Integrating a logarithmic-strain based hyperelastic formulation into a three-field mixed finite element formulation to deal with incompressibility in finite-strain elastoplasticity

This paper deals with the treatment of incompressibility in solid mechanics in finite-strain elastoplasticity. A finite-strain model proposed by Miehe, Apel and Lambrecht, which is based on a logarithmic strain measure and its work-conjugate stress tensor is chosen. Its main interest is that it allows for the adoption of standard constitutive models established in a small-strain framework. This model is extended to take into account the plastic incompressibility constraint intrinsically. In that purpose, an extension of this model to a three-field mixed finite element formulation is proposed, involving displacements, a strain variable and pressure as nodal variables with respect to standard finite element. Numerical examples of finite-strain problems are presented to assess the performance of the formulation. To conclude, an industrial case for which the classical under-integrated elements fail is considered.