This paper presents a novel micropolar-based hypoplastic model to reproduce the stress-strain relationship of face mask chips-sand mixtures (MSMs) and their localized deformation. Based on a critical state hypoplastic model, a non-polar hypoplastic model for MSMs is first developed with modifications and new features: (1) the cohesion induced by face mask chips is considered by introducing an additional stress tensor into the Cauchy stress tensor; (2) the initial stiffness variation in MSMs is described with a modified tangential modulus; and (3) the effective skeleton void ratio concept is introduced to capture the initial and critical void ratio variations in MSMs. The model is then extended to its micropolar terms by incorporating the micropolar theory, which includes an internal length parameter and a couple stress induced by particle rotation, with the advantage of overcoming the mesh dependency problem in the conventional finite element method (FEM) based simulations. Moreover, the new micropolar hypoplastic formulations are implemented into a FEM code. The onset and evolution of shear bands in MSMs are investigated by simulating a series of biaxial tests on both pure sand and MSMs. Numerical results are also compared to experimental observations, demonstrating that the developed micropolar hypoplastic model can adeptly capture the shear band propagation in MSMs and their mechanical responses.

Localized rock failures, like cracks or shear bands, demand specific attention in modeling for solids and structures. This is due to the uncertainty of conventional continuum-based mechanical models when localized inelastic deformation has emerged. In such scenarios, as macroscopic inelastic reactions are primarily influenced by deformation and microstructural alterations within the localized area, internal variables that signify these microstructural changes should be established within this zone. Thus, localized deformation characteristics of rocks are studied here by the preset angle shear experiment. A method based on shear displacement and shear stress differences is proposed to identify the compaction, yielding, and residual points for enhancing the model's effectiveness and minimizing subjective influences. Next, a mechanical model for the localized shear band is depicted as an elasto-plastic model outlining the stress-displacement relation across both sides of the shear band. Incorporating damage theory and an elasto-plastic model, a proposed damage model is introduced to replicate shear stressdisplacement responses and localized damage evolution in intact rocks experiencing shear failure. Subsequently, a novel nonlinear mathematical model based on modified logistic growth theory is proposed for depicting the shear band's damage evolution pattern. Thereafter, an innovative damage model is proposed to effectively encompass diverse rock material behaviors, including elasticity, plasticity, and softening behaviors. Ultimately, the effects of the preset angles, temperature, normal stresses and the residual shear strength are carefully discussed. This discovery enhances rock research in the proposed damage model, particularly regarding shear failure mode. (c) 2025 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/

An experimental study is made to understand the deformation characteristics and failure mechanism of sands subjected to severe plastic deformation in the ploughing model setup of in-plane orthogonal cutting. The cutting experiments were performed on sands over 3 orders of strain rates. High-speed imaging and concomitant image analysis were performed using the Particle Image Velocimetry algorithm to obtain the whole field velocity measurements of the material flow. The velocity field maps of the near tool tip region demonstrate a sharp change in the motion of sand particles along with the formation of a dead zone. The effective strain rate maps show regions of intense localized plastic deformation- termed shear bands. The inclination angle of these bands evolved periodically with time and showed a decreasing trend due to an increase in the surcharge and effective depth of cut. The morphology and overall characteristics of these mesoscale structures (shear bands) do not change significantly with strain rate. The cutting force signatures were oscillatory and suggested cyclic material softening (dilation)-hardening (compaction) ahead of the tool, which is also reflected in the periodic repositioning of shear bands. The limit equilibrium-based model was adequate to predict the tool-cutting forces well, even with the significant variation in strain rates.

This paper investigates shear banding as a possible failure mode for silt-clay transition soils under general three-dimensional stress conditions. Drained and undrained true triaxial tests with constant b values were performed on tall prismatic specimens of such soils with systematically varying silt contents. Based on the values of critical plastic hardening modulus, shear banding does not govern the strength characteristics of the soils for b values less than 0.2. For larger b values, shear band formation is essentially critical as it takes place in the hardening regime of the stress-strain curves prior to the smooth peak failure points. An increase in silt content appears to move the onset of shear banding to lower levels of shear in the stress-strain relations of the silt-clay transition soils. It is also demonstrated that a non- associated constitutive model with a single hardening law is capable of accurately predicting the onset of shear banding in normally consolidated silt-clay transition soils based on bifurcation theory. (c) 2024 Production and hosting by Elsevier B.V. on behalf of The Japanese Geotechnical Society. This is an open access article under the CC BY- NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Accurate simulation of laboratory undrained and cyclic triaxial tests on granular materials using the Discrete Element Method (DEM) is a crucial concern. The evolution of shear bands and non-uniform stress distribution, affected by the membrane boundary condition, can significantly impact the mechanical behavior of samples. In this work, the flexible membrane is simulated by using the Finite Element Method coupled with DEM. In addition, we introduce a hydro-mechanical coupling scheme with a compressible fluid to reproduce the different undrained laboratory tests by using the membrane boundary. The evolution of pore pressure is computed incrementally based on the variation of volumetric strain inside the sample. The results of the membrane boundary condition are compared with more classical DEM simulations such as rigid wall and periodic boundaries. The comparison at different scales reveals many differences, such as the initial anisotropic value for a given preparation procedure, fabric evolution, volumetric strain and the formation of shear bands. Notably, the flexible boundary exhibits more benefits and better aligns with experimental data. As for the undrained condition, the results of the membrane condition are compared with experimental data of Toyoura sand and rigid wall boundary with constant volume. Finally, stress heterogeneity during undrained monotonic and cyclic conditions using the membrane boundary is highlighted.

The present paper aims to compare the behaviour of dense granular soils inside and outside the Shear Band (SB) during the Plane Strain Compression (PSC) test using the Discrete Element Method (DEM). The flexible membrane in the PSC test was modelled by adopting a discrete element-finite difference (DEM-FDM) hybrid approach. In contrast with previous 2D studies, the present study employed 3D simulations to consider the effects of out-of-plane characteristics such as the intermediate principal stress. According to the findings, the minimum and intermediate principal stresses outside the SB were twice as high as those inside at the residual state. It was also found that mechanical coordination numbers and redundancy indexes both inside and outside the SB decreased up to the onset of the residual phase, with a higher reduction rate inside the SB. As far as fabric anisotropy is concerned, the degree of anisotropy increased both in and out the SB until the peak state, with a somewhat higher rate inside the SB. A further finding was that the distribution of normal contact forces outside the SB remained symmetrical around the vertical axis after shear banding, however, it became asymmetrical inside the SB.

To investigate the interaction mechanism between the sand-structure interface under cyclic loading, a series of cyclicdirect shear tests were conducted. These tests were designed with various surface roughness values represented by the jointroughness coefficient (JRC) of 0.4, 5.8, 9.5, 12.8, and 16.7, and normal stresses of 50, 100, 150, and 200 kPa. A 3D printerwas employed to accurately control the surface roughness and obtain concrete samples with varyingJRCvalues. The testresults were used to establish discrete element method models, which facilitated the analysis of the mesoscopic shearbehavior at the sand-structure interface during the cyclic direct shear process. The results revealed that the sand-concreteinterface demonstrated softening behavior. There is a critical value for the surface roughness corresponding to themaximum interface shear strength. The thickness of shear band, where the changes in porosity were concentrated within,increases with higher surface roughness and cycle number. The coordination number stabilizes after 80 cycles. Thedistributions of the contact normal direction and tangential contact force exhibited nearly isotropic characteristics aftercyclic loading. It was observed that surface roughness amplifies the deflection angle of the main axis in the normal contactforce distribution, while reducing that in the shear contact force distribution.

Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and concrete. In the Earth's crust, irreversible deformation can occur in brittle as well as in ductile regimes. Modeling of shear zones is essential in the geodynamic framework. Numerical modeling of strain localization remains challenging due to the non-linearity and multi-scale nature of the problem. We develop a numerical approach based on graphical processing units (GPU) to resolve the strain localization in two and three dimensions of a (visco)-hypoelastic-perfectly plastic medium. Our approach allows modeling both the compressible and incompressible visco-elasto-plastic flows. In contrast to symmetric shear bands frequently observed in the literature, we demonstrate that using sufficiently small strain or strain rate increments, a non-symmetric strain localization pattern is resolved in two- and three-dimensions, highlighting the importance of high spatial and temporal resolution. We show that elasto-plastic and visco-plastic models yield similar strain localization patterns for material properties relevant to applications in geodynamics. We achieve fast computations using three-dimensional high-resolution models involving more than 1.3 billion degrees of freedom. We propose a new physics-based approach explaining spontaneous stress drops in a deforming medium. Strain localization is the accumulation of strain in narrow regions of rocks and other materials like metals, soils, and concrete, occurring at different scales. The strength of most geomaterials, particularly rocks, is strongly pressure-dependent, with strength increasing with increasing pressure. We developed efficient numerical algorithms using High-Performance Computing (HPC) and graphical processing units (GPUs) to model strain localization in 2D and 3D for applications in geodynamics and earthquake physics. Unlike previous models, our method reveals non-symmetrical patterns by using very small strain increments, highlighting the need for high-detail modeling. We found that elasto-plastic and visco-plastic models show similar strain patterns for relevant materials. Our method also achieves fast, detailed computations with over 1.3 billion variables and offers a new explanation for sudden stress drops in deforming materials. We resolve material instability during deformation resulting in a non-symmetric pattern of strain localization We demonstrate the similarity in patterns of strain localization between frictional and time-dependent plasticity models We achieve fast numerical simulations in high-resolution model setups in three dimensions involving more than 500 million degrees of freedom

An important characteristic of some clays is their abundance of fissures. In the case study reported here, to investigate how the fissure inclination angle affects the deformation and strength of fissured clay, samples of undisturbed fissured clay with different inclination angles of its inherent fissures (0 degrees, 45 degrees, and 90 degrees) were subjected to consolidated undrained plane-strain shear tests using a true triaxial apparatus. Moreover, consolidated undrained triaxial tests were carried out on samples with the same inclination angles for comparison. The results showed that compared with the triaxial state, the degree of fissure influence on samples with different fissure angles is different under plane strain, which weakens the influence of the fissure inclination angle on the soil's mechanical behavior. Under the designed consolidation pressures, the peak stress of the 45 degrees fissured soil samples was the smallest, with a stress-strain curve that exhibits strain softening. The 0 degrees fissured soil samples exhibited the highest peak stress, with a stress-strain curve that exhibits strain hardening. The 90 degrees fissured soil samples fell in between, with a stress-strain curve that exhibits a relatively stable trend. The intermediate principal stress coefficient b-value showed different trends at different fissure angles, which also reflects the influence of fissure dip angle. According to the von Mises and Lade-Duncan strength criteria, the generalized plane-strain criterion for fissured soil was obtained. The dip angle of the shear band was calculated from Mohr-Coulomb theory, and the difference between the calculated and measured dip angles was found to be small.

Featured Application The failure analysis of soil in the field of geotechnical engineering.Abstract The localization of deformation in shear bands is a fundamental phenomenon in granular materials like soil. In this study, we focus on the characteristics of shear bands, particularly the size effect, by implementing biaxial discrete element method (DEM) modeling. Firstly, we describe the establishment of the biaxial experimental model with dense sands. Then, we implement analyses of specimens with different sizes and find that there is a clear size effect in the stress-strain curve after the peak strength point, and there is less of a size effect in the angle of the shear band; the angle is consistent with Arthur's theory. Finally, the reason for the size effect is analyzed using the width of the shear band and the porosity inside the shear band. As the specimen size increases, the ratio between the shear band area and the whole specimen decreases. This effect reduces as the isotropic confining stress increases. The difference in the proportion of the shear band area mainly causes the size effect that affects the specimen deformation characteristics. We also find that with the increase in isotropic confining stress, the type of shear band gradually changes from cross-type to single-type. Our study provides valuable insights into understanding the behavior of granular materials.