New sights in crenulation geometry developed in anisotropic materials undergoing simple shear deformation

<p>Deformation of foliated rocks commonly leads to crenulation or micro-folding, with the development of cleavage domains and microlithons. We here consider the effect of mechanical anisotropy due to a crystallographic preferred orientation (CPO) that defines the foliation, for example by of alignment of micas. Mechanical anisotropy enhances shear localisation (Ran, et al., 2018; de Riese et al., 2019), resulting in low-strain domains (microlithons) and high-strain shear bands or cleavage domains. We investigate the crenulation patterns that result from moderate strain simple shear deformation, varying the initial orientation of the mechanical anisotropy relative to the shear plane.  </p><p>We use the Viscoplastic Full-Field Transform (VPFFT) crystal plasticity code coupled with the modelling platform ELLE (http://www.elle.ws; Llorens et al., 2017) to simulate the deformation of anisotropic single-phase material with an initial given CPO in dextral simple shear in low to medium strain. Deformation is assumed to be accommodated by glide along the basal, prismatic and pyramidal slip systems of a hexagonal model mineral. An approximately transverse anisotropy is achieved by assigning a small critical resolved shear stress to the basal plane. An initially point-maximum CPO at variable angles to the shear plane defines the initial straight foliation at different angles to the shear plane, limiting ourselves to orientations in which the foliation is in the stretching field. The resulting crenulation geometries strongly depend on the orientation of the foliation and we observe four types of localisation behaviour: (1) synthetic shear bands, (2) antithetic shear bands, (3) initial formation of antithetic shear bands and subsequent development of synthetic shear bands, and (4) distributed, approximately shear-margin parallel strain localisation, but no distinct shear bands.</p><p>The numerical simulations not only show the evolving strain-rate field, but also the predicted finite strain pattern of existing visible foliations. We show the results for layers parallel to the foliation, but also cases where the visible layering is at an angle to the mechanical anisotropy (e.g. in case of distinct sedimentary layers and a cleavage that controls the mechanical anisotropy). A wide range of crenulation types form as a function of the initial orientation of the visible layering and mechanical anisotropy (comparable to C, C' and C'' shear bands and compressional crenulation cleavage). Most importantly, some of may be highly misleading and may easily be interpreted as indicating the opposite sense of shear.</p><p>Reference</p><p>de Riese, T., et al. (2019). Shear localisation in anisotropic, non-linear viscous materials that develop a CPO: A numerical study. Journal of Structural Geology, 124, 81-90. DOI: 10.1016/j.jsg.2019.03.006</p><p>Llorens, M.-G., et al. (2017). Dynamic recrystallisation during deformation of polycrystalline ice: insights from numerical simulations. Philosophical Transactions of the Royal Society A, Special Issue on Microdynamics of Ice, 375: 20150346. DOI: 10.1098/rsta.2015.0346.</p><p>Ran, H., et al. (2018). Time for anisotropy: The significance of mechanical anisotropy for the development of deformation structures. Journal of Structural Geology, 125, 41-47. DOI: 10.1016/j.jsg.2018.04.019</p>

Influence of initial preferred orientations on strain localisation and fold patterns in non-linear viscous anisotropic materials

<p>Deformation localisation in rocks can lead to a variety of structures, such as shear zones and shear bands that can range from grain to crustal scale, from discrete and isolated zones to anastomosing networks. The heterogeneous strain field can furthermore result in a wide range of highly diverse fold geometries.</p><p>We present a series of numerical simulations of the simple-shear deformation of an intrinsically anisotropic non-linear viscous material with a single maximum crystal preferred orientation (CPO) in dextral simple shear. We use the Viscoplastic Full-Field Transform (VPFFT) crystal plasticity code (e.g. Lebensohn & Rollett, 2020) coupled with the modelling platform ELLE (http://elle.ws) to achieve very high strains. The VPFFT-approach simulates viscoplastic deformation by dislocation glide, taking into account the different available slip systems and their critical resolved shear stresses. The approach is well suited for strongly non-linear anisotropic materials (de Riese et al., 2019). We vary the anisotropic behaviour of the material from isotropic to highly anisotropic (according to the relative critical resolved shear stress required to activate the different slip systems), as well as the orientation of the initial single maximum orientation, which we vary from parallel to perpendicular to the shear plane. To visualize deformation structures, we use passive markers, for which we also systematically vary the initial orientation.</p><p>At relatively low strains the amount of strain rate localisation and resulting deformation structures highly depend on the initial single maximum orientation in the material in all anisotropic models. Three regimes can be recognised: distributed shear localisation, synthetic shear bands and antithetic shear bands. However, at very high strains localisation behaviour always tends to converge to a similar state, independent of the initial orientation of the anisotropy.</p><p>In rocks, shear localisation is often detected by the deflection and/or folding of layers, which may be parallel to the anisotropy (e.g. cleavage formed by aligned mica), or by deflection/deformation of passive layering, such as original sedimentary layers. The resulting fold patterns vary strongly, depending on the original orientation of layering relative to the deformation field. This can even result in misleading structures that seem to indicate the opposite sense of shear. Most distinct deformation structures tend to form when the layering is originally parallel to the shear plane.</p><p> </p><p>de Riese, T., Evans, L., Gomez-Rivas, E., Griera, A., Lebensohn, R.A., Llorens, M.-G., Ran, H., Sachau, T., Weikusat, I., Bons, P.D. 2019. Shear localisation in anisotropic, non-linear viscous materials that develop a CPO: A numerical study. J. Struct. Geol. 124, 81-90.</p><p>Lebensohn, R.A., Rollett, A.D. 2020. Spectral methods for full-field micromechanical modelling of polycrystalline materials. Computational Mat. Sci. 173, 109336.</p>

Prediction of Shear Localisation in Granular Materials based on a Critical State Non-coaxial Model

Experimental evidence indicates that the shear localisation acts as a precursor to the failure in biaxial compression tests of granular materials. Once formed they are persistent and lead to progressive failure of most geotechnical structures. It is generally accepted that the primary mode of deformation within these shear bands is simple shear which is accompanied by rotation of principal axes. Hence, the conventional plasticity theories based on the assumption of coaxility is not sufficient to describe the behaviour within those shear bands. This paper highlights the influence of the non-coaxility on the initiation and orientation of shear bands in both drained and undrained sand. The con-coaxial plasticity theory is integrated into a critical state constitutive model enriched with the state parameter concept. The model is capable of taking account of the variation of lode angle under plane strain condition. Numerical plane strain biaxial compression tests are conducted to observe the effect of non-coaxility on shear localisation. Bifurcation criteria based on the acoustic tensor are checked to predict the onset and inclination of the shear band. Predictions from the non-coaxial model are compared with those of coaxial model. The influence of the initial void ratio for the formation of shear bands is explored. Results are compared qualitatively with experimental observations.