Quasi-incompressible finite elasticity in principal stretches. continuum basis and numerical algorithms

Abstract

The formulation and numerical analysis of constitutive equations for finite elasticity in terms of principal stretches is considered in detail. On the theoretical side, we develop closed-form expressions for the tangent moduli which appear not to have been previously recorded in full generality in the literature. Quasi-incompressible response is accounted for by means of a three-field variational principle which makes use of a multiplicative decomposition of the deformation gradient into volume preserving and dilatational parts. The incompressible limit is enforced by means of a simple and effective augmented Lagrangian procedure. Two possible implementations are discussed. Numerical examples are presented that illustrate the effectiveness of the proposed formulation.