where \(\alpha\) is internal hardening variable, \(\sigma_{y}\) yield stress and \(h>0\) hardening modulus. In Eq. (13),\(\mathbf{\varepsilon}^{e}\) and \(\mathbf{\varepsilon}^{p}\) are respectively the elastic and the plastic strain tensors, which are assumed to additively contribute to the total strain,\(\mathbf{\varepsilon}=\mathbf{\varepsilon}^{e}+\mathbf{\varepsilon}^{p}\). The plastic strain,\(\mathbf{\varepsilon}^{p}\), and the hardening variable,\(\ \alpha\), take the internal (state) variables form.36
The free energy functional formulation suggested therein lean on the,22