Toward a Complete Second-Order Evolution Law

Abstract

Material evolution laws, such as those implicit in theories of plasticity and growth, are subjected to a systematic treatment. Using some concepts borrowed from the theory of inhomogeneities, the evolution of the material structure for materials of first and second order is expressed in terms of first-order differential equations for a set of "transplant" maps. A number of formal restrictions are derived, including those arising from material symmetries, and the results are applied to the specific case of a material whose second-order nature is limited to a dependence on the spatial gradient of the density. Firstand second-order Eshelby tensors are used as possible sources of the evolution.