Kinematic and static assumptions for homogenization in micromechanics of granular materials

A study is made of kinematic and static assumptions for homogenization in micromechanics of granular materials for two cases. The first case considered deals with the elastic behaviour of isotropic, two-dimensional assemblies with bonded contacts. Using a minimum potential energy principle and estimated particle displacement and rotation fields, upper bounds for the elastic moduli are obtained that are an improvement over those obtained from the uniform strain assumption. The estimated displacement and rotation fields are determined from an approximate, local equilibrium argument. The second, more general case considered deals with biaxial deformation of two-dimensional non-bonded, frictional assemblies. Static and kinematic homogenization assumptions lead to micromechanical expressions for the shear strength and the dilatancy rate in terms of contact quantities. These expressions show that the dilatancy rate is determined primarily by geometrical anisotropy.