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.
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