Implicit Integration and Consistent Tangent Stiffness of Cyclic Plastic Constitutive Models Based on a General Form of Strain Hardening and Dynamic Recovery. 2nd Report. Numerical Verification.

Abstract

This report deals with verification of the integration algorithm and consistent tangent modulus obtained in the 1st report for strain hardening and dynamic recovery based cyclic plasticity models. First, it is shown that the nonlinear scalar equation in the integration algorithm can be solved iteratively using successive substitution ; i. e., the Lipschitz constant in this successive substitution is determined and proved to satisfy the condition of convergence. Then, the results derived in the 1st report are coded in a user subroutine UMAT of a commercially available FEM software ABAQUS, and thus uniaxial tensile deformation and cyclic loading of a notched bar are analyzed. A linear combination of the Armstrong-Frederick rule and the Ohno-Wang rule is employed for the coding. It is shown that the iteration for solving the nonlinear scalar equation converges well, that the integration algorithm is stable and allows us to take large increments of strain, and that the consistent tangent modulus really sffords the parabolic convergence in solving the nonlinear equilibrium equation in FEM.