Continual fracture of nonlinearly elastic bodies (Q758308)

A model of a medium is considered for which the development of microdefects, namely, microcracks, pores and intergrain vacancies, are substantial. Microdefect diffusion and polar phenomena are neglected. The approach used in this paper differs from the traditional approach in two main ways. Firstly, by the axiom of local energy balance and the inequality of dissipation. Following the mechanics of an isolated crack, a term describing the energy flux distributed over a volume that is related to transformation of part of the stored energy and the work of the stresses in the surface energy of the microcracks, is introduced into the local energy balance equation. The dissipation inequality differs from the Calusius-Duhem inequality by a component that is the dissipation of fracture. The second essential difference is the modification of the principle of macroscopic determinability. It is considered that the running reaction of a material element is a functional determined by the independent prehistories of the strain, entropy, and damage.