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The acquisition of lead-free piezoelectric films with large strain is the key factor in promoting micro-actuator development. A lead-free compound, Bi 0. 5 Na 0. 5 TiO 3 , exhibits extensive potential in achieving a large strain response and a high inverse piezoelectric coefficient. In this work, (1- x)Bi 0. 5 Na 0. 5 TiO 3 - x SrTiO 3 (BNT-100 x ST, x = 0.1, 0.2, 0.25) solid solution thin films have been prepared using the chemical solution deposition method. The dielectric nonlinearity and ferroelectric properties of BNT-ST thin films have been systematically studied to investigate the domain wall motion in the films. The most significant domain wall motion was observed in BNT-20ST thin film, in which film a large strain of 0.89 % was obtained. In addition, the relationship between structure and properties as a function of temperature was studied by the temperature-dependent dielectric properties and Raman spectra analysis. [ABSTRACT FROM AUTHOR]

A new simplified practical method for one‐dimensional nonlinear large‐strain consolidation of saturated homogenous soils is proposed. The derivation processes of the proposed method are introduced first, with a modification of Terzaghi's theory from a novel perspective to solve large‐strain consolidation problems. Verification checks of the proposed method with other solutions are then conducted. The proposed method is different from Lekha's solution because Lekha's analytical solution is based on the small strain theory. For linear consolidation, the proposed method shows excellent agreement with the Consolidation Settlement 2 (CS2) model. For nonlinear large‐strain consolidation, the new method is in good agreement with the CS2 model when Cc/Ck ≤ 1. After that, optimization of the proposed nonlinear solution is carried out for Cc/Ck > 1 with a more precise average constant coefficient of consolidation used in the simplified practical method, and good agreement is obtained between the solutions from the proposed method and the CS2 model. Overall, the proposed simplified method provides practical, reliable, and efficient solutions for analyzing linear and nonlinear large‐strain consolidation. [ABSTRACT FROM AUTHOR]

The existing theories or numerical models of thaw consolidation for frozen soil rarely consider the influence of the thermal effect, so it is difficult to analyze the problem of thaw thermoconsolidation for frozen soil under high temperature. Using the piecewise linear approach and finite-difference method, a one-dimensional large strain thaw thermoconsolidation model, called TTCS1, is established for frozen saturated soil under high temperature. The model couples the heat transfer with phase change of frozen soil and the thermoconsolidation deformation, and accounts for the nonlinear changes of soil parameters and large strain during the process of thaw thermoconsolidation under high temperature. When the thermal effect is ignored, TTCS1 shows excellent agreement with the existing large strain thaw consolidation model. When the thermal effect is considered, the numerical solutions of the TTCS1 model are basically consistent with the test values. The influences of the thermal effect, boundary temperature, and boundary conditions on the thaw thermoconsolidation for frozen silty clay are further discussed, and the settlement and settlement rate of frozen soil under high temperature will be significantly underestimated if the thermal effect is not considered. [ABSTRACT FROM AUTHOR]

This paper presents a new triangular multi-layer nonlinear shell finite element with incremental degrees of freedom, suitable for large displacements and rotations. This is a nonconforming element with 6 nodes, quadratic displacement and linear rotation field based on Rodrigues incremental rotation parameters, with a total of 21 DoFs. The novelty of this element is the extension to a multilayer, fully incremental situation of the T6-3iKL element, a kinematical model with properties from Kirchhoff-Love theory, approximating the shell director across layers as constant. The model is numerically implemented, and results are compared to different references in multiple examples, showing the capabilities of the formulation. It is believed that the possibly simplest multilayer extension, combined with fully incremental DoFs, simple kinematic, no necessity of artificial parameters such as penalties, a relatively small number of DoFs, possibility to use various 3D material models, easily connected with multiple branched shells and beams, and geometric exact theory create a simple yet powerful shell element. [ABSTRACT FROM AUTHOR]

We perform via Γ-convergence a 2d-1d dimension reduction analysis of a single-slip elastoplastic body in large deformations. Rigid plastic and elastoplastic regimes are considered. In particular, we show that limit deformations can essentially freely bend even if subjected to the most restrictive constraints corresponding to the elastically rigid single-slip regime. The primary challenge arises in the upper bound where the differential constraints render any bending without incurring an additional energy cost particularly difficult. We overcome this obstacle with suitable non-smooth constructions and prove that a Lavrentiev phenomenon occurs if we artificially restrict our model to smooth deformations. This issue is absent if the differential constraints are appropriately softened. [ABSTRACT FROM AUTHOR]

A series of plate loading tests on clay has been conducted in the centrifuge. The aim of the tests is to create a data set, which is freely downloadable, to validate numerical tools that account for geometrical nonlinearities. The tests include two sources of geometrical non-linearities. The first source is the reducing clay layer thickness below the plate, which causes an increase in resistance. The second source is the backflow of the clay around the tip of the plate. The backflow has a reducing effect on the plate resistance. This paper outlines four tests: two involving a wide plate and two with a small plate. Each plate geometry is investigated under both smooth and rough side model boundaries. An material point method (MPM) schematization is used for numerical analysis. The schematization and parameter selection are initially validated by comparing the MPM results against CPTu data in each test. The numerical analysis examines the impact of a finite layer thickness by analyzing various layer thicknesses. Furthermore, the analysis shows the influence of the backflow on the plate resistance by analyzing different ratios of shaft to plate width. In this study, the pore pressures below the plate and vertical and horizontal displacement fields are considered in addition to the load displacement curves. The MPM simulations are in good agreement with the centrifuge data. [ABSTRACT FROM AUTHOR]

Copyright of Engineering Mechanics / Gongcheng Lixue is the property of Engineering Mechanics Editorial Department and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Summary: The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first‐order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first‐order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex‐based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi‐discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation. [ABSTRACT FROM AUTHOR]

At present, many achievements have been made in the analytical theory of large strain consolidation. However, the consideration of nonlinearity of compression and permeability is not yet sufficient. In this study, a large number of compressibility and permeability test data have been investigated to verify the advantages of log-log relationships in describing nonlinear characteristics of compressibility and permeability of soft soils under both large strain and small strain, and the variation range of parameters in log-log relationships are also presented. Also, based on the log-log relationships, a one-dimensional nonlinear large strain consolidation model of thin soft soil layer is established by considering excess pore pressure as a variable, and the analytical solutions of the consolidation model are obtained under three conditions, respectively. Then, the reliability of analytical solutions is verified by comparing with the results observed in the field and degenerate solution, respectively. Finally, the influence of loading method, final load, compressibility and permeability parameters on consolidation behavior are analyzed. This study provides theoretical supports for the calculation of nonlinear large strain consolidation of actual soft soil layer. [ABSTRACT FROM AUTHOR]

Lead-based piezoelectric ceramics are the preferred material for commercial piezoelectric ceramic actuators due to their high performance and irreplaceability. However, the operating temperature (<100 °C) and strain (0.1 %∼0.2 %) of lead-based piezoelectric ceramics are still limited. Achieving large strain in a wide temperature range remains challenging. In this paper, a new strategy is proposed to effectively increase the strain value of lead-based piezoelectric ceramics through domain engineering. The new x PbTiO 3 -(0.97- x)PbZrO 3 -0.03(La 0.1 Sr 0.80.1)TiO 2.95 (x PT-PZ-LST) ternary piezoelectric ceramic system reaches a strain value as high as 0.5 % and exhibits extremely high temperature stability (13 %) in the range of 25–230 °C. By fine-tuning the content of PT components, the average length and width of a typical tetragonal domain are transformed from 800 nm to 80 nm (long and thin) to 300 nm and 200 nm (short and wide), relatively. From the experimental results of PFM and Rayleigh analysis, the high strain can be attributed to the synergistic effect of the reduced coercive field (E c), enhanced micro-region response, and regulated domain morphology, which ensures that high intrinsic and extrinsic contribution can be achieved at the same time. In this paper, a new strain regulation method is provided for lead-based piezoelectric ceramics, and a valuable large strain material is obtained via domain engineering. [ABSTRACT FROM AUTHOR]

A mathematical model was developed to investigate the consolidation behavior of soft soil deposits improved by prefabricated vertical drains. The smear effect caused by drain installation was incorporated into the model by assuming a parabolic variation of permeability and compressibility with radius. The non-Darcian flow of pore water in the soil and the well resistance effect caused by the limited discharge capacity of drain were also incorporated in the model. The void ratio dependence of permeability and compressibility was taken into consideration to account for their variation with time. The proposed model was validated by comparing the predicted results with experimental data and with existing analytical models. A parametric study was performed to evaluate the influence of various parameters such as non-Darcian flow, permeability ratio, and discharge capacity on the consolidation of the soil deposit. The average effective stress decreased by approximately 20% when the ratio of permeability in the undisturbed zone to the smear zone was increased from 1.5 to 5. The average excess pore-water pressure at the soil–drain interface reduced by approximately 80% when the discharge capacity was increased from 20 to 100 m3/year. The well resistance effect was more significant for non-Darcian flow as compared to Darcian flow. The rate of dissipation of average excess pore-water pressure increased by approximately 75% when the non-Darcian parameter n was increased from 1 to 2. However, the average excess pore-water pressure became independent of the non-Darcian parameter (n) for n greater than 2.5. [ABSTRACT FROM AUTHOR]

The vacuum preloading method effectively strengthens soft soil foundations with vertical drainage, which produces a smear effect when laying sand drains. Meanwhile, the seepage of pore water and soil deformation during consolidation exhibit nonlinear characteristics. Therefore, based on Gibson's 1D large-strain consolidation theory, this paper developed a more generalized large-strain radical consolidation model of sand-drained soft foundations under free-strain assumptions. In this system, the double logarithmic compression permeability relationships for soft soils with large-strain properties, the variation in the radical permeability coefficient in the smear zone, and the effect of the non-Darcy flow were all included. Then, the partial differential control equations were numerically solved by the finite difference method and validated with existing radical consolidation test results and derived analytical solutions. Finally, the influences of relevant model parameters on consolidation are discussed. The analysis shows that the greater the maximum dimensionless vacuum negative pressure P0, the faster the consolidation rate of sand-drained foundations. Meanwhile, the decrease in the negative pressure transfer coefficient k1 will result in a decreasing final settlement amount. Moreover, the consolidation rate of sand-drained foundations is slower considering the non-Darcy flow, but the final settlement is unaffected. [ABSTRACT FROM AUTHOR]

High strain with low hysteresis is crucial for commercial applications in high precision actuators. However, the clear conflict between the high strain and low hysteresis in BNT-based ceramics has long been an obstacle to actual precise actuating or positioning applications. To obtain piezoceramics with high strain and low hysteresis, it is necessary to enhance the electrostrictive effect and develop an ergodic relaxor (ER) and nonergodic relaxor (NR) phase boundary under ambient conditions. In this work, (Co0.5Nb0.5)4+ doped 76Bi0.5Na0.5TiO3-24SrTiO3 (BNST24) relaxors were fabricated using the conventional solid state reaction route. X-ray diffraction patterns revealed the B-site substitution in BNST24 ceramics. By adjusting the (Co0.5Nb0.5)4+ doping in BNST24, we effectively tuned the TNR-ER and Td close to ambient temperature, which contributed to the development of the ergodic relaxor phase and enhanced the electrostrictive effect at ambient temperature. The I-P-E loops and bipolar strain curves verified the gradual evolution from NR to ER states, while the enhanced electrostrictive effect was verified by the nearly linear S-P2 curves and improved electrostrictive coefficient of the BNST24-xCN relaxors. An enhanced strain of 0.34% (d*33 = 483 pm/V) with low hysteresis of 8.9% was simultaneously achieved in the BNST24-0.02CN relaxors. The enhanced strain was mainly attributed to the proximity effect at the ER and NR phase boundary of BNST24-0.02CN, while the improved electrostrictive effect contributed to the reduced strain hysteresis. Our work demonstrates an effective strategy for balancing the paradox of high strain and low hysteresis in piezoceramics. [ABSTRACT FROM AUTHOR]

The simple shear test shows significant advantages when measuring the hardening and shear properties of thin sheet metal at large strains. However, previous shear tests had an end effect caused by local stress concentration and a boundary effect caused by deformation overflow, resulting in non-uniform strain distribution in the shear zone. Therefore, a unique V-shaped double-shear-zone specimen is proposed to measure the Bauschinger effect under cyclic shear loading conditions in this paper. Simple shear experiments and three different types of cycle shear experiments are conducted to analyze the uniformity of deformation in the shear zone and the effect of pre-strain and the number of cyclic loads on the Bauschinger effect of Q890 high-strength steel sheets. The results indicate that the proposed V-shaped double-shear-zone specimen can still maintain uniform shear deformation in forward/reverse cyclic loading experiments, even at large strains. Q890 high-strength steel exhibits a significant Bauschinger effect, which is more pronounced with the increase in shear pre-strain and loading cycles. The results of this paper provide a new approach for studying the hardening characteristics under large strain and the mechanical properties under cyclic shear loading for metal sheets. [ABSTRACT FROM AUTHOR]

Vacuum‐assisted prefabricated horizontal drain (PHD) can be used to accelerate the consolidation process of dredged mud slurry with high water content, and this method exhibits advantages over traditional treatment methods that use prefabricated vertical drain (PVD). However, large‐strain model that can simulate soil consolidation induced by vacuum‐assisted PHDs is missing in the literature, although the large‐strain models for PVD‐induced radial consolidation are abundant. This study presents a piecewise‐linear plane‐strain model for large‐strain consolidation induced by vacuum‐assisted prefabricated horizontal drains. The model is called PCS, abbreviation for Plane‐strain Consolidation Settlement. PCS model can account for complex conditions including large strain, multiple layers of PHD boards, staged filling of soil layers, varying spacing of PHD boards, time‐dependent surcharge and/or vacuum loading, soil self‐weight, nonlinear compressibility, and hydraulic conductivity during the consolidation process, vertical and horizontal flows, and non‐Darcian flow. The PCS is validated using the two‐dimensional Terzaghi's consolidation theory (small strain) and a large‐scale laboratory model test (large strain), which involves multiple soil layers filled in stages, multiple PHD layers, and different horizontal spacings of PHD boards. Lastly, the proposed model is applied to a case study conducted at Shimokita Peninsula (Aomori Prefecture, Japan), where vacuum‐assisted PHDs have been used to treat the dredged mud slurry for a duration of 330 days. [ABSTRACT FROM AUTHOR]

Copyright of Bulletin of the Chinese Ceramic Society is the property of Bulletin of the Chinese Ceramic Society Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Over the past decades, many advances have occurred for theories on large-strain nonlinear consolidation of soft soils with regard to traditional drainage boundaries, which are completely permeable and impermeable cases and which may not truly reflect the whole process of drainage boundary. Thus, some further considerations related to a time-dependent drainage boundary are adopted in the analysis of soft soil consolidation by incorporating biologarithmic compressibility and permeability models. Also, the analytical solutions are obtained by means of variable substitution and Laplace transform. Additionally, the proposed solution is degenerated and compared with the existing solution and the laboratory tests to validate its correctness and feasibility. Finally, the soil consolidation behavior is analyzed under different values of the interface parameter, nonlinear compressibility and permeability, and external loading. The results indicate that the drainage boundary permeability is largely determined by the interface parameter; the larger the interface parameter, the better the boundary permeability. Besides, the consolidation rate decreases with the increasing value of Ic(α − 2) when the external loading remains constant. While the parameter Ic(α − 2) is a constant value, the consolidation rate varies with the external loading. Therefore, appropriate parameter values are more conducive to the full consolidation of soft soil foundations. [ABSTRACT FROM AUTHOR]

The fracture criterion is a critical topic in fracture mechanics. However, the equality of J-Integral (J) and energy release rate (G) has not been numerically verified under large strain theory. This paper aims to numerically justify the condition for equality in brittle and small-scale plastic fracture. The computation of the J in this study was performed using the commercial finite element program LS-DYNA and postprocessor LS-PrePost. The G was measured by node release method in LS-DYNA. Our result numerically verified the equality of G = J in elasticity, but not in plasticity. This is also supported by the analytical derivation. The critical energy release values in this work are considered in a reasonable range compared with experiment data. Note: The entire paper, with the exception of equations, was rephrased using ChatGPT. This was achieved by requesting ChatGPT to rewrite the original manuscript written by humans, paragraph by paragraph.

Two different types of shear bands generate in ultrafine-grained (UFG) CoCrFeMnNi high-entropy alloys deformed at 77 K, i.e. commonly-observed low angle grain boundary (LAGB) type and unusual twin-coupled type. Twin-coupled shear bands exhibit a misorientation of 56–67° with the matrix, in contrast to the LAGB shear band with a misorientation of 6–12°. Both annealing twins and deformation twins can act as precursor for twin-coupled shear bands, where dislocation accumulation along twin boundaries can tune the orientation of twin lamella. These observations suggest that twin-coupled shear bands can act as an important plastic carrier in materials deformed under extreme conditions.

Based on the piecewise-linear approach, a large strain nonlinear radial thermo-consolidation model for saturated soil foundation, called RTCS1, is established. The model uses the finite difference method to solve the governing equations of radial heat transfer in the soil layer and couples it with large strain radial consolidation. RTCS1 accounts for thermal effect, thermal expansion, time-dependent load increment and time-dependent heat source temperature, unload/reload effects, radial and vertical flows, equal strain and equal stress, and the nonlinear changes of soil parameters during thermo-consolidation process. Validation of the model is conducted through laboratory and field test of thermo-consolidation from existing literature, and the RTCS1 numerical solution for settlement is in good agreement with the test values. Computational examples are presented to explore the effect of strain condition, strain magnitude, and heating mode on the thermo-consolidation of saturated soil foundations. The findings indicate that the consolidation rate under equal strain condition is greater than that under equal stress condition, the lager strain leads to faster heat transfer. Under the cyclic heating modes, the excess pore pressure cannot be completely dissipated, and the soil settlement, temperature and excess pore pressure fluctuated with time. [ABSTRACT FROM AUTHOR]

The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to consider more general irreversible processes such as thermo-elasticity and thermo-visco-plasticity. This requires the incorporation of the first law of thermodynamics, expressed in terms of the entropy density, as an additional conservation law. To disassociate material particles from mesh positions, the framework introduces an additional reference configuration, extending beyond conventional material and spatial descriptions. The determination of the mesh motion involves the solution of a conservation-type momentum equation, ensuring optimal mesh movement and contributing to maintaining a high-quality mesh and improving solution accuracy, particularly in regions undergoing large plastic flows. To maintain equal convergence orders for all variables (strains/stresses, velocities/displacements and temperature/entropy), the standard deformation gradient tensor (measured from material to spatial configuration) is evaluated through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both are obtained through additional first-order conservation laws. The exploitation of the hyperbolic nature of the underlying system, together with accurate wave speed bounds, ensures the stability of explicit time integrators. For spatial discretisation, a vertex-centred Godunov-type Finite Volume method is employed and suitably adapted to the formulation at hand. To guarantee stability from both the continuum and the semi-discretisation standpoints, a carefully designed numerical interface flux is presented. Lyapunov stability analysis is carried out by evaluating the time variation of the Ballistic energy of the system, aiming to ensure the positive production of numerical entropy. Finally, a variety of three dimensional benchmark problems are presented to illustrate the robustness and applicability of the framework. • Incorporation of irreversible and thermally coupled constitutive responses within a conservative ALE framework. • The introduction of a conservation law for the material motion associated with a fictitious constitutive response. • Demonstration of numerical entropy production through the use of the Ballistic free energy. • Implementation into the open source software OpenFoam with a vertex centred Finite Volume method. [ABSTRACT FROM AUTHOR]

The vacuum preloading method effectively strengthens soft soil foundations with vertical drainage, which produces a smear effect when laying sand drains. Meanwhile, the seepage of pore water and soil deformation during consolidation exhibit nonlinear characteristics. Therefore, based on Gibson’s 1D large-strain consolidation theory, this paper developed a more generalized large-strain radical consolidation model of sand-drained soft foundations under free-strain assumptions. In this system, the double logarithmic compression permeability relationships for soft soils with large-strain properties, the variation in the radical permeability coefficient in the smear zone, and the effect of the non-Darcy flow were all included. Then, the partial differential control equations were numerically solved by the finite difference method and validated with existing radical consolidation test results and derived analytical solutions. Finally, the influences of relevant model parameters on consolidation are discussed. The analysis shows that the greater the maximum dimensionless vacuum negative pressure P0, the faster the consolidation rate of sand-drained foundations. Meanwhile, the decrease in the negative pressure transfer coefficient k1 will result in a decreasing final settlement amount. Moreover, the consolidation rate of sand-drained foundations is slower considering the non-Darcy flow, but the final settlement is unaffected.

This article presents a vertex‐centered finite volume algorithm for the explicit dynamic analysis of large strain contact problems. The methodology exploits the use of a system of first order conservation equations written in terms of the linear momentum and a triplet of geometric deformation measures (comprising the deformation gradient tensor, its co‐factor, and its Jacobian) together with their associated jump conditions. The latter can be used to derive several dynamic contact models ensuring the preservation of hyperbolic characteristic structure across solution discontinuities at the contact interface, a clear advantage over the standard quasi‐static contact models where the influence of inertial effects at the contact interface is completely neglected. Taking advantage of the conservative nature of the formalism, both kinetic (traction) and kinematic (velocity) contact interface conditions are explicitly enforced at the fluxes through the use of appropriate jump conditions. Specifically, the kinetic condition is enforced in the usual linear momentum equation, whereas the kinematic condition can now be easily enforced in the geometric conservation equations without requiring a computationally demanding iterative algorithm. Additionally, a total variation diminishing shock capturing technique can be suitably incorporated in order to improve dramatically the performance of the algorithm at the vicinity of shocks. Moreover, and to guarantee stability from the spatial discretization standpoint, global entropy production is demonstrated through the satisfaction of semi‐discrete version of the classical Coleman–Noll procedure expressed in terms of the time rate of the so‐called Hamiltonian energy of the system. Finally, a series of numerical examples is examined in order to assess the performance and applicability of the algorithm suitably implemented in OpenFOAM. The knowledge of the potential contact loci between contact interfaces is assumed to be known a priori. [ABSTRACT FROM AUTHOR]

Over the past 50 years the Ogden model has been widely used in material modelling owing to its ability to match accurately the experimental data on elastomers at large strain, as well as its mathematical properties, such as polyconvexity. In this paper, these characteristics are exploited to formulate a finite-strain model that incorporates, through the phase-field approach recently proposed by Wu (Wu 2017 J. Mech. Phys. Solids103, 72–99) for small strains, a cohesive damage mechanism which leads to the progressive degradation of the material stiffness and to failure under tension. By properly tailoring the constitutive parameters, the model is capable of encompassing a wide range of effects, from brittle to pseudo-ductile failure modes. A plane stress problem is formulated to test the model against experiments on double-network elastomers, which display a pseudo-ductile damage behaviour at large strain, and on conventional rubber compounds with brittle failure. The results show that the proposed model is applicable to fracture coalescence and propagation in a wide range of materials. This article is part of the theme issue 'The Ogden model of rubber mechanics: Fifty years of impact on nonlinear elasticity'. [ABSTRACT FROM AUTHOR]

The ground response curve (GRC) depicts the relationship between support reaction force and ground displacement, which improves the understanding of ground-support interaction and provides important references to the tunnel design. However, it is difficult to anticipate the tunneling-induced large deformation with sufficient reliability in soft rock with high geostress since the small strain theory is not applicable. When large deformation occurs, the tunnel needs to be over-excavated. Thus, the GRC should be modified considering the enlarged excavation radius since the actual excavation radius is usually greater than the designed one. To overcome the shortcomings of small strain theory in recognizing ground-support interaction under large deformation circumstances, a new large strain numerical approach for modifying the GRC was proposed considering over-excavation in strain-softening rock masses based on the generalized Zhang-Zhu strength criterion. A case study was conducted based on the Lianchengshan tunnel in China. The modified GRC was employed to investigate the ground-support behavior for different support schemes and to explore the applicability of the stress release measures. Combined with field tests, the proposed approach was validated. By comparing with GRCs proposed by previous work, the present modified GRC was proved to be superior to others. Parametric studies were conducted and it is found that over-excavation, for example, reserving a very large clearance between the surrounding rock and the support, is necessary to reduce ground pressure to a large extent. The yielding supports which can provide high support pressure during the process of deformation are highly recommended when tunneling in high geostress environment. However, if the initial geostress is not very high, it is not necessary to pursue unwarranted over-excavation since the ground pressure applied on the support is mainly the loosening stress when the deformation is large. Ample support stiffness should be provided in the process of deformation to prevent uncontrolled large deformation of surrounding rock.

The one-dimensional (1D) large strain consolidation (LSC) of saturated soft materials that are deposited at very low-density usually exhibit time-variant compressibility (void ratio vs vertical effective stress (e-σv′)) relation. The 1D column-like model test serves as an effective approach for characterizing this consolidation characteristic if all the physical parameters (including the settlement rate, pore pressure and density) are measured. Unfortunately, the density measurement is not always realistic due to its high cost (e.g., with X-rays) and the time-effect must be roughly neglected by using an average compressibility relation. This can further lead to erroneous estimations of the materials’ permeability (k) relation (permeability vs void ratio (k-e)) in the LSC analysis. This paper presents two modifications on two conventional equations for compressibility and permeability, respectively. The first one describes the compressibility curve’s movement in the lne-lnσv′ plane, and the other quantifies the ratio between the permeability calibrated by neglecting time-effect and its true value. These modifications originate from deep comparative analyses of several physical parameters between the column test and numerical prediction. Meanwhile, a simple hand-calculation procedure is proposed to estimate the new constants.

The present study consists of two parts. The first part supplies an exact semi-analytical solution for a general model of rigid plastic strain hardening material at large strains. The second part applies this solution to tube hydroforming design. The solution provides stress and velocity fields in a hollow cylinder subject to simultaneous expansion and elongation/contraction. No restriction is imposed on the hardening law. A numerical method is only required to evaluate ordinary integrals. The solution is facilitated using Lagrangian coordinates. The second part of the paper is regarded as an alternative to the finite element design of tube hydroforming processes, restricted to rather simple final shapes. An advantage of this approach is that the hardening law is not required for calculating many process parameters. Therefore, the corresponding design is universally valid for all strain hardening materials if these parameters are of concern. In particular, the prediction of fracture initiation at the outer surface is independent of the hardening law for widely used ductile fracture criteria. The inner pressure is the only essential process parameter whose value is controlled by the hardening law. [ABSTRACT FROM AUTHOR]

Prefabricated horizontal drain (PHD) assisted by vacuum pressure has been used in practice to accelerate the consolidation process of dredged soft mud. However, very few studies have investigated the large-strain nonlinear consolidation caused by vacuum-assisted PHD. Therefore, based on the piecewise-linear method, this study proposes a one-dimensional consolidation model (called VCS herein) for the soft soil consolidation induced by vacuum-assisted PHD. The proposed VCS model has the capability to consider the large strain, PHD assisted by time-dependent vacuum pressure, soil self-weight, time-dependent surcharge loading and nonlinear changes of the geotechnical parameters and is thus superior to the existing models in the literature. The VCS was validated by comparing with the analytical and semi-analytical solutions reported in the literature. In addition, model test of PHD-vacuum preloading consolidation was designed and performed to further verify the proposed model, and excellent agreement was observed. Based on this model, a parametric study was performed to investigate the effect of several relevant parameters on the vacuum preloading consolidation. Moreover, the differences between PHD-vacuum consolidation and PVD-vacuum radial consolidation were investigated. The results indicate that the initial soil height, vacuum pressure and boundary condition considerably influence the performance of vacuum preloading (e.g., time rate of consolidation and final settlement), whereas the time-dependent vacuum preloading affects only the time rate of the vacuum preloading consolidation and not the final settlement magnitude. For the same soil layer, the final settlement of PHD-vacuum consolidation and PVD-vacuum radial consolidation is relatively close. However, the consolidation rate of PHD-vacuum consolidation is obviously faster than that of PVD-vacuum consolidation. [ABSTRACT FROM AUTHOR]

The concept of representative directions allows for automatic generation of multi-axial constitutive equations, starting from simplified uni-axial material models. In this paper, a modification of the concept is considered suitable for the analysis of fibrous polymeric materials, which are anisotropic in the as-received state. The modification of the concept incorporates an orientation probability density function (OPDF), which explicitly accounts for the material anisotropy. Two versions of the concept are available. The first version utilizes the homogeneous distribution of the representative directions, with the entire anisotropy being contained in the weighting factors. The second encapsulates the anisotropy in the distribution of the representative directions. Due to its nature, the second version allows for a more efficient use of computational power. To promote this efficient version of the concept, we present new algorithms generating required sets of representative directions that match a given OPDF. These methods are based (i) on the minimization of a potential energy, (ii) on the equilibration method, and (iii) on the use of Voronoi cells. These three methods are tested and compared in terms of various OPDFs. The applicability of the computationally efficient modeling method to mechanical behavior of an anisotropic polymeric material is demonstrated. In particular, a calibration procedure is suggested for the practically important case when the OPDF is not known a-priori. [ABSTRACT FROM AUTHOR]

The use of prefabricated vertical drain (PVD) in conjunction with vacuum and heat preloading is an effective improvement approach for dredged marine slurry. Despite it being a typical large-strain thermal-hydro-mechanical (THM) problem, there is currently a lack of reliable large-strain analysis methods for this problem. This study therefore develops a large-strain radial consolidation model, considering a thermal elastoplastic constitutive model of soft clays, self-weight of dredged slurry, radial and vertical flows, nonlinear hydraulic conductivity, nonlinear compressibility during the consolidation process, heat conduction, and heat convection process. The modified alternative direction implicit (ADI) difference approach is used to solve the proposed model. The numerical algorithm is then verified by degraded verification with a well-established radial-large strain consolidation model. A laboratory experiment has been employed to show the effectiveness of the proposed model in predicting the consolidation behavior. A graphical user interface (GUI) has been programmed for potential users based on the proposed model and numerical algorithm. The results indicate that heat preloading improves the permeability of soil, resulting in a larger settlement of soil. Heat preloading serves as an effective method to enhance the efficiency of PVD. [ABSTRACT FROM AUTHOR]

In this paper, we use molecular dynamics (MD) simulations to investigate the origin of strain hardening in glassy polymers, with a particular focus on the influences of strain rate and temperature. We demonstrate that strain hardening in uniaxial tension arises from bond stretching and is relaxed by bond rotation, characterized by the evolution of dihedral angles. Based on this rotational relaxation, strain rate plays a role analogous to temperature, resulting in a steady state behavior in the hardening region identifiable by strain rate and temperature. Following these observations, we propose a constitutive model to describe the rate- and temperature-dependent strain hardening behavior of glassy polymers using a viscous potential as a function of strain rate. To capture the elastic and yield behavior at small strains, we integrate this viscous potential with a conventional elasto-viscoplastic (EVP) model, giving rise to our V-EVP model. The V-EVP model is shown to be thermodynamically consistent and is validated by comparison to MD simulation results of glassy polymers undergoing uniaxial tension tests across a broad range of temperatures and strain rates. • We addressed the physical origin of rate- and temperature-dependent strain hardening, • observed steady-state stress response in the hardening region, • proposed a new constitutive model framework for the steady-state hardening behavior. [ABSTRACT FROM AUTHOR]

This paper introduces a novel Smooth Particle Hydrodynamics (SPH) computational framework that incorporates an Arbitrary Lagrangian Eulerian (ALE) formalism, expressed through a system of first-order conservation laws. In addition to the standard material and spatial configurations, an additional (fixed) referential configuration is introduced. The ALE conservative framework is established based on the fundamental conservation principles, including mass, linear momentum and the first law of thermodynamics represented through entropy density. A key contribution of this work lies in the evaluation of the physical deformation gradient tensor, which measures deformation from material to spatial configuration through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both of the deformation tensors are obtained via additional first-order conservation equations. Interestingly, the new ALE conservative formulation will be shown to degenerate into alternative mixed systems of conservation laws for solid dynamics: particle-shifting, velocity-shifting and Eulerian formulations. The framework also considers path- and/or strain rate-dependent constitutive models, such as isothermal plasticity and thermo-visco-plasticity, by integrating evolution equations for internal state variables. Another contribution of this paper is the evaluation of ALE motion (known as smoothing procedure) by solving a conservation-type momentum equation. This procedure is indeed useful for maintaining a regular particle distribution and enhancing solution accuracy in regions characterised by large plastic flows. The hyperbolicity of the underlying system is ensured and accurate wave speed bounds in the context of ALE description are presented, crucial for ensuring the stability of explicit time integrators. For spatial discretisation, a Godunov-type SPH method is employed and adapted. To guarantee stability from the semi-discretisation standpoint, a carefully designed numerical stabilisation is introduced. The Lyapunov stability analysis is carried out by assessing the time rate of the Ballistic energy of the system, aiming to ensure non-negative entropy production. In order to ensure the global conservation of angular momentum, we employ a three-stage Runge–Kutta time integrator together with a discrete angular momentum projection algorithm. Finally, a range of three dimensional benchmark problems are examined to illustrate the robustness and applicability of the framework. The developed ALE SPH scheme outperforms the Total Lagrangian SPH framework, particularly excelling in capturing plasticity regimes with optimal computational efficiency. [Display omitted] • A new ALE SPH algorithm is introduced for the analysis of solid dynamics. • The ALE formulation degenerates into particle-shifting and velocity-shifting formulations. • The hyperbolicity of the system is exploited to ensure the stability of explicit time integrators. • A Godunov-type SPH method is proposed to ensure non-negative entropy production. • A simple projection technique is implemented to ensure total conservation of angular momentum. [ABSTRACT FROM AUTHOR]

Two different types of shear bands generate in ultrafine-grained (UFG) CoCrFeMnNi high-entropy alloys deformed at 77 K, i.e. commonly-observed low angle grain boundary (LAGB) type and unusual twin-coupled type. Twin-coupled shear bands exhibit a misorientation of 56–67° with the matrix, in contrast to the LAGB shear band with a misorientation of 6–12°. Both annealing twins and deformation twins can act as precursor for twin-coupled shear bands, where dislocation accumulation along twin boundaries can tune the orientation of twin lamella. These observations suggest that twin-coupled shear bands can act as an important plastic carrier in materials deformed under extreme conditions. Atomic structure of twin-coupled shear band is unveiled in an UFG CoCrFeMnNi HEA deformed at 77 K, which involves in dislocation-twin boundary coupled mechanism, based on delicate structural characterization via high resolution transmission electron microscopy. [ABSTRACT FROM AUTHOR]

Ultrasound elastography performed under small strain conditions has been intensively studied. However, small deformations may be not sufficiently large to differentiate some abnormal tissues. By combining quasi-static and shear wave elastography, we developed a non-invasive method to estimate the localized stress- strain curve of materials. This method exerts progressive multistep uniaxial compression on the materials, and shear wave measurements were performed at every compression step. This method estimates the 2-D displacements between steps via a 2-D region growing motion tracking method and accumulates these displacements to obtain the large material displacements with respect to the initial configuration. At each step, the shear modulus and stress were calculated according to linear elastic theory. The proposed method was tested on custom-made tissue-mimicking phantoms. Mechanical compression testing was conducted on the samples made of the same material as the phantoms and taken as the reference. The stress-strain curves for the same material from the proposed method and from mechanical testing are in good agreement. The root mean square error (RMSE) and area percentage error (APE) of the stress-strain curve between ultrasound measurement and mechanical testing for soft materials ranged from 0.18 to 0.26 kPa and from 5.6% to 7.8%, respectively. The RMSE and APE for stiff materials ranged from 0.56 to 1.17 kPa and 8.0% to 17.9%. Therefore, our method was able to provide good estimates of the stress-strain curve for tissue-mimicking materials. [ABSTRACT FROM AUTHOR]

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Transformation induced plasticity (TRIP) steels present a remarkable balance of strength and ductility. However, their post-necking hardening behavior, which is required for press-forming and automobile crash simulation, is unreliable because of their stress-triaxiality dependency. Therefore, we analyzed the stress-triaxiality hardening in the post-necking strain regions of tensile loaded TRIP steel to accurately evaluate the stress and strain distribution. Tensile tests were accordingly conducted on small, round-bar specimens to evaluate the true stress vs. cross-sectional reduction ratio curves up to fracture. Additionally, the stress distribution inside each specimen was measured using synchrotron X-ray diffraction. Using these measurements, the hardening law for the TRIP steel was identified through a series of finite element (FE) simulations, in which a simplified phenomenological strain and stress-triaxiality hardening were found to agree well with the measurements in the post-necking strain region. As a result, the hardening rate of the TRIP steel showed a sudden decrease at the uniform elongation limit strain. The FE simulations including stress-triaxiality hardening successfully reproduced this hardening behavior up to the fracture, and the FE simulation including stress-triaxiality hardening and its saturation presented values closest to the XRD measurements. This simulation also agreed well with the measurements obtained in the tensile direction away from the neck center. A microstructural analysis of the retained austenite at the neck supported this result. The FE simulations revealed that a combination of the TRIP effect and its deactivation accelerates the localized deformation at the specimen neck under tensile loading.

Prediction for self-weight consolidation of dredged sludge is important for its reuse in civil engineering applications. In this work, considering the special nonlinear relationships of e – k and e – σ′ for dredged sludge, Gibson's large strain consolidation equation was modified to simulate the self-weight consolidation process of dredged sludge. Using the finite difference method (FDM), the influences of four main parameters, including initial height, initial void ratio, void ratio at the liquid limit, and specific gravity of soil particles, on the consolidation process of dredged slurry were analyzed. For the aforementioned four parameters, the self-weight consolidation of dredged slurry is most sensitive to the variation of void ratio at the liquid limit, whereas its response to the change of specific gravity of soil particles is relatively subtle. Consolidation behaviors under other commonly used constitutive models were also calculated for comparison. It was found that the total settlement obtained by the present relation is larger than the results obtained using typical nonlinear constitutive relations, and the speed of consolidation is higher. [ABSTRACT FROM AUTHOR]

In the determination of full-range hardening curve with compression test, the influence of friction and the corresponding stress correction have always been an enormous challenge. In this study, a hyperbolic shaped specimen is designed to conduct compression test for the determination of hardening curve in large range of strains without the effect of friction. The associated stress correction method is firstly derived by performing a series of finite element simulations of compression tests using the proposed specimen with the hardening curves composed with different combinations of initial yield stresses and strain hardening exponents. Finally, the hardening curves of mild steel Q420 obtained from the compression test using the proposed specimen are implemented in the simulation and verified with experimental data. The results show that the hyperbolic shaped compression specimen can not only remove the undesirable effect of friction but also determine the hardening curve in large range of strains. The established stress correction method for the hyperbolic shaped compression specimen is solely dependent on the strain hardening exponent, which can provide accurate hardening curve merely based on the experimental measurement of load vs. displacement curve and radius of middle cross section. Moreover, the hyperbolic shaped compression specimen provides a feasible approach to determine the strain hardening exponent of material.

The need for mechanical metamaterials with large strain range and lightweight properties are evidenced to engineering applications. In this regard, novel helical structures are proposed as suitable unit cell’s components of mechanical metamaterials. Three-dimensional helical structures composed of varying coil numbers, defined in a cylindrical spatial domain are shape optimized through genetic algorithm in a finite element script for conflicting objectives of minimum mass and maximum tensile range. The superior performance of the shape optimized helical structure is highlighted in terms of structural rigidity, large deformation capability, buckling and vibrational modal analysis in compare to equivalent coil springs of identical weight and comparable domain. Deformation mechanism is analyzed carefully to justify the improved performances of proposed structure. Tensile and compressive experimental analysis are undertaken to validate the enhanced strain ranges. One dimensional metamaterials implementations with various tessellation arrangements are simulated. Results show that the proposed design can effectively generate lightweight substitutes of metamaterials unit cells ligaments to improve the strain range performance. Planar and lattice metamaterial concepts employing shape optimized helical structure are illustrated to demonstrate the possibilities of promoting lightweight structural integrities in the design of mechanical metamaterials.

Accurate and efficient estimation and prediction of the nonlinear behavior of materials during plastic working is a major issue in academic and industrial settings. Studies on property meta-models are being conducted to estimate and predict plastic working results. However, accurately representing strong nonlinear properties using power-law and exponential models, which are typical meta-models, is difficult. The combination meta-model can be used to solve this problem, but the possible number of parameters increases. This causes a cost problem when using FE simulation. In this study, the accuracy of the nonlinear properties of materials and the number of iterations were compared for three typical meta-models and the proposed advanced meta-models considering stress–strain properties. A material property test was conducted using ASTM E8/E8M, and the meta-model was initialized using ASTM E646 and MATLAB Curve Fitting Toolbox. A finite element (FE) simulation was conducted for the meta-models, and the test and simulation results were compared in terms of the engineering stress–strain curve and the root-mean-square error (RMSE). In addition, an inverse method was applied for the FE simulation to estimate the true stress–strain properties, and the results were analyzed in terms of the RMSE and the number of iterations and simulations. Finally, the need for an advanced meta-model that exhibits strong nonlinearity was suggested. [ABSTRACT FROM AUTHOR]

Transformation induced plasticity (TRIP) steels present a remarkable balance of strength and ductility. However, their post-necking hardening behavior, which is required for press-forming and automobile crash simulation, is unreliable because of their stress-triaxiality dependency. Therefore, we analyzed the stress-triaxiality hardening in the post-necking strain regions of tensile loaded TRIP steel to accurately evaluate the stress and strain distribution. Tensile tests were accordingly conducted on small, round-bar specimens to evaluate the true stress vs. cross-sectional reduction ratio curves up to fracture. Additionally, the stress distribution inside each specimen was measured using synchrotron X-ray diffraction. Using these measurements, the hardening law for the TRIP steel was identified through a series of finite element (FE) simulations, in which a simplified phenomenological strain and stress-triaxiality hardening were found to agree well with the measurements in the post-necking strain region. As a result, the hardening rate of the TRIP steel showed a sudden decrease at the uniform elongation limit strain. The FE simulations including stress-triaxiality hardening successfully reproduced this hardening behavior up to the fracture, and the FE simulation including stress-triaxiality hardening and its saturation presented values closest to the XRD measurements. This simulation also agreed well with the measurements obtained in the tensile direction away from the neck center. A microstructural analysis of the retained austenite at the neck supported this result. The FE simulations revealed that a combination of the TRIP effect and its deactivation accelerates the localized deformation at the specimen neck under tensile loading. [ABSTRACT FROM AUTHOR]

Soil structure is an important mechanics property which has drawn much attention from researchers. A piecewise‐linear numerical model, called SCS, is developed to investigate the large strain consolidation of structured soils. SCS accommodates large strain, soil self‐weight, vertical flows, time‐dependent loading, unloading/reloading, seepage force, soil heterogeneity, and soil structure. A three‐stage formulation is proposed to specify the compressibility behaviors of structured soils in SCS. The accuracy of SCS in the cases of small strain and large strain is checked comparing with analytical solutions and numerical solutions respectively. The effect of the main factors impacting soil structure on the consolidation processes of structured soils is investigated using several SCS simulations. Finally, a few SCS simulations with multiple structured soil layers are conducted. [ABSTRACT FROM AUTHOR]