ひずみ硬化/動的回復の一般形に基づく繰返し塑性構成式の陰的積分およびコンシステント接線剛性 : (第2報, 数値的検証)

抄録

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.