| This thesis is dedicated to developing the computational procedures required in implementing the finite element method for finite deformation, rate-independent plasticity and finite deformation viscoplasticity theory based on overstress.; The classical rate-independent, von Mises plasticity is formulated using both hypoelastic-plastic model and hyperelastic-plastic model. In the hypoelastic-plastic model, a relationship between an objective rate of Kirchhoff stress, based on a new recently proposed logarithmic spin [13], and the elastic part of rate of deformation tensor is postulated. In the hyperelastic-plastic model, the deformation gradient is decomposed into elastic and plastic deformations, a relationship between Kirchhoff stress and the logarithm of the elastic left stretch tensor is used. Numerical procedures for the integration of both models are developed.; The isotropic, viscoplasticity theory based on overstress consisting of a flow law and two tensor valued and one 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. 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. The model does not contain a strain like quantity. Two integration schemes are considered: (i) a one step time integration scheme based on the forward gradient approximation and (ii) unconditionally stable implicit integration scheme based on backward Euler.; The finite deformation, anisotropic, viscoplasticity theory based on overstress is formulated. A hypoelastic relation between the Lagrangian, rotated, logarithmic Cauchy stress rate and the rotated rate of deformation is used. The deformation induced anisotropy is modeled using a compliance tensor that allowed to grow according to Armstrong-Frederick law for fourth order tensors that needs no further constants, except for a function that influences how quickly the compliance tensors grow. An implicit numerical integration scheme based on backward Euler is used. |
