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.

Enum value: SoftMaterialType::ActiveNeoHookean

Formulation

The strain energy density is the sum of two components:

$$\Psi(\mathbf{F}) = \Psi_{\mathrm{neo}}(\mathbf{F}) + \Psi_{\mathrm{aniso}}(\mathbf{F})~.$$

Passive Isotropic Component

The passiveIsotropic component uses the inversion-robust Neo-Hookean formulation of Smith et al. (2018).

Active Anisotropic Component

The activeAnisotropic component follows Kim et al. (2019) and penalizes deviation of the fiber stretch from a target length:

• anisoDir is the unit fiber direction.
• alpha is the anisotropic stiffness.
• length is the target fiber length; values below 1 produce contraction relative to the reference configuration.

The stress and tangent are sums of the passive and active component contributions.

Parameters

Parameter	Default	Units	Description
passiveIsotropic.youngsModulus	100,000	Pa	Passive isotropic stiffness
passiveIsotropic.poissonRatio	0.45	--	Passive isotropic compressibility
passiveIsotropic.psdStrategy	Projection	--	Passive component PSD strategy
activeAnisotropic.alpha	1,000	Pa	Fiber stiffness
activeAnisotropic.length	1.0	--	Target fiber length
activeAnisotropic.anisoDir	(1, 0, 0)	--	Unit fiber direction
activeAnisotropic.psdStrategy	Projection	--	Active component PSD strategy

PSD strategies are configured independently for the two subcomponents. The passive Neo-Hookean component supports the concrete strategies None, Projection, Fast, and AbsEigenProjection; the active anisotropic component supports None, Projection, and AbsEigenProjection. For either component, MaterialDefault resolves to Projection.

When to Use

• Muscle tissue simulation where fibers contract along a preferred direction.
• Soft actuators with embedded directional stiffness.
• Any scenario requiring combined passive elasticity and active contraction.

References

• T. Kim et al., Anisotropic Elasticity for Inversion-Safety and Element Rehabilitation, 2019.
• B. Smith, F. de Goes, and T. Kim, Stable Neo-Hookean Flesh Simulation, 2018.