On thermodynamic extremal principles in gradient plasticity with energetic forces

Incremental energy minimization is revisited as a method of determining an incremental solution for rate-independent dissipative solids undergoing isothermal quasi-static deformation. The incremental minimization is applied to the total internal energy of the compound thermodynamic system that consists of a deforming body with internal variables, a conservative loading device, and an ambient heat reservoir. It is shown that the difference between the virtual and actual dissipation rates plays a fundamental role in this minimization, which is related to thermodynamic extremal principles of local and global type. The analysis is carried out within the gradient plasticity framework with the energetic forces derived as the variational derivative of the Helmholtz free energy depending on the spatial gradient of arbitrary internal variables. Specifications are given for existing models of gradient plasticity.

Automated summary

This study revisits incremental energy minimization as a method for determining an incremental solution for rate-independent dissipative solids undergoing isothermal quasi-static deformation. The analysis shows that the difference between virtual and actual dissipation rates is crucial in this minimization process, which is related to thermodynamic extremal principles. The study is conducted within the framework of gradient plasticity theory and existing models of gradient plasticity are specified.