Incremental shear strain chain: a mesoscale concept for slip lines in 2D granular materials

Constitutive behaviors of granular materials are driven by both particle interactions and geometric arrangements of contact network. To bridge the gap between the grain scale and the sample scale, the mesoscale is of great importance as it corresponds to the smallest scale at which geometrical effect can be accounted for. Meso shear structures (sometimes called microbands) have been observed frequently on incremental strain maps in granular materials under shearing, while the Rudnicki and Rice localization criterion for shear band is not fulfilled yet. These meso structures are thin, quasi-linear and they involve a few grains as well as their surrounding voids. This paper introduces the concept of “incremental shear strain chain” (simply called “shear chain”) to provide a specific quantitative definition of such mesostructures. “Shear chains” are defined based on incremental deviatoric strain fields in 2D biaxial simulations. Particular attention is paid to demonstrate that the shear chain orientation is a material scale property, insensitive to boundary conditions, loading paths and sample densities. Since shear chains are shown to be closely related to sliding mechanisms, they can stand for a mesoscale definition of the concept of slip lines as defined in the standard elasto-plasticity theory.