External penalized mixed functional algorithms for unilateral contact and friction in a large strain finite element framework

Abstract

New contact boundary modelling is achieved with a basic set of 2 and 3 dimension contact primitives. Contact constraints are originally introduced in the variational equations and associated Newton—Raphson scheme via an external penalty formulation using primitive equations. Consequently, penalty part of external load vector and tangent stiffness matrices are developed for all contact primitives. In this way, contact prescribed boundary displacements are also taken into account. Contact treatment is then completed with Newton—Raphson elements for elastic and plastic regularized friction constitutive models. In this paper, the process is extended to elastoplastic models. Finally, we propose a self acting procedure with contact algorithms (interiority, sliding and contact loss) and related subroutines for implementation in finite element framework. We illustrate these developments by means of two‐dimensional open die forging and three‐dimensional plate coining typical benchmarks with reference to bulk elastoplastic and viscoplastic constitutive models.