Linear tet fem

Elastic Energy

WuKong implements StVK and Neohookean energy models

\[\begin{equation} E_{\mathrm{StVK}} = V \ \frac{\lambda}{2}||\mathrm{E}||^2 + \mu \text{tr}(\mathbf{E}) \ , \end{equation}\]

\[\begin{equation} E_{\mathrm{NH}} = V \ \frac{\mu}{2}( \text{tr}(\mathbf{F}^T)\mathbf{F} - 3.0 - 2.0 \log(\det(\mathbf{F}))) + \frac{\lambda}{2} \log(\det(\mathbf{F}))^2 \end{equation}\]

where \(\mathbf{F}\) is the deformation gradient, \(\mathbf{E}\) is Green strain, \(\lambda\) and \(\mu\) are Lame parameters, and \(V\) is the undeformed volume.