[FEM.HyperElastic] Integration of hyperelasticity from Elasticity plugin to SOFA

[alxbilger]

Introduction of hyperelasticity with a few materials, and validation scenes

[with-all-tests]

Note that Ogen was added in alxbilger/Elasticity#6 by @th-skam

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• it builds with SUCCESS for all platforms on the CI.
• it does not generate new warnings.
• it does not generate new unit test failures.
• it does not generate new scene test failures.
• it does not break API compatibility.
• it is more than 1 week old (or has fast-merge label).

[th-skam]

Few comments and porting corrections from SOFA's Ogden.h here.

[th-skam]

Suggested change

	sofa_find_package(Sofa.Component.SolidMechanics.FEM.Elastic QUITE REQUIRED)
	sofa_find_package(Sofa.Component.SolidMechanics.FEM.Elastic QUIET REQUIRED)

[th-skam]

A last pass on the guards with ELASTICITY prefix.

[th-skam]

It's not initialized somewhere so user cannot set it.

[th-skam]

Suggested change

	// The SelfAdjointEigenSolver is normally the suitable choice for symmetric matrices
	// However, it has produced wrong results in some previous tests
	// Disable temporarilly until fixed /*Eigen::SelfAdjointEigenSolver<EigenMatrix>*/
	Eigen::EigenSolver<EigenMatrix> EigenProblemSolver(CEigen, true);
	Eigen::SelfAdjointEigenSolver<EigenMatrix> EigenProblemSolver(CEigen, Eigen::ComputeEigenvectors);

Have changed this in old Ogden.

[th-skam]

Suggested change

	// Disable temporarilly until fixed /*Eigen::SelfAdjointEigenSolver<EigenMatrix>*/
	Eigen::EigenSolver<EigenMatrix> EigenProblemSolver(CEigen, true);
	Eigen::SelfAdjointEigenSolver<EigenMatrix> EigenProblemSolver(CEigen, Eigen::ComputeEigenvectors);

[th-skam]

Suggested change

	const auto eigenvectors = EigenProblemSolver.eigenvectors().real().eval();
	const auto eigenvalues = EigenProblemSolver.eigenvalues().real().eval();
	const auto eigenvectors = EigenProblemSolver.eigenvectors();
	const auto eigenvalues = EigenProblemSolver.eigenvalues();

These are not needed after the SelfAdjoint change.

[th-skam]

Suggested change

	const auto eigenvectors = EigenProblemSolver.eigenvectors().real().eval();
	const auto eigenvalues = EigenProblemSolver.eigenvalues().real().eval();
	const auto eigenvectors = EigenProblemSolver.eigenvectors();
	const auto eigenvalues = EigenProblemSolver.eigenvalues();

[th-skam]

Suggested change

	const Real eigenvalueMultiplier =
	std::fabs(eigenvalues[n] - eigenvalues[m]) < std::numeric_limits<Real>::epsilon()
	? aBy2Minus1 * eigenvaluePowers2(n)
	: (eigenvaluePowers1(n) - eigenvaluePowers1(m)) / (eigenvalues(n) - eigenvalues(m));
	constexpr Real tol = static_cast<Real>(1e-8);
	const Real maxEval = std::max(std::fabs(eigenvalues(n)), std::fabs(eigenvalues(m)));
	const bool isDegenerate = std::fabs(eigenvalues(n) - eigenvalues(m)) < maxEval * tol;
	const Real eigenvalueMultiplier = isDegenerate
	? aBy2Minus1 * eigenvaluePowers2(n)
	: (eigenvaluePowers1(n) - eigenvaluePowers1(m)) / (eigenvalues(n) - eigenvalues(m));

This is ported from Ogden.h already in SOFA. The eigenvalue difference should be scaled by their magnitudes.