Nonholonomic elastoplastic analysis involving unilateral frictionless contact as a mixed complementarity problem

Abstract

This paper deals with the elastoplastic analysis of suitably discretized elastoplastic structures under frictionless unilateral contact conditions. Whilst the mathematical programming formulation we adopt can cater equally for hardening as well as softening path-dependent (nonholonomic) plasticity, the state problem involving softening is by far the more difficult to solve in view of the inherent nonconvex nature of the underlying mathematical program. We propose a novel description of a fairly general class of piecewise linear softening laws and investigate use of an approximate stepwise holonomic (path-independent) approach for capturing the evolution of the structure with softening and/or hardening constitutive laws. This finite-step problem is formulated in a specific way to take advantage of the use of a robust and industry-standard complementarity solver named PATH from within the GAMS modeling environment. We illustrate its application on truss-like structures.