On nonlocal gradient model of inelastuc heterogeneous media

The aim of this paper is to investigate the influence of nonlocality on the physical and material field equations of heterogeneous media. Taking into account that plastic deformations in metals or damage in brittle and ductile materials are governed by physical mechanisms observed on levels with different lengthscales, we introduce a 6-dimensional kinematical concept with two locally defined vectors to model the material behaviour on a macro- and meso- or microlevel.

Using a variational procedure the physical and material balance laws, boundary and transversality conditions are derived for macro- and microdeformations of heterogeneous media. The dissipation inequality including relaxation terms for transport processes is presented. The constitutive equations are formulated with macro- and microstrain measures, their gradients and time rates, and the anisotropy tensor as arguments, where the latter can be considered as a coupling measure between the deformed macrostates with compatible microstates.

The model presented in this paper delivers a framework, which enables one to derive various nonlocal and gradient theories by introducing simplifying assumptions. As the special case a solid-void model is considered.