Elasticity-Based Displacement Propagation¶

When you prescribe displacements on a subset of mesh vertices (e.g. a moving boundary, a deformable inclusion, an injection face) and need a smooth field on the rest of the mesh, mmgpy ships two propagators:

propagate_displacement — solves Laplace's equation on the mesh graph, no extra dependency.
propagate_displacement_elasticity — solves a linear elasticity problem on the mesh via the optional fedoo backend.

The two methods give noticeably different fields whenever the geometry involves bending, re-entrant corners, or large boundary displacements. The elasticity-based propagator captures the bending kinematics and concentrates strain at re-entrant corners; the Laplacian one only knows about graph distances.

When to use the elasticity-based path¶

Scenario	Recommended
Small displacements, smooth geometry	Laplacian (cheap, no dependency)
Cantilevers, brackets, levers	Elasticity (captures bending)
Sharp re-entrant corners under load	Elasticity (correct stress concentration)
Large deformations near element inversion	Elasticity (resists inversion better)

2D demo: L-bracket cantilever¶

The free tip of the foot is pinned and the top of the post is pulled upward. The Laplacian field linearly interpolates the prescribed values along graph distances, so the bracket pivots like a rigid body. Linear elasticity captures the bending: the post curves backward at the re-entrant corner and the foot bows visibly.

Laplacian vs elasticity on a 2D L-bracket

from mmgpy.lagrangian import (
    propagate_displacement,
    propagate_displacement_elasticity,
)

# vertices: (N, 2), elements: (M, 3), boundary_mask: (N,) bool
# boundary_displacement: (N, 2), zero on interior, prescribed on boundary

field_lap = propagate_displacement(
    vertices, elements, boundary_mask, boundary_displacement,
)
field_ela = propagate_displacement_elasticity(
    vertices, elements, boundary_mask, boundary_displacement,
    E=1e6, nu=0.3,
)

Full script: examples/mmg2d/elasticity_propagation.py.

3D demo: extruded L-bracket¶

Same geometry extruded in z. The pure Laplacian solver moves only the prescribed face and produces a rigid pivot. Elasticity propagates the loading through the corner, bending the entire bracket.

Laplacian vs elasticity on a 3D L-bracket

Full script: examples/mmg3d/elasticity_propagation.py.

PyVista accessor¶

The accessor's move() method exposes the propagator via the propagation_method keyword:

import numpy as np
import pyvista as pv
import mmgpy  # noqa: F401  -- registers the .mmg accessor

mesh = pv.read("bracket.mesh")
displacement = np.zeros((mesh.n_points, 3))
# ...prescribe values on the boundary indices you care about...

# Default Laplacian
moved_lap = mesh.mmg.move(displacement, propagate=True)

# Elasticity-based propagation (requires fedoo)
moved_ela = mesh.mmg.move(
    displacement,
    propagate=True,
    propagation_method="elasticity",
)

Installing the `fedoo` extra¶

uv sync --extra fem
# or
pip install "mmgpy[fem]"

fedoo is an optional dependency; mmgpy still imports cleanly without it and the Laplacian path keeps working. Only propagate_displacement_elasticity and propagation_method="elasticity" need it.

conda-forge users¶

fedoo is published on PyPI but not on conda-forge, so the [fem] extra isn't reachable via conda install mmgpy. Install fedoo separately into the same environment:

conda install -c conda-forge mmgpy
pip install fedoo                # PyPI (recommended)
# or:
conda install -c set3MAH fedoo   # the upstream maintainers' personal channel