\[\mathbf{FEA} \to \mathbf{PFC(Hydroelastic Contact)}\]

PFC1 implementation2

fast tet-tet intersections

contact abstraction (patches, not points!)

offline + online

Contact problem with contact point $f_n=\left(-k \phi-d v_n\right)_{+}$:

\[\begin{array}{ll} \mathbf{M}_0\left(\mathbf{v}-\mathbf{v}_0\right)=\delta t \mathbf{k}_0+\delta t \mathbf{J}_0^T \mathbf{f}, & \\ 0 \leq \phi_{0, i}+\left(\delta t+d_i c_i\right) v_{n, i}+c_i f_{n, i} \\ \quad \perp f_{n, i} \geq 0, & i \in \mathscr{C}\left(\mathbf{q}_0\right) \\ \mu_i f_{n, i} \boldsymbol{v}_{t, i}+\lambda_i \mathbf{f}_{t, i}=\mathbf{0}, & i \in \mathscr{C}\left(\mathbf{q}_0\right) \\ 0 \leq \lambda_i \perp \mu_i f_{n, i}-\left\|\mathbf{f}_{t, i}\right\| \geq 0, & i \in \mathscr{C}\left(\mathbf{q}_0\right) \\ \mathbf{q}=\mathbf{q}_0+\delta t \mathbf{N}_0 \mathbf{v} & \end{array}\]

point contact approximation of PFC $f_{n, e}=(-k \phi)_{+}$, where

\[\begin{aligned} k & =g A_0, \\ \phi_0 & =-\frac{p_{c, 0}}{g}, \\ \phi & =\phi_0+\delta t v_n \end{aligned}\]