A variational constitutive update algorithm for a set of isotropic hyperelastic–viscoplastic material models

In three-dimensional formulations of plasticity, the rate of plastic deformation is usually decomposed in direction and amplitude. In the most simple cases of von Mises type flows, this allows to assume a known radial flow direction and computations are reduced to the determination of the amplitude of the plastification. In the context of a variational formulation of finite plasticity, it is verified that this decomposition between constitutive and kinematic aspects is accomplished by the choice of a quadratic elastic potential (Hencky model). The aim of this paper is to show that a wide set of simple hyperelastic–plastic isotropic models not restricted to quadratic elastic behavior can be constructed by relaxing the classical decomposition amplitude/direction by the sum of spectral quantities. In addition, this approach allows for a unified and efficient numerical implementation in which a particular hyperelastic–viscoplastic behavior is obtained by a specific choice of the elastic, plastic and dissipative (pseudo)potentials.