Finite Elasticity Solutions Using Hybrid Finite Elements Based on a Complementary Energy Principle

Abstract

The possibility of deriving a complementary energy principle, for the incremental analysis of finite deformations of nonlinear-elastic solids, in terms of incremental Piola-Lagrange (unsymmetric) stress alone, is examined. A new incremental hybrid stress finite-element model, based on an incremental complementary energy principle involving both the incremental Piola-Lagrange stress, and an incremental rotation tensor which leads to discretization of rotational equilibrium equations, is presented. An application of this new method to the finite strain analysis of a compressible nonlinear-elastic solid is included, and the numerical results are discussed.