ABSTRACT

In order to derive a macroscopic (continuum) constitutive relation from the microscopic (contact) constitutive relation, a kinematic or static assumption is needed for the relation between contact quantities (relative displacement or force) and macroscopic quantities (strain or stress). In the literature one almost exclusively finds the uniform strain assumption for the relation between relative displacements and macroscopic strain. Results from two-dimensional Discrete Element simulations with a linear elastic contact constitutive relation and bonded contacts are used to investigate the validity of this assumption. It is found that the uniform strain assumption is only valid for very dense assemblies. Therefore, the uniform strain assumption is inadequate in general. Some alternative kinematic and static assumptions from the literature are reviewed.