Configurational entropy, non-associativity and uniqueness in granular media

SummaryIt has long been recognized that fabric, i.e., the grain configuration in a domain, plays a significant role in the constitutive response of granular media. Here we establish that this effect has bearing on the suitability of non-associative plasticity laws that describe the observed deviation of the plastic strain rate, from the normal to the yield surface. It is known that when non-associated plasticity laws are used, uniqueness of the solution of the initial value problem cannot be proved.Here it is shown that the introduction of configurational entropy and temperature into the theory, gives rise to a thermodynamic framework, specifically athermoplastic potential, with respect to which the plasticity law is associative. However, the inelastic strain is the sum of a plastic and a configurational strain. While the plastic strain rate is still normal to the potential (yield) surface, the inelastic strain rate,which is what is measured in the laboratory, is not. It is further shown that despite the non-normality of the inelastic strain rate to the plastic potential surface, the solution of the coupled initial value — configurational diffusion problem is unique.In the process of development of the underlying configurational thermodynamics, the concept of configurational flux is introduced and a time indifferent configurational diffusion law is inferred on the basis of uniqueness requirements. Thus the foundation is laid for the mode of propagation of chaos in granular media.