Abstract
We use the method of virtual power to rigorously establish the balance equations and boundary conditions in the context of a micromorphic theory developed by Gologanu, Leblond, Perrin and Devaux (GLPD) to solve the pathological mesh size effects in numerical simulations of problems involving ductile rupture. As an example, we derive these equations for the problem of circular bending of a beam deformed in plane strain. Also, we provide links between the outcome of the method and the micromorphic theory of Germain. In particular, we show that, with a minor modification, the modified GLPD theory, which can easily fit into a finite element subroutine, is equivalent to Germain micromorphic theory. The paper ends with some comparisons with the general second gradient theory.
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