jaxdem.forces.spring

Linear spring force model.

Classes

SpringForce([required_material_properties, laws])

A ForceModel implementation for a linear spring-like interaction between particles.

class jaxdem.forces.spring.SpringForce(required_material_properties: Tuple[str, ...] = ('young_eff',), laws: Tuple[ForceModel, ...] = ())

Bases: ForceModel

A ForceModel implementation for a linear spring-like interaction between particles.

Notes

• The ‘effective Young’s modulus’ (\(k_{eff,\; ij}\)) is retrieved from the jaxdem.System.mat_table based on the material IDs of the interacting particles.

• The force is zero if \(i == j\).

• A small epsilon is added to the squared distance (\(r^2\)) before taking the square root to prevent division by zero or NaN issues when particles are perfectly co-located.

The penetration \(\delta\) (overlap) between two particles \(i\) and \(j\) is:

\[\delta = (R_i + R_j) - r\]

where \(R_i\) and \(R_j\) are the radii of particles \(i\) and \(j\) respectively, and \(r = ||r_{ij}||\) is the distance between their centers.

The scalar overlap \(s\) is defined as:

\[s = \max \left(0, \frac{R_i + R_j}{r} - 1 \right)\]

The force \(F_{ij}\) acting on particle \(i\) due to particle \(j\) is:

\[F_{ij} = k_{eff,\; ij} s r_{ij}\]

The potential energy \(E_{ij}\) of the interaction is:

\[E_{ij} = \frac{1}{2} k_{eff,\; ij} s^2\]

where \(k_{eff,\; ij}\) is the effective Young’s modulus for the particle pair.

static force(i: int, j: int, state: State, system: System) → jax.Array

Compute linear spring-like interaction force acting on particle \(i\) due to particle \(j\).

Returns zero when \(i = j\).

Parameters:

• i (int) – Index of the first particle.

• j (int) – Index of the second particle.

• state (State) – Current state of the simulation.

• system (System) – Simulation system configuration.

Returns:

Force vector acting on particle \(i\) due to particle \(j\).

Return type:

jax.Array

static energy(i: int, j: int, state: State, system: System) → jax.Array

Compute linear spring-like interaction potential energy between particle \(i\) and particle \(j\).

Returns zero when \(i = j\).

Parameters:

• i (int) – Index of the first particle.

• j (int) – Index of the second particle.

• state (State) – Current state of the simulation.

• system (System) – Simulation system configuration.

Returns:

Scalar JAX array representing the potential energy of the interaction between particles \(i\) and \(j\).

Return type:

jax.Array

classmethod registry_name() → str

property type_name: str