Quantification of Numerical Stiffness for a Unified Viscoplastic Constitutive Model

Abstract

Here the question of numerical stiffness pertaining to a unified viscoplastic constitutive model is examined. The viewpoint maintained throughout this study is the state variable approach. Stiffness is quantified by examining, analytically, the eigenvalues of the associated Jacobian matrix. Specific results, in the form of stiffness contours, for the material parameters characterizing the copper alloy NARloy-Z are presented in the associated uniaxial state space. The results indicate that the potential for numerical stiffness does exist, however the severity is highly dependent upon the location of the state point within the state space. Finally a qualitative analogy between the maximum difference in stiffness indicating eigenvalues and the G vectors of the corresponding state space is suggested.