The numerical simulations show that pore air pressure is nonzero and nonuniform in the process of progressive failure in unsaturated soils. The heterogeneity of pore air pressure may also play a significant role in the onset of localized deformation of unsaturated soils. Therefore, a three-phase model considering the pore air phase is physically more appropriate for modeling strain localization in unsaturated soils. [ABSTRACT FROM AUTHOR]

This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force-displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson's ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem. [ABSTRACT FROM AUTHOR]

This paper investigates localized shear deformation around a borehole due to internal pressure in the well such as by fluid injection. Using an elasto-visco-plastic formulation combined with damage mechanics for the effect of shear cracking, we first benchmark the model against analytical solutions and then provide bifurcation criteria for the onset of localized cracking at different temperature conditions. We report that at increased temperatures of the rock formation, hot fluid injection promotes shear stimulation, while cold fluid suppresses it. This counter-intuitive result can offer new pathways of effective stimulation in high-temperature environments, like those encountered in enhanced geothermal systems. [ABSTRACT FROM AUTHOR]

Failure prediction assessment is conducted based on validated finite element simulations of impact tests performed on 1.8 mm dual-phase and 1.0 mm martensitic steel sheets. The sheets were clamped between two steel rings and subjected to lateral loading by a punch with a hemispherical nose. Three different specimen geometries were applied. These were chosen to provide membrane loading in stress states near uniaxial tension, plane-strain tension and equi-biaxial tension. Thus, the most important stress states that may occur for thin sheets in an impact situation are covered. Finite element simulations of the impact tests are run with the nonlinear code LS-DYNA. The plastic behaviour of the materials is modelled using the Hershey yield function in combination with the associated flow rule and isotropic hardening. The specimens are discretized by shell elements, thus imposing a state of plane stress. Three different approaches for modelling ductile failure are evaluated by comparing the experimental and simulated force-displacement curves from the experiments on the two steel materials. [ABSTRACT FROM AUTHOR]

This paper concerns the application of a finite element squared approach for modelling hydromechanical coupling in the simulation of gallery excavation in the context of radioactive waste repositories. The micromechanics of Callovo-Oxfordian claystone is modelled at the microscale, taking into account the interaction of different mechanical constituents and its interaction with pore fluid. In a framework of computational homogenization, the micromechanical behaviour is coupled to the macroscale boundary value problem of a poromechanical continuum with local second gradient paradigm. The simulations concern several cases of the “Transverse action” benchmark by Andra, in the context of which the model is used. [ABSTRACT FROM AUTHOR]

Damage-induced strain softening is of vital importance for the modeling of localized failure in frictional-cohesive materials. This paper addresses strain localization of damaging solids and the resulting consistent frictional-cohesive crack models. As a supplement to the framework recently established for stress-based continuum material models in rate form (Wu and Cervera 2015, 2016), several classical strain-based damage models, expressed usually in total and secant format, are considered. Upon strain localization of such damaging solids, Maxwell's kinematics of a strong (or regularized) discontinuity has to be reproduced by the inelastic damage strains, which are defined by a bounded characteristic tensor and an unbounded scalar related to the damage variable. This kinematic constraint yields a set of nonlinear equations from which the discontinuity orientation and damage-type localized cohesive relations can be derived. It is found that for the "Simó and Ju 1987" isotropic damage model, the localization angles and the resulting cohesive model heavily depend on lateral deformations usually ignored in classical crack models for quasi-brittle solids. To remedy this inconsistency, a modified damage model is proposed. Its strain localization analysis naturally results in a consistent frictional-cohesive crack model of damage type, which can be regularized as a classical smeared crack model. The analytical results are numerically verified by the recently-proposed mixed stabilized finite element method, regarding a singly-perforated plate under uniaxial tension. Remarkably, for all of the damage models discussed in this work, the numerically-obtained localization angles agree almost exactly with the closed-form results. This agreement, on the one hand, consolidates the strain localization analysis based on Maxwell's kinematics and, on the other hand, illustrates versatility of the mixed stabilized finite element method. [ABSTRACT FROM AUTHOR]

• Developed framework for synthetic microstructures of additively manufactured Ti-6Al-4V. • Virtual microstructures explicitly modeled prior β boundaries and α laths features. • Prior β boundaries and hard-soft α laths are likely locations of fatigue crack initiation. • The inclusion of prior β boundaries resulted in a reduced mean predicted fatigue life. • Microplasticity at prior β boundaries is evident at loads below the percolation limit. Microstructure-based models of additive manufactured (AM) Ti-6Al-4V should faithfully represent the unique microstructural features of these materials to provide a more thorough understanding of their role in the mechanical performance of the material. For AM Ti-6Al-4V, the prior β boundaries are likely sites of microscopic plastic strain localization, often leading to fatigue crack initiation. Within the context of crystal plasticity finite element methods, there is an existing gap in the current literature for creating synthetic microstructures of Ti-6Al-4V that capture both the prior β boundaries and α laths. This work focuses on generating such statistically equivalent microstructures, where the prior β boundaries and α laths are explicitly modeled. The framework can generate synthetic microstructures that consider one prior β grain or multiple β grains (and thus prior β grain boundaries) and their associated α laths forming a Widmanstätten microstructure, which are used as inputs for fatigue simulations. Within the fatigue model, the critical accumulated plastic strain energy density (APSED) is a metric used to predict the location and number of cycles of crack initiation. From a statistical average perspective, the presence of prior β grain boundaries was detrimental to the fatigue performance. The effectiveness of the prior β grain boundary in impeding slip, and therefore localizing APSED, is dependent on the loading conditions, prior β orientations, and α variants present in neighboring prior β grains. A higher percentage of failures occurred at the prior β grain boundary in the case of lower applied stress amplitudes, where the applied loads were below the percolation limit of the material and microplasticity was localized to a few locations relative to the microstructure. Additionally, for the case of crack initiation associated with the α variants within a given prior β grain, a combination of soft-hard α lath orientations resulted in sites of APSED localization and predicted fatigue crack initiation. The framework generated in this paper to create representative synthetic microstructures of the Widmanstätten microstructures associated with AM Ti-6Al-4V and the associated fatigue modeling enables trade-off studies between microstructural features and fatigue performance. [Display omitted] [ABSTRACT FROM AUTHOR]

High-pressure turbine disks are subjected to extreme mechanical and thermal loadings throughout their lifetime. This is the reason why during the design of turboshaft engines, regulation rules impose on manufacturers to demonstrate the integrity of rotating parts, especially turbine disks, with over-speed experiments. To improve the prediction of rotation speed at burst, it is essential to study the viscoplastic behavior and the fracture of the material. The present work focuses on the approach used to calibrate accurately a viscoplastic behavior model at high temperature (500 °C) of nickel-based superalloy Inconel718. The experimental testing campaign includes standard tensile tests on axisymmetric and flat specimens with and without notches. The behavior is described using the McCormick model for dynamic strain aging. This model accounts for the viscoplastic behavior including the range of negative strain rate sensitivity and the Portevin–Le Chatelier (PLC) effect. In addition to global measurements, digital image correlation at high temperature using a speckle directly engraved on the specimen is used to detect and measure the strain carried by the PLC bands. This information is used in the parameter calibration. The consideration of the machine stiffness is shown to be essential in the analysis for a correct description of serrations and of the critical strain for PLC effects. 3D simulations on full specimen geometries samples are performed to validate the finite element model. Finally, a full 3D representative disk geometry simulation is performed to detect instabilities and their propagation due to geometrical singularities. • Experimental database for identification of PLC effect in Inconel718 at 500°C • Calibration of MacCormick elastoviscoplastic model including dynamic strain ageing • Accounting for the machine stiffness into the finite element simulations is necessary • A stress controlled test is performed to mimic the loading of rotating turbine disks • The model predicts the occurrence of strain bursts in a rotating disk until failure [ABSTRACT FROM AUTHOR]

An experimental-numerical approach is applied to determine the strain localization and ductile fracture of high-strength dual-phase and martensitic steel sheet materials. To this end, four different quasi-static material tests were performed for each material, introducing stress states ranging from simple shear to equi-biaxial tension. The tests were analysed numerically with the nonlinear finite element method to estimate the failure strain as a function of stress state. The effect of spatial discretization on the estimated failure strain was investigated. While the global response is hardly affected by the spatial discretization, the effect on the failure strain is large for tests experiencing necking instability. The result is that the estimated failure strain in the different tests scales differently with spatial discretization. Localization analysis was performed using the imperfection band approach, and applied to estimate onset of failure of the two steel sheet materials under tensile loading. The results indicate that a conservative failure criterion for ductile materials may be established from localization analysis, provided strain localization occurs prior to ductile fracture. [ABSTRACT FROM AUTHOR]

A hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media. Central to the multiscale approach is a hierarchical coupling of finite element method (FEM) and discrete element method (DEM), wherein the FEM is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a granular assembly embedded at each of the FEM Gauss integration points as the representative volume element (RVE). While being effective in reproducing the complex mechanical responses of granular media, the hierarchical approach helps to bypass the necessity of phenomenological constitutive models commonly needed by conventional FEM studies and meanwhile offers a viable way to link the macroscopic observations with their underlying microscopic mechanisms. To model the phenomenon of strain localization, key issues pertaining to the selection of proper RVE packings are first discussed. The multiscale approach is then applied to simulate the strain localization problem in a cubical specimen and a cylindrical specimen subjected to either conventional triaxial compression (CTC) or conventional triaxial extension (CTE) loading, which is further compared to a case under plane-strain biaxial compression (PBC) loading condition. Different failure patterns, including localized, bulging and diffuse failure modes, are observed and analyzed. Amongst all testing conditions, the PBC condition is found most favorable for the formation of localized failure. The CTC test on the cubical specimen leads to a 3D octopus-shaped localization zone, whereas the cylindrical specimen under CTC shows seemingly bulging failure from the outlook but rather more complex failure patterns within the specimen. The CTE test on a uniform specimen normally ends in a diffuse failure. Different micro mechanisms and controlling factors underlying the various interesting observations are examined and discussed. [ABSTRACT FROM AUTHOR]

The macroscopic behavior of materials is affected by their inner micro-structure. Elementary considerations based on the arrangement, and the physical and mechanical features of the micro-structure may lead to the formulation of elastoplastic constitutive laws, involving hardening/softening mechanisms and non-associative properties. In order to model the non-linear behavior of micro-structured materials, the classical theory of time-independent multisurface plasticity is herein extended to Cosserat continua. The account for plastic relative strains and curvatures is made by means of a robust quadratic-convergent projection algorithm, specifically formulated for non-associative and hardening/softening plasticity. Some important limitations of the classical implementation of the algorithm for multisurface plasticity prevent its application for any plastic surfaces and loading conditions. These limitations are addressed in this paper, and a robust solution strategy based on the singular value decomposition technique is proposed. The projection algorithm is then implemented into a finite element formulation for Cosserat continua. A specific finite element is considered, developed for micropolar plates. The element is validated through illustrative examples and applications, showing able performance. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Crystal plasticity finite element simulations of tensile tests on thin polycrystalline samples with grain orientations representative of the microstructure in Al–Cu–Li rolled sheets are carried out to study the influence of grain-to-grain interactions on plastic strain localization. Anisotropic work-hardening and rate-sensitivity of the material behavior are assumed. The grains are modeled as thin platelets in the through-thickness direction, elongated in the rolling and transverse directions. The only distinctive feature of the present simulations with respect to standard crystal plasticity calculations is the enforcement of tangential continuity conditions on the elastic and plastic distortion rates along grain boundaries, which introduces grain-to-grain interactions and renders the simulations nonlocal. Whereas standard crystal plasticity calculations do not predict any significant plastic strain pattern, slanted shear bands spontaneously emerge throughout the sample in the simulations involving tangential continuity, in agreement with experimental observations. Also in agreement with experimental data, shear banding is delayed when the tensile axis shifts from rolling to transverse direction, and the trend to shear banding is enhanced when grain thickness is decreased, particularly in loading along the rolling direction. [ABSTRACT FROM AUTHOR]

In this work, the consequences of using several different discrete element granular assemblies for the representation of the microscale structure, in the framework of multiscale modeling, have been investigated. The adopted modeling approach couples, through computational homogenization, a macroscale continuum with microscale discrete simulations. Several granular assemblies were used depending on the location in the macroscale finite element mesh. The different assemblies were prepared independently as being representative of the same material, but their geometrical differences imply slight differences in their response to mechanical loading. The role played by the micro-assemblies, with weaker macroscopic mechanical properties, on the initiation of strain localization in biaxial compression tests is demonstrated and illustrated by numerical modeling of different macroscale configurations. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper presents an explicit mixed finite element formulation to address compressible and quasi-incompressible problems in elasticity and plasticity. This implies that the numerical solution only involves diagonal systems of equations. The formulation uses independent and equal interpolation of displacements and strains, stabilized by variational subscales. A displacement sub-scale is introduced in order to stabilize the mean-stress field. Compared to the standard irreducible formulation, the proposed mixed formulation yields improved strain and stress fields. The paper investigates the effect of this enhancement on the accuracy in problems involving strain softening and localization leading to failure, using low order finite elements with linear continuous strain and displacement fields ( P1 P1 triangles in 2D and tetrahedra in 3D) in conjunction with associative frictional Mohr-Coulomb and Drucker-Prager plastic models. The performance of the strain/displacement formulation under compressible and nearly incompressible deformation patterns is assessed and compared to analytical solutions for plane stress and plane strain situations. Benchmark numerical examples show the capacity of the mixed formulation to predict correctly failure mechanisms with localized patterns of strain, virtually free from any dependence of the mesh directional bias. No auxiliary crack tracking technique is necessary. [ABSTRACT FROM AUTHOR]

In this paper, the non-isothermal elasto-plastic behaviour of multiphase geomaterials in dynamics is investigated with a thermo-hydro-mechanical model of porous media. The supporting mathematical model is based on averaging procedures within the hybrid mixture theory. A computationally efficient reduced formulation of the macroscopic balance equations that neglects the relative acceleration of the fluids, and the convective terms is adopted. The modified effective stress state is limited by the Drucker-Prager yield surface. Small strains and dynamic loading conditions are assumed. The standard Galerkin procedure of the finite element method is applied to discretize the governing equations in space, while the generalized Newmark scheme is used for the time discretization. The final non-linear set of equations is solved by the Newton method with a monolithic approach. Coupled dynamic analyses of strain localization in globally undrained samples of dense and medium dense sands are presented as examples. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A numerical study of the regularization properties of the finite element model is shown and discussed. A non-isothermal case of incipient strain localization induced by temperature increase where evaporation takes place is also analysed. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]