Large Strain Elasto/Viscoplastic Constitutive Model. Theory And Numerical Scheme.

Abstract

In this paper an extension of a large strain elastoplastic constitutive model based on hyperelasticity and multiplicative decomposition of deformation gradient tensor due to García Garino is extended to viscous case following a previous work of Ponthot based on Perzyna type model. The integration of constitutive model is based on numerical scheme originally designed for the elastoplastic problem that naturally includes the rate dependent case. Consequently the algorithm proposed by Ponthot for viscoplasticity is easily taken into account in the framework of hyperelasticity and irreversible thermodynamics of solids. For the case of metals, a unified stress update algorithms for elastoplastic and elasto-viscoplastic constitutive equations submitted to large deformations is obtained. The plastic corrector step is, in case of J2 flow theory material behavior, an extension to the viscoplastic range of the classical radial return algorithm for plasticity. The resulting unified implicit algorithm is both efficient and very inexpensive. Moreover, if there is no viscosity effect (rate-independent material) the presented algorithm degenerates exactly into the classical radial return algorithm for plasticity.