Modeling isochoric and non-isochoric deformations in a polar elasto-plastic material

Abstract

In this article, the response of an interfacial layer developed along a particulate–continuum interface is explored under two opposite normal confining constraints. To this end, a cohesionless granular strip subjected to both isochoric and non-isochoric conditions is monotonously sheared against an adjacent wall of different surface roughness values. Numerical simulations are performed using a finite element method formulated within an elasto-plastic polar continuum, equipped by granular rotation, couple stress, and average grain size. Along the wall in motion, the slide and rotation resistance of the first layer of boundary grains are innovatively determined by the additional polar boundary conditions, taking into account a ratio between slip and granular rotation along the wall, asperities of wall surface, and grain size. In particular, the combined interaction of material dilatancy constraint and wall roughness are examined on the frictional resistance and deformation of the interfacial layer. It is shown that the normal confinement and the roughness geometry of the wall surface have visible impacts on the stress-displacement response of the interfacial layer. The evolution of stresses and couple stresses is entirely different in isochoric and non-isochoric conditions. However, the stationary value of the interfacial strength is independent of how the bounding wall confines the granular body. Besides, the deformations manifested out of the interfacial layer are more pronounced in isochoric shearing than non-isochoric shearing. Nevertheless, the location and progression of the interfacial layer do not necessarily depend on the applied confining constraint after large shearing.

Keywords:

• Surface asperity
• volumetric behavior
• isochoric condition
• non-isochoric condition
• granular rotation resistance
• updated Lagrangian formulation

Acknowledgments

The first author sincerely appreciates the Highest Prestigious Scientific and Professional National Foundation, Iran's National Elites Foundation (INEF), for its encouragement and moral support. The authors acknowledge editors and anonymous reviewers for their constructive comments and valuable suggestions that helped to improve the quality of the article.