Question

The strain energy density U, volumetric strain energy density Uy, and distortional strain energy density Upare defined as: U=\left(\frac{1}{2}\right) \sigma_{i j} \epsilon_{i j} U_{V}=\left(\frac{1}{6}\right) \sigma_{k k} \epsilon_{p p} U_{D}=\left(\frac{1}{2}\right) s_{i

j} e_{i j} \text { where, } \epsilon_{i j}=\left(\frac{1}{F}\right)\left[(1+v) \sigma_{i j}-v \sigma_{k k} \delta_{i j}\right] \text { am and the terms } S_{i j} \text { and } e_{i j} \text { are the deviatoric part of } \text { stress and strain tensors defined as } S_{i j}=\sigma_{i j}-\left(\frac{1}{3}\right) \epsilon_{k k} \delta_{i j} \text { and } e_{i j}=\epsilon_{i j}-\left(\frac{1}{3}\right) \epsilon_{k k} \delta_{i j}

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