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A severe, spurious dependence of numerical simulations on the mesh size and orientation can be observed in elasto-plastic models with a non-associated flow rule. This is due to the loss of ellipticity and may also cause a divergence in the incremental-iterative solution procedure. This paper first analyses the dependence of the shear band inclination in a biaxial test on the mesh size as well as on the mesh orientation. Next, a Cosserat continuum model, which has been employed successfully for strain-softening plasticity, is proposed to prevent loss of ellipticity. Now, numerical solutions result for shear band formation which are independent of the size and the orientation of the discretisation. [ABSTRACT FROM AUTHOR]

The paper addresses the numerical simulation of strain localisation in stiff clays that exhibit softening behaviour. An elastoplastic constitutive model developed to incorporate key features of stiff clay behaviour is described first. A non-local formulation is then introduced for the regularisation of the analysis of localisation. A series of analyses were conducted to explore relevant aspects of the numerical simulation of localisation. A 3D analysis was also performed to assess the suitability of the approach presented for 3D applications. Finally, application to the simulation of a laboratory test on Beaucaire marl results in an excellent reproduction of experimental observations. [ABSTRACT FROM AUTHOR]

Sedimentary geomaterials such as rocks frequently exhibit cross-anisotropic properties and their behaviour depends on the direction of loading with respect to their microstructure. As far as material rupture is concerned, localised deformation in shear band mode appears generally before cracks and material failure. The influence of cross-anisotropy on the shear strain localisation remains an important issue and is investigated in the present study. To do so, a constitutive elastoplastic cross-anisotropic model that includes anisotropy both on the elastic and plastic characteristics is defined. For the plastic part of the model, the anisotropy of a strength parameter is introduced with a microstructure fabric tensor. Then, the fractures are modelled with finite element methods by considering the development of shear strain localisation bands and an enriched model is used to properly reproduce the shear banding. The cross-anisotropy influence on shear banding is studied through numerical applications of small and large-scale geotechnical problems that engender fractures. The two considered applications are a plane-strain biaxial compression test and an underground gallery excavation. The numerical results provide information about the influence of cross-anisotropy on the appearance and development of shear bands. It has been noticed, among other observations, that the material strength vary with the loading direction and that the development and the shape of the excavation fractured zone that develops around a gallery is strongly influenced by the material anisotropy. [ABSTRACT FROM AUTHOR]

The occurrence of large landslides in sensitive clays, such as spreads, can be modelled by progressive development of large inelastic shear deformation zones (shear bands). The main objective of the present study is to perform large deformation finite-element modelling of sensitive clay slopes to simulate progressive failure and dislocation of failed soil mass using the coupled Eulerian Lagrangian (CEL) approach available in Abaqus finite-element software. The degradation of undrained shear strength with plastic shear strain (strain-softening) is implemented in Abaqus CEL, which is then used to simulate the initiation and propagation of shear bands due to river bank erosion. The formation of horsts and grabens and dislocation of soil masses that lead to large-scale landslides are simulated. This finite-element model explains the displacements of different blocks in the failed soil mass and also the remoulding of soil around the shear bands. The main advantages of the present finite-element model over other numerical models available in the literature are that it can simulate the whole process of progressive failure leading to spread. The finite-element results are consistent with previous conceptual models proposed from field observations. The parametric study shows that, depending upon geometry and soil properties, toe erosion could cause three types of shear band formation: () only a horizontal shear band without any global failure; () global failure of only one block of soil; () global failure of multiple blocks of soil in the form of horsts and grabens. [ABSTRACT FROM AUTHOR]

This paper presents a multiscale investigation on the interplay among inherent anisotropy, fabric evolution and strain localisation in granular soils, based on a hierarchical multiscale framework with rigorous coupling of the finite-element method (FEM) and discrete-element method (DEM). DEM assemblies with elongated particles are generated to simulate inherent anisotropy and are embedded to the Gauss points of the FEM mesh to derive the required constitutive relation. Specimens prepared with different bedding plane angles are subjected to biaxial shear under either smooth or rough loading platens. Key factors and physical mechanisms contributing towards the occurrence and development of strain localisation are examined. The competing evolutions of two sources of anisotropy, one related to particle orientations and the other related to contact normals, are found to underpin the development of the shear band. A single band pattern is observed under smooth boundary conditions, and its orientation relative to the bedding plane depends critically on the relative dominance between the two anisotropies. Under rough boundary conditions, the non-coaxial material response and the boundary constraint jointly lead to cross-shaped double shear bands. The multiscale simulations indicate that the DEM assemblies inside the shear band(s) undergo extensive shearing, fabric evolution and particle rotation, and may reach the critical state, while those located outside the shear band(s) experience mild loading followed by unloading. The particle-orientation-based fabric anisotropy needs significantly larger shear and dilation for mobilisation than the contact-normal based one. The asynchrony in evolution of the two fabric anisotropies can cause non-coaxial responses for initially coaxial packings, which directly triggers strain localisation. [ABSTRACT FROM AUTHOR]

[Display omitted] • Microstructurally small fatigue crack growth (FCG) rate is studied by DIC. • FCG rate retardation is associated with shear strain localisations. • Grain boundaries control interaction between strain localization and FCG. • Shear strain localisations lead to formation of grain sub-structures. • Intense cross slip facilitates the overcoming of the strain localisation zone. Microstructurally small fatigue crack growth (FCG) rate in body-centred cubic (BCC) ferritic stainless steel is investigated by using a novel domain misorientation approach for EBSD microstructural deformation analyses, in conjunction with in situ digital imaging correlation (DIC). The DIC analyses revealed that shear strain localisations occur ahead of the crack tip during propagation and correlate well with the FCG rate retardations. Grain boundaries can be found at both peaks and valleys of the FCG rate curve and alter the interaction between crack growth and shear strain localisations. At the microstructural level, the deformation is associated with the dislocation-mediated plastic deformation process, showing increased formation of grain sub-structures in the regions of the strain localisation. Consequently, material experiences local hardening causing the FCG retardation events. If the crack avoids the hardened material region through a macroscopic cross-slip mechanism, retardation is minor. On the contrary, if the crack penetrates the hardened region, retardation is significant. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this study was to investigate mechanisms of progressive shear surface development using a series of specialised triaxial cell tests. Intact and remoulded samples of Gault Clay from the Ventnor Undercliff on the Isle of Wight in southern England were subjected to pore pressure reinflation (PPR) testing in a triaxial cell, in which failure is generated by increasing pore pressure under a constant total stress state. In addition, a novel very long term (>500days) creep test was undertaken, in which the sample eventually failed at a constant stress state below the failure envelope. The experiments showed that undisturbed samples of the Gault Clay failed in a brittle manner, generating a linear trend when plotted using the Saito technique. On the other hand, remoulded samples showed ductile behaviour, as indicated by a non-linear Saito trend. A number of otherwise identical PPR tests were conducted in which the rate of increase in pore water pressure was varied. These tests showed that strain rate generated at any point in the PPR tests depended on both the effective stress and the rate of change of effective stress. The latter is important because a change in stress generates a change in strain. Thus, whilst tests at different rates of change of effective stress are similar when plotted in q–p′ space and in strain–p′ space, they are markedly different in strain rate–p′ space. The long term creep test failed when the stress state had been constant for over 80days. This mechanism was reminiscent of creep rupture, occurring below the failure envelope defined in the conventional experiments. We conclude that first time failure in the Gault Clay is a progressive mechanism dominated by the development of micro-cracking, which leads to strain localisation and the development of one or more shear surfaces at failure. Whilst this mechanism may usually occur in response to a change in stress, the study indicates that failure can develop progressively. In the remoulded Gault Clay shear strains cannot localise along a singular shear surface. The results provide new insight into the mechanisms of landslide movement operating within the Ventnor landslide complex and indicate that present movements are likely to be occurring on a pre-existing shear surface. The lab tests suggest that this material is unlikely to undergo catastrophic failure. [Copyright &y& Elsevier]

Abstract: Microstructural deformation mechanisms in adiabatic shear bands in Ti6Al4V are studied using traditional TEM and selected area diffraction, and more advanced microstructural characterisation techniques such as energy dispersive X-ray spectroscopy, high angle annular dark field STEM and conical dark field TEM. The shear bands under investigation are induced in Ti6Al4V samples by high strain rate compression of cylindrical and hat-shaped specimens in a split Hopkinson pressure bar setup. Samples from experiments interrupted at different levels of deformation are used to study the evolution of the microstructure in and nearby the shear bands. From the early stages of adiabatic shear band formation, TEM revealed strongly elongated equiaxed grains in the shear band. These band-like grains become narrower towards the centre of the band and start to fraction even further along their elongated direction to finally result in a nano-crystalline region in the core. In fully developed shear bands, twins and a needle-like martensite morphology are observed near the shear band. [Copyright &y& Elsevier]

The numerical challenges that arise in modelling shear bands in soft sensitive (SS) clays have not yet been fully resolved. Convincing and well-accepted solutions have yet to be found. This paper presents some novel information related to the shear band phenomenon in SS clays. In this study, the hypothesis is that the generation and dissipation of excess pore pressure from shear bands could regularise the strain softening and result in a mesh independent shear band thickness. The generation and dissipation of excess pressure is modelled by a coupled consolidation process. The simulation aims at modelling two counteracting mechanisms in the SS clay. First, the shear band narrows because of strain softening. Second, the internal pore water pressure drainage reduces the rate of strain softening. This counteracting mechanism provides an inherent regularisation technique for SS clays. This study presents some numerical results involving these two counteracting mechanisms. This study also shows that an inherent internal parameter applicable for SS clays can be defined by the ratio between soil permeability and the applied strain rate. In the case of SS clays, the range of this parameter varies from 0 to 0.0002 mm. [ABSTRACT FROM AUTHOR]

Precise knowledge of the post-peak constitutive response occurring within shear bands in sands is of keen interest in geomechanics, particularly for accurate modelling of progressive failure phenomena. There is mounting evidence that the displacement field within shear bands in sands is non-uniform and distinguished by distinct meso-scale features: namely, particle force chains. Experimental validation of such features will help elucidate the precise nature of the deformation field within shear bands. This paper presents experimental evidence of the kinematic signatures of force chain activity within shear bands in sands. The meso-scale kinematics are quantified from digital-image-correlation-based, grain-scale displacement analyses performed on digital images of specimens undergoing plane strain compression. As in previous work, the data reveal distinct, systematic patterns in the kinematics along the length of the shear band, which serve as indirect evidence of force chain build-up and collapse. Herein, local volume changes are shown to integrate into this pattern. Temporal changes in these patterns with the progress of deformation are also tracked. It is argued that the changes observed in the kinematics from softening to critical state provide a physical, meso-scale explanation for the progress of global stress-strain response through the post-peak regime. [ABSTRACT FROM AUTHOR]

The paper presents a quantitative assessment of particle orientation, contacts and spatial variation of void ratio in a sand specimen loaded under plane-strain conditions. The specimen has a prismatic shape, and measures 57 mm wide × 121 mm long × 180 mm high. It was prepared using a dry natural silica sand known as F-75 Ottawa sand at a dense packing, and was sheared until failure. The specimen failed along a well-defined single shear band. It was then stabilised by slowly percolating a low-viscosity epoxy. Cylindrical subsamples 8 mm in diameter and 50 mm high were cored from the stabilised specimen at regions of interest for further investigation. A synchrotron X-ray microtomography technique was used to acquire high-resolution three-dimensional images of the cores. The scans have a voxel size of 15·06 m, which is high enough to visualise individual sand particles. Post-scanning analyses included mapping the spatial distribution of void ratio and particle contacts inside and outside the shear band. A good correlation was found between void ratio and particle contacts. Statistical distributions of particle orientation within and outside the shear band were calculated: they show that most particles inside the shear band orient in the - plane towards the -axis, which is perpendicular to the shear band with angle in the range 70-90°. Particles outside the shear band have no preferred orientation in the - plane, and form chains with preferred angles of 30-60° from the direction of the applied major principal stress. [ABSTRACT FROM AUTHOR]

A detailed study of spatial variation of void ratio and shear band thickness measurements is presented in this paper. A prismatic sand specimen that initially measured 57·4 mm wide × 120·5 mm long × 182·1 mm high was sheared under plane-strain (biaxial) loading conditions. The specimen was prepared at a relative density of 79% using F-75 Ottawa sand. X-ray computed tomography was used to scan the specimen before shearing and after the onset of the shear band. The specimen failed through a single shear band with an inclination angle of 65·6° measured from the direction of the minor principal stress. Computer algorithms were developed to calibrate CT images and quantify void ratio (e) variation within the specimen. CT data analysis revealed cross-sectional spatial variation in void ratio where density is higher in regions close to the edges of the specimen due to membrane effects and confining pressure with no significant variation in void ratio in the axial direction (top to bottom) before shearing. The shear band was easily identified from the CT images, and analysis of void ratio showed a noticeable jump in void ratio profile across the shear band. A detailed statistical summary of the thickness of the shear band and variation of void ratio across the shear band is presented and discussed. [ABSTRACT FROM AUTHOR]

Laboratory tests on samples of sand typically show instabilities in response related to shear band nucleation and evolution. Influences of constitutive characteristics (for instance, plastically driven elastic anisotropy), sensitivity to changes in constitutive parameters, and effects of testing conditions (for instance, related to stress conditions or to membrane penetration or stretching) on different types of material instability occurring in the post-localisation behaviour of sand specimens are investigated. Comparison between model prediction and available experiments shows that certain constitutive and testing features, which do not much influence the global response of a sample, may nevertheless strongly affect the critical and post-critical behaviours. The results obtained show that the proposed approach is general enough to permit the investigation of effects of experimental features that have not previously been studied. [ABSTRACT FROM AUTHOR]