Analysis of dilatancy relation and shear‐band formation in granular materials based on Eshelby‐Mandel tensor

The theory of configurational or material forces based on the Eshelby stress tensor (also called energy-momentum tensor) has provided a general and efficient way to describe motion defects other inhomogeneities within framework continuum mechanics. In this paper, we explore how use behavior homogeneous granular materials by considering characteristics both discrete particle levels. particular, dissipative driving Eshelby-Mandel are utilized as force configuration variations in form shear-induced volume change. energy dissipation induced relative sliding at contacts is considered forces. To characterize dilation with uniform deformation, virtual plane introduced facilitate analysis derive dilatancy formulation. With consideration shear-band geometry requirement equilibrium across boundary shear-band, condition for onset shear band derived. For specimens subjected biaxial compression, analyses recover well-known Rowe's formulation yield orientation identical that obtained from classical bifurcation elasto-plasticity.