Numerical limit analysis and plasticity criterion of a porous Coulomb material with elliptic cylindrical voids

Abstract

The paper is devoted to a numerical Limit Analysis of a hollow cylindrical model with a Coulomb solid matrix (of confocal boundaries) considered in the case of a generalized plane strain. To this end, the static approach of Pastor et al. (2008) [18] for Drucker-Prager materials is first extended to Coulomb problems. A new mixed-but rigorously kinematiccode is elaborated for Coulomb problems in the present case of symmetry, resulting also in a conic programming approach. Owing to the good conditioning of the resulting optimization problems, both methods give very close bounds by allowing highly refined meshes, as verified by comparing to existing exact solutions. In a second part, using the identity of Tresca (as special case of Coulomb) and von Mises materials in plane strain, the codes are used to assess the corresponding results of Mariani and Corigliano (2001) [13] and of [11] for circular and elliptic cylindrical voids in a von Mises matrix. Finally, the Coulomb problem is investigated, also in terms of projections on the coordinate planes of the principal macroscopic stresses.

Variational approach for nonsmooth elasto-plastic dynamics with contact and impacts

“…More recently, several methods of modern numerical optimization have been successfully used to solve elasto-plastic problems: sequential quadratic programming method (Wieners, 2007), complementarity problem solvers (Tangaramvong et al, 2012;Zheng et al, 2020), accelerated gradient algorithms (Kanno, 2016;Shimizu and Kanno, 2020). Limit and shakedown analyses are problems for which an optimization approach of plasticity is natural, using second order cone programming technique and quadratic optimisation (Bisbos et al, 2005;Delbecq et al, 1977;Makrodimopoulos and Martin, 2005a,b;Mercier, 1976;Pastor, Thoré, et al, 2008;Pastor, Pastor, et al, 2015). In (Krabbenhøft, Lyamin, Sloan, and Wriggers, 2007;Krabbenhøft, Lyamin, Hjiaj, et al, 2005), developments are carried out for Mohr-Coulomb yield criterion in the context of cone variational inequality, extending the pioneering works of Berga and De Saxcé (1994) and Hjiaj et al (2003).…”