friction

Frictional pair force classes apply a force, and torque on every particle in the simulation state. The following general expression for Markovian tangential friction forces is implemented for interactions between two spherical particles and is discussed in detail in Hofmann et. al. 2025. For two particles ii and jj with radii Ri,jR_{i,j}, center positions ri,j\mathbf{r}_{i,j}, angular velocities ωi,j\mathbf{\omega}_{i,j}, and translational velocities vi,j\mathbf{v}_{i,j}, their surface velocities at the contact point are given by

ui=vi+ωi×r^ijRiuj=vj−ωj×r^ijRj ,\begin{align*} \mathbf{u}_i &= \mathbf{v}_i+\mathbf{\omega}_i \times \mathbf{\hat{r}}_{ij}R_i \\ \mathbf{u}_j &= \mathbf{v}_j-\mathbf{\omega}_j \times \mathbf{\hat{r}}_{ij}R_j \, , \end{align*}

where r^ij=rij/ri,j\mathbf{\hat{r}}_{ij}=\mathbf{r}_{ij}/r_{i,j}. With these expressions, we calculate the relative tangential velocity ui,j⊥\mathbf{u}^\perp_{i,j} at the contact point

ui,j⊥=P(r^ij)(vj−vi)−(ωiRi+ωjRj)×r^ij ,\mathbf{u}^\perp_{i,j} = \mathbf{P}(\mathbf{\hat{r}}_{ij})(\mathbf{v}_j -\mathbf{v}_i) -(\mathbf{\omega}_iR_i+\mathbf{\omega}_jR_j) \times \mathbf{\hat{r}}_{ij}\, ,

wit the projection operator P(r^ij)=1−r^ijr^ij\mathbf{P}(\mathbf{\hat{r}}_{ij})=1 -\mathbf{\hat{r}}_{ij}\mathbf{\hat{r}}_{ij}. We model the tangential friction force at the contact point very general as

Fif,contact=−Fjf,contact=f(ui,j⊥,ri,j)u^i,j⊥\mathbf{F}^\mathrm{f,contact}_i = -\mathbf{F}^\mathrm{f,contact}_j = f(u^\perp_{i,j} ,r_{i,j})\mathbf{\hat{u}}^\perp_{i,j}

with u^i,j⊥=ui,j⊥/ui,j⊥\mathbf{\hat{u}}^\perp_{i,j}=\mathbf{u}^\perp_{i,j}/u^\perp_{i,j}, where f(ui,j⊥,ri,j)f(u^\perp_{i,j},r_{i,j}) is an arbitrary function. The surface force Fif,contact\mathbf{F}^\mathrm{f,contact}_i generates a center-of-mass force and torque acting on particle ii,

Fijf=Fif,contactτijf=Rir^ij×Fif,contact ,\begin{align*} \mathbf{F}^\mathrm{f}_{ij} &= \mathbf{F}^\mathrm{f,contact}_i \\ \mathbf{\tau}^\mathrm{f}_{ij} &= R_i\mathbf{\hat{r}}_{ij} \times \mathbf{F}^\mathrm{f,contact}_i\, , \end{align*}

which is a pair friction force and torque resulting from the friction with the particle jj.

The functional form of f(ui,j⊥,ri,j)f(u^\perp_{i,j},r_{i,j}) specifies the frictional model.

FrictionalPair does not support any shifting modes.

Classes