On The Role of the Eshelby Energy-Momentum Tensor in Materials with Multiple Natural Configurations

Abstract

We discuss the connection between two important parallel developments in continuum mechanics that has gone unnoticed despite intense activity in both these seemingly disparate areas: the first stems from the pioneering work of Eckart on the role of the evolution of “natural configurations” in the inelastic response of solids; the second stems from the seminal work of Eshelby concerning the energy-momentum tensor associated with the driving forces that arise as a consequence of inhomogeneities and defects during the deformations of solids. We show that a variety of driving forces manifest themselves as a consequence of the evolution of natural configurations, depending on the particular process under consideration. Our study makes it clear that no new balance laws need be invoked in order to accommodate such driving forces, the usual balances laws of mechanics being sufficient.