Finite element formulation for finite deformation, isotropic viscoplasticity theory based on overstress (FVBO)

Abstract

The isotropic, unified state variable theory based on overstress consisting of a flow law and two tensor-valued and two scalar-valued stress-like state variables is extended to finite deformation. To this end the Cauchy stress rate and the rates of the two tensor-valued state variables are interpreted as Eulerian tensors. Their objective rates are based on the recently proposed logarithmic spin [Acta Mech. 124 (1997) 89] and on the fact that the logarithmic integration of the rate of deformation tensor results in the Hencky strain [Acta Mech. 124 (1997) 89]. The rate of deformation is equal to the sum of the elastic (the rate form of Hooke's law) and the inelastic rate of deformation, which depends on the overstress. Computational procedures are derived for the one-step forward gradient and the backward Euler methods. Numerical experiments show that no oscillations are observed in simple shear and that the integration of the elastic rate of deformation exhibits proper elastic behavior. Other numerical experiments show nonlinear rate sensitivity and the absence of strain rate history effects.