INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS Int. J. Numer. Anal. Meth. Geomech. 2017; 00:1–38 Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nag Diffuse bifurcations engraving diverse shear bands in granular materials Yuki Yamakawa 1* , Kiyohiro Ikeda 1 , Isao Saiki 1 , Jacques Desrues 2 , Reiko J. Tanaka 3 1 Department of Civil and Environmental Engineering, Tohoku University, Sendai 980-8579, Japan 2 Laboratoire 3SR, Domaine Universitaire, BP53, 38041 Grenoble Cedex 9, France 3 Department of Bioengineering, Imperial College London, London SW7 2AZ, UK SUMMARY Shear bands with characteristic spatial patterns observed in an experiment for a cubic or parallelepiped specimen of dry dense sand were simulated by numerical bifurcation analysis using the Cam-clay plasticity model. By incorporating the subloading surface concept into the plasticity model, the model became capable of reproducing hardening/softening and contractive/dilative behavior observed in the experiment. The model was re-formulated to be compatible with the multiplicative hyperelasto-plasticity for finite strains. This enhanced constitutive model was implemented into a finite-element code reinforced by a stress updating algorithm based on the return-mapping scheme, and by an efficient numerical procedure to compute critical eigenvectors of elastoplastic tangent stiffness matrix at bifurcation points. The emergence of diamond-like and column-like diffuse bifurcation modes breaking uniformity of the materials, followed by the evolution of shear bands through strain localization, was observed in the analysis. In the bifurcation analysis of plane strain compression test, unexpected bifurcation modes, which break out-of-plane uniformity and lead to three-dimensional diamond-like patterns, were detected. Diffuse bifurcations, which are difficult to observe by experiments, have thus been found as a catalyst creating diverse shear band patterns. Copyright © 2017 John Wiley & Sons, Ltd. Received . . . KEY WORDS: Cam-clay plasticity; diffuse bifurcation; granular materials; shear bands; strain localization 1. INTRODUCTION Diverse geometrical patterns emerge in shear bands of granular materials. Figure 1, for example, shows shear bands on cubic sand specimens displaying apparent geometrical patterns [1]. Spatially- periodic hexagonal and stripe patterns on uniform granular materials have been observed and understood as a consequence of pattern formation [2, 3]. On the other hand, the direct bifurcating patterns of a cubic domain were obtained as † * Correspondence to: Department of Civil and Environmental Engineering, Tohoku University, Sendai 980-8579, Japan. E-mail: [email protected] † The symmetry of this domain with periodic boundaries was labeled by a group O(2)× O(2)× O(2) and possible direct and secondary bifurcating patterns of this domain were found in [4] by group-theoretic analysis [5, 6]. Copyright © 2017 John Wiley & Sons, Ltd. Prepared using nagauth.cls [Version: 2010/05/13 v2.00]
Diffuse bifurcations engraving diverse shear bands in granular materials
Jun 24, 2023
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