jaxdem.forces.cundall_strack#
Cundall-Strack linear spring-dashpot contact force model.
Classes
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Cundall-Strack linear spring-dashpot normal and tangential force model with rolling friction. |
- class jaxdem.forces.cundall_strack.CundallStrackForce(laws: tuple[ForceModel, ...] = ())#
Bases:
ForceModelCundall-Strack linear spring-dashpot normal and tangential force model with rolling friction.
Computes the interaction between two spheres with a linear elastic assumption, viscous damping, and Coulomb friction.
Effective Properties The model computes the effective mass \(m_{eff}\), restitution coefficient \(e_{eff}\), and friction coefficient \(\mu\) as:
\[m_{eff} = \left( \frac{1}{m_i} + \frac{1}{m_j} \right)^{-1}, \quad e_{eff} = \min(e_i, e_j), \quad \mu = \min(\mu_i, \mu_j)\]The model computes the shear modulus \(G\) per particle from Young’s modulus \(E\) and Poisson’s ratio \(\nu\):
\[G = \frac{E}{2(1 + \nu)}\]The model treats the effective stiffnesses for the normal (\(k_n\)) and tangential (\(k_t\)) directions as springs in series:
\[k_n = \frac{2 E_i R_i E_j R_j}{E_i R_i + E_j R_j}, \quad k_t = \frac{2 G_i R_i G_j R_j}{G_i R_i + G_j R_j}\]The viscous damping coefficient \(\beta\) and the directional damping coefficients are:
\[\beta = \frac{-\ln(e_{eff})}{\sqrt{\pi^2 + \ln^2(e_{eff})}}\]\[\gamma_n = 2 \beta \sqrt{k_n m_{eff}}, \quad \gamma_t = 2 \beta \sqrt{k_t m_{eff}}\]Forces The normal force \(F_n\) includes spring repulsion and viscous damping, limited to repulsive values:
\[F_n = \max(0, k_n \delta_n - \gamma_n v_n)\]Note on Tangential Force: True Cundall-Strack uses an integrated shear displacement history. This stateless implementation does not track shear history per pair. It approximates the tangential force with the viscous dashpot, capped by the Coulomb sliding friction limit:
\[\mathbf{F}_{t, trial} = -\gamma_t \mathbf{v}_t\]\[\mathbf{F}_t = \min(\|\mathbf{F}_{t, trial}\|, \mu F_n) \frac{\mathbf{v}_t}{\|\mathbf{v}_t\|}\]Rolling Friction The rolling friction torque resists the relative angular velocity at the contact:
\[\boldsymbol{\tau}_{\text{roll}} = -\mu_r \, R_{\text{eff}} \, F_n \, \hat{\omega}_{\text{rel}}\]where \(\mu_r = \min(\mu_{r,i}, \mu_{r,j})\) is the effective rolling friction coefficient, \(R_{\text{eff}} = R_i R_j / (R_i + R_j)\), and \(\hat{\omega}_{\text{rel}}\) is the unit relative angular velocity. Setting \(\mu_r = 0\) (the default) disables rolling friction.
References
- static force(i: int, j: int, pos: jax.Array, state: State, system: System) tuple[jax.Array, jax.Array][source]#
Compute Cundall-Strack normal and tangential forces and torque.