Modified Maximum Mechanical Dissipation Principle for Rate-Independent Metal Plasticity

The approach regarding the plastic process as a constrained optimization problem (Simo, J. C., and Hughes, T. J. R., 1998, Computational Inelasticity, Springer, New York) is discussed and found to be limited in considering nonlinear kinematic hardening and mechanical dissipation. These limitations are virtually common in elastoplastic modeling in both theoretical studies and industrial applications. A modified maximum mechanical dissipation principle is proposed to overcome the limitations and form an energy-based framework of nonlinear hardening laws. With the control functions introduced into the framework, not only are the relationships between existing hardening models clarified against their ad hoc origins, but modeling nonsaturating kinematic hardening behavior is also achieved. Numerical examples are presented to illustrate the capability of the nonsaturating kinematic hardening model to describe the phenomena of the permanent softening as well as the cyclic loading. These applications indicate the concept of the control function can be nontrivial in material modeling. Finally, the methodology is also extended to incorporate the multiterm approach.