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 using a linear elastic assumption combined with viscous damping and Coulomb friction.
Effective Properties The effective mass \(m_{eff}\), restitution coefficient \(e_{eff}\), and friction coefficient \(\mu\) are taken 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 Shear Modulus \(G\) is computed per particle from Young’s modulus \(E\) and Poisson’s ratio \(\nu\):
\[G = \frac{E}{2(1 + \nu)}\]The effective stiffnesses for the normal (\(k_n\)) and tangential (\(k_t\)) directions are modelled 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 resulting 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, constrained to be strictly repulsive:
\[F_n = \max(0, k_n \delta_n - \gamma_n v_n)\]Note on Tangential Force: True Cundall-Strack uses an integrated shear displacement history. Because this stateless implementation does not track tangential history per pair, the tangential force is approximated using the dynamic viscous dashpot strictly 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 A resistive torque opposing 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.
- static energy(i: int, j: int, pos: jax.Array, state: State, system: System) jax.Array[source]#
Compute conservative potential energy for the interaction.
\[U_{ij} = \frac{1}{2} k_n \delta_n^2\]
- property required_material_properties: tuple[str, ...][source]#
A static tuple of strings specifying the material properties required by this force model.
These properties (e.g., ‘young_eff’, ‘restitution’, …) must be present in the
System.mat_tablefor the model to function correctly. This is used for validation.