Sliding and rolling dissipation in Cosserat plasticity

Abstract

Based on micromechanical considerations at the level of grain contacts and taking into account the way in which kinematic and static quantities are "transported" between grain surface and grain centre, we identify appropriate measures related to energy dissipation due to rolling and sliding between grains, within both a discrete and a Cosserat continuum description. This allows us, within the framework of Cosserat plasticity, to identify appropriate invariants and formulate simple forms of the respective yield surfaces. The resulting model is shown to be a multiple-yield-surface generalisation of the model by Mühlhaus and Vardoulakis (Géotechnique, 1987). By introducing separate and clearly identified rolling-and sliding-resistance parameters, the model allows for separate activation of the respective dissipative mechanisms. Keywords Cosserat continuum • plasticity • granular micromechanics • sliding • rolling • energy dissipation 1 Introduction When describing a granular medium, we usually associate each particle with its centre. It is clear, however, that it is at the contacts between particles that all interesting phenomena take place. As stated by Cole & Peters [9] ".. . the relationship between the contact motions and resisting forces define the micro-scale properties of the medium". The contact between particles may include both sliding and rolling. Earlier studies of granular media silently assumed that almost all energy dissipation takes place at slid-ERC grant agreement n o 228051

Thermo‐poro‐mechanics of chemically active creeping faults: 3. The role of serpentinite in episodic tremor and slip sequences, and transition to chaos

“…When applied to geomaterials, localized failure is modeled as a discontinuity in the velocity field, requiring continuity of the stresses, revealing that shear zones appear as pairs and have a finite thickness d (Figure a). Within the framework of the solid mechanical instabilities, this thickness emerges as a solution depending on the microstructure [ Muhlhaus and Vardoulakis , ; Papanicolopulos and Veveakis , ], as well as the hydraulic and thermal ambient conditions [ Sulem et al , ; Veveakis et al , , ]. In the field, these solid mechanical failure instabilities extend the laboratory‐scale derivations of centimeter‐thick shear bands, appearing as meter‐wide fault zones [ Regenauer‐Lieb et al , ].…”

Discrete Element Modeling of a fault reveals that viscous rolling relaxation controls friction weakening

“…We are going to explore the influence of the rolling resistance model. Experimental results [25], [26], and numerical ones [27], [28], [29] have highlighted that grains rolling has a real impact on the sample behavior. A lot of rolling models have been formulated [30], [31].…”

“…As such, we introduce and explore the influence of the rolling resistance between grains to the macroscopic strength of a granular sheared layer. Experimental results [33,34], and numerical ones [35][36][37] have highlighted that grain rolling has a real impact on the sample behavior with many rolling models being formulated since [38,39]. In the literature the elastic-plastic spring dashpot model is identified as the benchmark for this response [40,41] and has been extended to conclude that: (i) rolling helps the formation of shear bands and decrease the sample strength [42][43][44][45];…”

Developments in micromechanical modelling of granular materials

“…Inspired by early discussions with Vardoulakis and his team, Alonso-Marroquin [2] presents a micromechanical derivation of the Cosserat continuum based on intra-granular stress, giving special emphasis to the asymmetry of stress, a favourite preoccupation of Vardoulakis. Papanicolopulos and Veveakis [3] contribute with a Cosserat-type plasticity theory, by integrating several ideas and concepts proposed by Vardoulakis: equivalent continuum, fabric averaging, and the energetics of rolling and sliding dissipation. Mühlhaus et al [4] develop a non-coaxial Cosserat continuum model based on a double-slip mechanism, a model that has interesting applications in describing deformation of the lithosphere.…”