Authors: Koffi Enakoutsa
Addresses: Center for Advanced Vehicular Systems, Mississippi State University, 200 Research Boulevard, Mississippi State, MS 39762, USA
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.
Keywords: principle of virtual work; micromorphic theory; ductile fracture; GLPD theory; virtual power; metals; Gologanu; Leblond; Perrin; Devaux; finite element method; FEM; pathological mesh size; numerical simulation; ductile rupture; circular bending; beam deformation; plane strain.
International Journal of Theoretical and Applied Multiscale Mechanics, 2013 Vol.2 No.4, pp.311 - 322
Received: 17 Jul 2013
Accepted: 24 Sep 2013
Published online: 31 May 2014 *