Materials

A material is a free-energy density W(F; fields, stimuli). The package builds F = variable(I + grad u) once, calls matto.materials.Material.energy(), and takes the first Piola-Kirchhoff stress as diff(W, F).

from matto.materials import Material, simp, director

class MyMaterial(Material):
    fields = ("rho", "theta")
    stimuli = {"B_app": (2,)}
    parameters = {"G0": None, "p_rho": 3.0, "eps_rho": 1.0e-6}

    def energy(self, F, fields, stimuli):
        mu = self.G0 * simp(fields["rho"], self.p_rho, self.eps_rho)
        n = director(fields["theta"])
        ...
        return W

fields names the design fields the energy reads; which of them are optimized is the input file’s choice. stimuli maps each stimulus to its shape, () for a scalar and (dim,) for a vector; the load cases supply the values. parameters gives a default or None for a required value; construction refuses unknown or missing names.

The class can live in the package, next to the input scripts, or in the input script itself. Before using a new model in an optimization, run matto.materials.check_material() on it: it checks a stress-free reference, frame indifference with any vector stimulus rotated along, and that a moderate stretch raises the stored energy.

Shipped models

class	fields	stimulus
HardMagneticSoftMaterial	rho, phi, theta	B_app, a vector
LiquidCrystalElastomer	rho, phi, theta	activation
MagnetoActiveElastomer	rho, phi	h
AnisotropicMagnetoActiveElastomer	rho, phi, theta	h
LinearElastic	rho	none

The hard-magnetic model takes dim=3 for a 3D problem. The linear elastic model is small-strain and exists so a compliance problem can be run with the settings of a linear-elastic code and compared.