An implicit integration scheme for generalized viscoplasticity with dynamic recovery

This paper is concerned with the development of a general implicit time-stepping integrator for the flow and evolution equations in a recent representative class of generalized viscoplastic models, involving both hardening and dynamic recovery mechanisms. To this end, the computational framework is developed on the basis of the unconditionally stable, backward Euler difference scheme. Its mathematical structure is of sufficient generality to allow a systematic treatment of several internal variables of the tensorial and scalar types. The matrix forms developed are directly applicable in general (three-dimensional) situations as well as subspace applications (i.e., plane stress/ strain, axisymmetric, generalized plane stress in shells). The closed-form expressions for residual vectors and the algorithmic, (consistent) material tangent stiffness array are given explicitly, with the maximum matrix sizes "optimized" to depend only on the number of independent stress components, but not the number of internal state variables involved. Several numerical simulations are given to assess the performance of the developed schemes.