Vega FEM Library (v1.1) User's Manual - University of Southern ...

virtual void ComputeEnergyHessian(int elementIndex,
double * invariants, double * hessian) = 0
Given the three invariants invariants[0],invariants[1],invariants[2] computes the second derivative
of the energy with respect to the invariants and writes the result to hessian where hessian[0] =
∂ 2 Ψ/∂I 2 , hessian[1] = ∂ 2 Ψ/∂I∂II, hessian[2] = ∂ 2 Ψ/∂I∂III, hessian[3] = ∂ 2 Ψ/∂II 2 , hessian[4]
= ∂ 2 Ψ/∂II∂III, and hessian[5] = ∂ 2 Ψ/∂III 2
To define your own isotropic hyperelastic material, simply derive from IsotropicMaterial and implement
functions ComputeEnergy, ComputeEnergyGradient, ComputeEnergyHessian.
class StVKIsotropicMaterial : public IsotropicMaterial StVK material that supports spatially
varying material parameters. Provides functions to compute the energy, gradient, and Hessian of the StVK
material given the three invariants I, II, III. The implemented StVK material is described in [BW08], page
158.
StVKIsotropicMaterial(TetMesh * tetMesh)
The material parameters are read from the tet mesh, and are cached in the constructor. Throws an
exception if the provided tet mesh does not consist of materials specifying E, ν.
class HomogeneousIsotropicStVKMaterial : public IsotropicMaterial StVK material with homogeneous
(spatially global) material parameters. Provides functions to compute the energy, gradient, and
Hessian of the StVK material given the three invariants I, II, III.
HomogeneousIsotropicStVKMaterial(double E, double nu)
Initializes the Young’s modulus E and the Poisson ratio nu of the material.
class NeoHookeanIsotropicMaterial : public IsotropicMaterial Neo-Hookean material that supports
spatially varying material parameters. Provides functions to compute the energy, gradient, and Hessian
of the Neo-Hookean material given the three invariants I, II, III. The implemented neo-Hookean material
is described in [BW08], page 162.
NeoHookeanIsotropicMaterial(TetMesh * tetMesh)
The material parameters are read from the tet mesh, and are cached in the constructor. Throws an
exception if the provided tet mesh does not consist of materials specifying E, ν.
class HomogeneousNeoHookeanIsotropicMaterial : public IsotropicMaterial Neo-Hookean material
with homogeneous (spatially global) material parameters. Provides functions to compute the energy,
gradient, and Hessian of the neo-Hookean material given the three invariants I, II, III.
HomogeneousNeoHookeanIsotropicMaterial(double E, double nu)
Initializes the Young’s modulus E and the Poisson ratio nu of the material.
class MooneyRivlinIsotropicMaterial : public IsotropicMaterial Mooney-Rivlin material that supports
spatially varying material parameters.
MooneyRivlinIsotropicMaterial(TetMesh * tetMesh)
The material parameters are read from the tet mesh, and are cached in the constructor. Throws an
exception if the provided tet mesh does not consist of Mooney-Rivlin materials. Provides functions to
compute the energy, gradient, and Hessian of the Mooney-Rivlin material given the three invariants I, II, III.
The implemented Mooney-Rivlin material is described in Section 3.5.5 of [Bow09].
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