jaxdem.bonded_forces.plastic_perimeter_deformable_particle#

Implementation of the plastic perimeter deformable particle model.

Classes

PlasticPerimeterDeformableParticleModel(...)

Deformable particle model with perimeter-level plasticity.
class jaxdem.bonded_forces.plastic_perimeter_deformable_particle.PlasticPerimeterDeformableParticleModel(elements: Array | None, edges: Array | None, element_adjacency: Array | None, element_adjacency_edges: Array | None, elements_id: Array | None, initial_body_contents: Array | None, initial_element_measures: Array | None, initial_edge_lengths: Array | None, initial_bendings: Array | None, w_b: Array | None, em: Array | None, ec: Array | None, eb: Array | None, el: Array | None, gamma: Array | None, edges_id: Array | None = None, tau_s: Array | None = None)#

Bases: DeformableParticleModel

Deformable particle model with perimeter-level plasticity.

Elastic forces match DeformableParticleModel. The model keeps the edge-spring, measure, content, bending, and surface-tension terms. See the DeformableParticleModel docstring for the full energy definition and shape conventions. The only difference is the plastic update rule.

Instead of relaxing each edge rest length independently (as in PlasticDeformableParticleModel), the total reference perimeter of each body relaxes toward the current total perimeter. Uniform rescaling then distributes the change back to the individual edges:

\[\begin{split}P_{K,0}^{\text{new}} &= P_{K,0} + \frac{1}{\tau_{s,K}} (P_K - P_{K,0})\,dt \\ L_{e,0}^{\text{new}} &= L_{e,0}\;\frac{P_{K,0}^{\text{new}}}{P_{K,0}} \qquad \forall\, e \in K\end{split}\]

where \(P_K = \sum_{e \in K} L_e\) is the current perimeter, \(P_{K,0} = \sum_{e \in K} L_{e,0}\) the reference perimeter, \(\tau_{s,K}\) the per-body relaxation time, and \(dt\) the time step. Uniform rescaling preserves relative edge proportions within each body.

This model requires an edges_id mapping (shape (E,)) that assigns each edge to its body, analogous to elements_id for elements. For a single body without edges_id, all edges belong to body 0.

Shapes (see DeformableParticleModel for definitions of K, M, E, A):

  • edges_id: (E,)

  • tau_s: (K,)

edges_id: Array | None#

(E,). edges_id[e] == k means edge e belongs to body k. Required for perimeter-level plasticity.

Type:

Array of body IDs for each edge. Shape

tau_s: Array | None#

(K,). Controls how fast the total reference perimeter of each body relaxes toward the current perimeter.

Type:

Plastic relaxation time for each body. Shape

classmethod Create(*, vertices: Array | ndarray | bool | number | bool | int | float | complex | None = None, elements: Array | ndarray | bool | number | bool | int | float | complex | None = None, edges: Array | ndarray | bool | number | bool | int | float | complex | None = None, element_adjacency: Array | ndarray | bool | number | bool | int | float | complex | None = None, element_adjacency_edges: Array | ndarray | bool | number | bool | int | float | complex | None = None, elements_id: Array | ndarray | bool | number | bool | int | float | complex | None = None, edges_id: Array | ndarray | bool | number | bool | int | float | complex | None = None, initial_body_contents: Array | ndarray | bool | number | bool | int | float | complex | None = None, initial_element_measures: Array | ndarray | bool | number | bool | int | float | complex | None = None, initial_edge_lengths: Array | ndarray | bool | number | bool | int | float | complex | None = None, initial_bendings: Array | ndarray | bool | number | bool | int | float | complex | None = None, em: Array | ndarray | bool | number | bool | int | float | complex | None = None, ec: Array | ndarray | bool | number | bool | int | float | complex | None = None, eb: Array | ndarray | bool | number | bool | int | float | complex | None = None, el: Array | ndarray | bool | number | bool | int | float | complex | None = None, gamma: Array | ndarray | bool | number | bool | int | float | complex | None = None, tau_s: Array | ndarray | bool | number | bool | int | float | complex | None = None, w_b: Array | ndarray | bool | number | bool | int | float | complex | None = None) → Self[source]#
update_reference_state(pos: jax.Array, state: State, system: System) → DeformableParticleModel[source]#

Relax each body’s reference perimeter toward its current perimeter.