engine3d/materials.py

"""The 5-material zoo from W4-5 and its analytic admissible-set rules.

Single source of truth for material definitions and the analytic local
projection they imply (mirrors PDSolver3D._project_local); W7's fluid
token extends this list with "water" at index 5.
"""
import numpy as np

MATERIALS = {
    "steel":     dict(stiffness=5e6, strain_limit=0.012),
    "rubber":    dict(stiffness=1e5, strain_limit=0.35, incompressible=True),
    "foam":      dict(stiffness=2e5,   # volumetric free, shear-limited
                      strain_limit=[0.30, 0.30, 0.30, 0.06, 0.06, 0.06]),
    "composite": dict(stiffness=8e5,   # compliant along x, stiff crosswise
                      strain_limit=[0.20, 0.02, 0.02, 0.12, 0.02, 0.12]),
    "gel":       dict(stiffness=1.2e5, strain_limit=0.15),
}


def apply_limit(e, mat):
    """The material's admissible-set projection on (N,6) strain."""
    lim = mat.get("strain_limit")
    if np.ndim(lim) > 0:
        e = np.clip(e, -np.asarray(lim), np.asarray(lim))
    elif lim is not None:
        norm = np.linalg.norm(e, axis=1)
        e = e * np.minimum(1.0, lim / np.maximum(norm, 1e-12))[:, None]
    if mat.get("incompressible"):
        e = e.copy()
        e[:, :3] -= e[:, :3].mean(axis=1, keepdims=True)
    return e