📄️ Overview
SuperDex Physics supports several material models for soft body simulation. Each model is defined by a strain energy density $\Psi(\mathbf)$, where $\mathbf{F}$ is the deformation gradient. The first Piola–Kirchhoff stress $\mathbf{P} = \partial\Psi/\partial\mathbf{F}$ and material tangent $\partial\mathbf{P}/\partial\mathbf{F}$ follow from this energy.
📄️ Linear Elastic
Small-strain linear elasticity is the simplest and fastest material model, but has an extremely limited range of validity, requiring both small strains and small rotations of the material.
📄️ Neo-Hookean
The Neo-Hookean model is the recommended default for general-purpose deformable simulation. SuperDex Physics uses the inversion-robust formulation of Smith et al. (2018).
📄️ Saint Venant–Kirchhoff
Saint Venant–Kirchhoff extends linear elasticity to finite deformation using the Green–Lagrange strain. The constitutive relation is linear in that nonlinear strain measure, making the model frame-indifferent but unreliable under large compression.
📄️ ARAP
ARAP penalizes deformation that differs from a rigid rotation, preserving local shape rather than matching a conventional isotropic elastic law. SuperDex Physics follows the rotation-variant SVD treatment described by Kim and Eberle (2022).
📄️ Active Neo-Hookean
Active Neo-Hookean is a composite material that combines passive Neo-Hookean elasticity with active anisotropic fiber contraction. It is intended for directionally actuated materials such as muscle tissue.
📄️ Active Shape Targeting ARAP
Active Shape Targeting ARAP extends ARAP with a user-controlled local shape target. It follows the shape-targeting model of Klár et al. (2020) and can represent contraction, expansion, or shear while allowing rigid rotation.