Where \(k_{n}=\lambda+2\frac{\mu}{n}\) ,\(\left\langle a\right\rangle_{\pm}=\frac{1}{2}(a\pm\left|a\right|)\)and\(\mathbf{\varepsilon}_{\text{dev}}=\mathbf{\varepsilon}-\frac{\mathbf{1}}{\mathbf{3}}\text{tr}(\mathbf{\varepsilon})\mathbf{I}\)as well as the split based on the spectral decomposition of the strain
tensor\(\mathbf{\varepsilon}=\sum_{I=1}^{3}\left\langle\varepsilon_{I}\right\rangle\mathbf{n}_{I}{\bigotimes\mathbf{n}}_{I}\), where \(\left\{\mathbf{\varepsilon}_{I}\right\}_{I=1}^{3}\) and\(\left\{\mathbf{n}_{I}\right\}_{I=1}^{3}\) are the principal
strains and principal strain directions,
respectively8,9.\(\ \)In this
case,\(\ \mathbf{\varepsilon}_{\pm}=\sum_{I=1}^{3}\left\langle\varepsilon_{I}\right\rangle_{\pm}\mathbf{n}_{I}{\bigotimes\mathbf{n}}_{I}\)and, eventually,