Numerical simulation of finite strain viscoplastic problems

A large strain elastoplastic constitutive model based on hyperelasticity and multiplicative
decomposition of deformation gradient tensor is extended to viscous case, in a framework
similar to the one that has been proposed by Ponthot in an hypoelastic context. In this way
a very useful framework can be obtained, able to deal with both rate dependent and rate
independent problems.
In this work a review of theoretical details and numerical implementation of the model
are discussed. Similarly to what is done in rate independent plasticity, a Newton–Raphson
scheme has been used to solve the non linear consistency condition in order to compute
the viscoplastic multiplier.
A plane strain plate with a central circular hole under tension is simulated in order to
test the proposed model. Large deformation effects are considered in all the simulations
carried out. Different parameters of the constitutive model are varied in order to study the
sensitivity of the proposed algorithm.