Finite Element Elasto-Dynamics initial value problem with Dirichlet boundary conditions using BDF (backward differentiation formula) as the time discretization. More...

#include <FemElastoDynamics.h>

Public Types
using	MeshType = fem::Mesh<TElement, Dims, TScalar, TIndex>
	Mesh type.

using	ElementType = TElement
	Element type.

using	ElasticEnergyType = THyperElasticEnergy
	Elastic energy type.

using	BdfType = integration::Bdf<TScalar, TIndex>
	BDF time integrator type.

using	ScalarType = TScalar
	Floating point scalar type.

using	IndexType = TIndex
	Integer index type.

Public Member Functions
	FemElastoDynamics ()=default
	Construct an empty FemElastoDynamics problem.

	FemElastoDynamics (Eigen::Ref< Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic > const > const &V, Eigen::Ref< Eigen::Matrix< IndexType, Eigen::Dynamic, Eigen::Dynamic > const > const &C)
	Construct an FemElastoDynamics problem on the mesh domain (V,C).

void	Construct (Eigen::Ref< Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic > const > const &V, Eigen::Ref< Eigen::Matrix< IndexType, Eigen::Dynamic, Eigen::Dynamic > const > const &C)
	Construct an FemElastoDynamics problem on the mesh domain (V,C).

template<class TDerivedX0, class TDerivedV0>
void	SetInitialConditions (Eigen::DenseBase< TDerivedX0 > const &x0, Eigen::DenseBase< TDerivedV0 > const &v0)
	Set the initial conditions for the initial value problem.

void	SetMassMatrix (ScalarType rho)
	Compute, lump and set the mass matrix with homogeneous density \( \rho \).

void	SetElasticEnergy (ScalarType mu, ScalarType lambda)
	Set the elastic energy quadrature for a homogeneous material with Lame coefficients \( \mu \) and \( \lambda \).

void	SetExternalLoad (Eigen::Vector< ScalarType, kDims > const &b)
	Compute and set the external load vector given by fixed body forces \( b \).

void	SetTimeIntegrationScheme (ScalarType dt=ScalarType(1e-2), int s=1)
	Set the BDF (backward differentiation formula) time integration scheme.

template<typename TDerivedDirichletMask>
void	Constrain (Eigen::DenseBase< TDerivedDirichletMask > const &D)
	Set the Dirichlet boundary conditions.

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedRhog>
void	SetMassMatrix (Eigen::DenseBase< TDerivedEg > const &eg, Eigen::MatrixBase< TDerivedWg > const &wg, Eigen::MatrixBase< TDerivedXg > const &Xg, Eigen::MatrixBase< TDerivedRhog > const &rhog)
	Compute, lump and set the mass matrix with variable density \( \rho(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedMug, class TDerivedLambdag>
void	SetElasticEnergy (Eigen::DenseBase< TDerivedEg > const &eg, Eigen::DenseBase< TDerivedWg > const &wg, Eigen::MatrixBase< TDerivedXg > const &Xg, Eigen::DenseBase< TDerivedMug > const &mug, Eigen::DenseBase< TDerivedLambdag > const &lambdag)
	Compute and set the elastic energy quadrature for a heterogeneous material with variable Lame coefficients \( \mu(X) \) and \( \lambda(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedBg>
void	SetExternalLoad (Eigen::DenseBase< TDerivedEg > const &eg, Eigen::MatrixBase< TDerivedWg > const &wg, Eigen::MatrixBase< TDerivedXg > const &Xg, Eigen::MatrixBase< TDerivedBg > const &bg)
	Compute and set the external load vector given by variable body forces \( b(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

void	SetupTimeIntegrationOptimization ()
	Set the BDF inertial target for elasto dynamics.

void	ComputeElasticEnergy (int eElasticComputationFlags, fem::EHyperElasticSpdCorrection eSpdCorrectionFlags)
	Compute the quadrature point elastic energies of the current configuration into Ug, Gg, Hg.

auto	M () const
	k-dimensional mass matrix

auto	aext () const
	External acceleration.

bool	IsDirichletNode (IndexType node) const
	Check if a node is Dirichlet constrained.

bool	IsDirichletDof (IndexType i) const
	Check if a coordinate is Dirichlet constrained.

auto	DirichletNodes () const
	Array of Dirichlet constrained nodes.

auto	DirichletCoordinates () const
	Dirichlet nodal positions.

auto	DirichletVelocities () const
	Dirichlet nodal velocities.

auto	DirichletCoordinates ()
	Dirichlet nodal positions.

auto	DirichletVelocities ()
	Dirichlet nodal velocities.

auto	FreeNodes () const
	Array of unconstrained nodes.

auto	FreeCoordinates () const
	Free nodal positions.

auto	FreeVelocities () const
	Free nodal velocities.

auto	FreeCoordinates ()
	Free nodal positions.

auto	FreeVelocities ()
	Free nodal velocities.

void	Serialize (io::Archive &archive) const
	Serialize to HDF5 group.

void	Deserialize (io::Archive const &archive)
	Deserialize from HDF5 group.

Public Attributes
MeshType	mesh
	FEM mesh.

BdfType	bdf
	BDF time integration scheme.

Eigen::Matrix< ScalarType, kDims, Eigen::Dynamic >	fext
	`kDims x \|# nodes\|` matrix of external forces at nodes

Eigen::Vector< ScalarType, Eigen::Dynamic >	m
	`\|# nodes\| x 1` lumped mass matrix

Eigen::Matrix< ScalarType, kDims, Eigen::Dynamic >	xtilde
	`kDims x \|# nodes\|` inertial targets

Eigen::Matrix< ScalarType, kDims, Eigen::Dynamic >	x
	`kDims x \|# nodes\|` positions

Eigen::Matrix< ScalarType, kDims, Eigen::Dynamic >	v
	`kDims x \|# nodes\|` velocities

Eigen::Vector< IndexType, Eigen::Dynamic >	egU

Eigen::Vector< ScalarType, Eigen::Dynamic >	wgU
	`\|# quad.pts.\| x 1` vector of quadrature weights for elastic potential

Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic >	GNegU

Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic >	lamegU
	`2 x \|# quad.pts.\|` matrix of Lame coefficients at quadrature points

Eigen::Vector< ScalarType, Eigen::Dynamic >	UgU
	`\|# quad.pts.\| x 1` vector of elastic energy density at quadrature points

Eigen::Matrix< ScalarType, kDims *ElementType::kNodes, Eigen::Dynamic >	GgU

Eigen::Matrix< ScalarType, kDims *ElementType::kNodes, Eigen::Dynamic >	HgU

IndexType	ndbc
	Number of Dirichlet constrained nodes.

Eigen::Vector< IndexType, Eigen::Dynamic >	dbc

Eigen::Vector< bool, Eigen::Dynamic >	dmask

Static Public Attributes
static auto constexpr	kDims = Dims
	Dimensionality of the mesh.

Detailed Description

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>
struct pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >

Finite Element Elasto-Dynamics initial value problem with Dirichlet boundary conditions using BDF (backward differentiation formula) as the time discretization.

Represents the problem

\[\min_x \frac{1}{2} || x - \tilde{x} ||_M^2 + \tilde{\beta}_\text{bdf-s}^2 U(x) , \]

where \( M \) is the mass matrix, \( \tilde{x} \) is the BDF inertial target, \( \tilde{\beta}_\text{bdf-s} \) is the forcing term's coefficient, and \( U(x) \) is the hyper-elastic potential.

Template Parameters

TElement	Element type
Dims	Dimensionality of the mesh
THyperElasticEnergy	Hyper elastic energy type
TScalar	Floating point scalar type
TIndex	Integer index type

Constructor & Destructor Documentation

◆ FemElastoDynamics()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FemElastoDynamics	(	Eigen::Ref< Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic > const > const &	V,
		Eigen::Ref< Eigen::Matrix< IndexType, Eigen::Dynamic, Eigen::Dynamic > const > const &	C )

inline

Construct an FemElastoDynamics problem on the mesh domain (V,C).

All FemElastoDynamics quantities are initialized to sensible defaults, i.e. rest pose positions, zero velocities, homogeneous rubber-like material properties, and gravitational load.

Parameters

V	`kDims x \|# verts\|` matrix of mesh vertex positions
C	`\|# cell nodes\| x \|# cells\|` matrix of mesh cells

Member Function Documentation

◆ aext()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::aext ( ) const

inline

External acceleration.

Returns: kDims x |# nodes| external acceleration

◆ ComputeElasticEnergy()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::ComputeElasticEnergy	(	int	eElasticComputationFlags,
		fem::EHyperElasticSpdCorrection	eSpdCorrectionFlags )

inline

Compute the quadrature point elastic energies of the current configuration into Ug, Gg, Hg.

Parameters

eElasticComputationFlags	Flags for computing elastic potential, gradient, and/or hessian
eSpdCorrectionFlags	Flags for SPD correction of element hessians

◆ Constrain()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<typename TDerivedDirichletMask>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::Constrain ( Eigen::DenseBase< TDerivedDirichletMask > const & D )

inline

Set the Dirichlet boundary conditions.

Parameters

D	`\|# nodes\| x 1` mask of Dirichlet boundary conditions s.t. `D(i) == true` if node `i` is constrained

Precondition: D.size() == mesh.X.cols()

◆ Construct()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::Construct	(	Eigen::Ref< Eigen::Matrix< ScalarType, Eigen::Dynamic, Eigen::Dynamic > const > const &	V,
		Eigen::Ref< Eigen::Matrix< IndexType, Eigen::Dynamic, Eigen::Dynamic > const > const &	C )

inline

Construct an FemElastoDynamics problem on the mesh domain (V,C).

All FemElastoDynamics quantities are initialized to sensible defaults, i.e. rest pose positions, zero velocities, homogeneous rubber-like material properties, and gravitational load.

Parameters

V	`kDims x \|# verts\|` matrix of mesh vertex positions
C	`\|# cell nodes\| x \|# cells\|` matrix of mesh cells

◆ Deserialize()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::Deserialize ( io::Archive const & archive )

inline

Deserialize from HDF5 group.

Parameters

archive Archive to deserialize from

◆ DirichletCoordinates() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::DirichletCoordinates ( )

inline

Dirichlet nodal positions.

Returns: kDims x ndbc matrix of Dirichlet constrained nodal positions

◆ DirichletCoordinates() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::DirichletCoordinates ( ) const

inline

Dirichlet nodal positions.

Returns: kDims x ndbc matrix of Dirichlet constrained nodal positions

◆ DirichletNodes()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::DirichletNodes ( ) const

inline

Array of Dirichlet constrained nodes.

Returns: ndbc x 1 array of Dirichlet constrained nodes

◆ DirichletVelocities() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::DirichletVelocities ( )

inline

Dirichlet nodal velocities.

Returns: kDims x ndbc matrix of Dirichlet constrained nodal velocities

◆ DirichletVelocities() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::DirichletVelocities ( ) const

inline

Dirichlet nodal velocities.

Returns: kDims x ndbc matrix of Dirichlet constrained nodal velocities

◆ FreeCoordinates() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FreeCoordinates ( )

inline

Free nodal positions.

Returns: kDims x |# nodes - ndbc| matrix of unconstrained nodal positions

◆ FreeCoordinates() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FreeCoordinates ( ) const

inline

Free nodal positions.

Returns: kDims x |# nodes - ndbc| matrix of unconstrained nodal positions

◆ FreeNodes()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FreeNodes ( ) const

inline

Array of unconstrained nodes.

Returns: |# nodes - ndbc| x 1 array of unconstrained nodes

◆ FreeVelocities() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FreeVelocities ( )

inline

Free nodal velocities.

Returns: kDims x |# nodes - ndbc| matrix of unconstrained nodal velocities

◆ FreeVelocities() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::FreeVelocities ( ) const

inline

Free nodal velocities.

Returns: kDims x |# nodes - ndbc| matrix of unconstrained nodal velocities

◆ IsDirichletDof()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

bool pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::IsDirichletDof ( IndexType i ) const

inline

Check if a coordinate is Dirichlet constrained.

Parameters

i	Coordinate index

Returns: true if the coordinate is Dirichlet constrained, false otherwise

◆ IsDirichletNode()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

bool pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::IsDirichletNode ( IndexType node ) const

inline

Check if a node is Dirichlet constrained.

Parameters

node	Node index

Returns: true if the node is Dirichlet constrained, false otherwise

◆ M()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

auto pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::M ( ) const

inline

k-dimensional mass matrix

Returns: kDims * |#nodes| x 1 vector of the kDims-dimensional lumped mass matrix diagonal coefficients

◆ Serialize()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::Serialize ( io::Archive & archive ) const

inline

Serialize to HDF5 group.

Parameters

archive Archive to serialize to

◆ SetElasticEnergy() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedMug, class TDerivedLambdag>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetElasticEnergy	(	Eigen::DenseBase< TDerivedEg > const &	eg,
		Eigen::DenseBase< TDerivedWg > const &	wg,
		Eigen::MatrixBase< TDerivedXg > const &	Xg,
		Eigen::DenseBase< TDerivedMug > const &	mug,
		Eigen::DenseBase< TDerivedLambdag > const &	lambdag )

inline

Compute and set the elastic energy quadrature for a heterogeneous material with variable Lame coefficients \( \mu(X) \) and \( \lambda(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

Template Parameters

TDerivedEg	Eigen dense expression type for element indices
TDerivedWg	Eigen dense expression type for quadrature weights
TDerivedXg	Eigen dense expression type for quadrature points
TDerivedMug	Eigen dense expression type for 1st Lame coefficients
TDerivedLambdag	Eigen dense expression type for 2nd Lame coefficients

Parameters

eg	`\|# quad.pts.\| x 1` vector of element indices at quadrature points
wg	`\|# quad.pts.\| x 1` vector of quadrature weights
Xg	`\|# dims\| x \|# quad.pts.\|` matrix of quadrature points
mug	`\|# quad.pts.\| x 1` vector of 1st Lame coefficients at quadrature points
lambdag	`\|# quad.pts.\| x 1` vector of 2nd Lame coefficients at quadrature points

◆ SetElasticEnergy() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetElasticEnergy	(	ScalarType	mu,
		ScalarType	lambda )

inline

Set the elastic energy quadrature for a homogeneous material with Lame coefficients \( \mu \) and \( \lambda \).

Parameters

mu	1st Lame coefficient \( \mu \)
lambda	2nd Lame coefficient \( \lambda \)

◆ SetExternalLoad() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedBg>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetExternalLoad	(	Eigen::DenseBase< TDerivedEg > const &	eg,
		Eigen::MatrixBase< TDerivedWg > const &	wg,
		Eigen::MatrixBase< TDerivedXg > const &	Xg,
		Eigen::MatrixBase< TDerivedBg > const &	bg )

inline

Compute and set the external load vector given by variable body forces \( b(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

Template Parameters

TDerivedEg	Eigen dense expression type for element indices
TDerivedWg	Eigen dense expression type for quadrature weights
TDerivedXg	Eigen dense expression type for quadrature points
TDerivedBg	Eigen dense expression type for body forces

Parameters

eg	`\|# quad.pts.\| x 1` vector of element indices at quadrature points
wg	`\|# quad.pts.\| x 1` vector of quadrature weights
Xg	`\|# dims\| x \|# quad.pts.\|` matrix of quadrature points
bg	`kDims x \|# quad.pts.\|` matrix of body forces at quadrature points

◆ SetExternalLoad() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetExternalLoad ( Eigen::Vector< ScalarType, kDims > const & b )

inline

Compute and set the external load vector given by fixed body forces \( b \).

Parameters

b	`kDims x 1` fixed body forces

◆ SetInitialConditions()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedX0, class TDerivedV0>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetInitialConditions	(	Eigen::DenseBase< TDerivedX0 > const &	x0,
		Eigen::DenseBase< TDerivedV0 > const &	v0 )

inline

Set the initial conditions for the initial value problem.

Parameters

x0	`kDims x \|# nodes\|` matrix of initial nodal coordinates
v0	`kDims x \|# nodes\|` matrix of initial nodal velocities

◆ SetMassMatrix() [1/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

template<class TDerivedEg, class TDerivedWg, class TDerivedXg, class TDerivedRhog>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetMassMatrix	(	Eigen::DenseBase< TDerivedEg > const &	eg,
		Eigen::MatrixBase< TDerivedWg > const &	wg,
		Eigen::MatrixBase< TDerivedXg > const &	Xg,
		Eigen::MatrixBase< TDerivedRhog > const &	rhog )

inline

Compute, lump and set the mass matrix with variable density \( \rho(X) \) at quadrature points \( X_g \) of the given quadrature rule \( (w_g, X_g) \).

Template Parameters

TDerivedEg	Eigen dense expression type for element indices
TDerivedWg	Eigen dense expression type for quadrature weights
TDerivedXg	Eigen dense expression type for quadrature points
TDerivedRhog	Eigen dense expression type for mass density

Parameters

eg	`\|# quad.pts.\| x 1` vector of element indices at quadrature points
wg	`\|# quad.pts.\| x 1` vector of quadrature weights
Xg	`\|# dims\| x \|# quad.pts.\|` matrix of quadrature points
rhog	`\|# quad.pts.\| x 1` vector of mass density at quadrature points

◆ SetMassMatrix() [2/2]

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetMassMatrix ( ScalarType rho )

inline

Compute, lump and set the mass matrix with homogeneous density \( \rho \).

Parameters

rho	Mass density of the material

◆ SetTimeIntegrationScheme()

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar, common::CIndex TIndex>

void pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::SetTimeIntegrationScheme	(	ScalarType	dt = ScalarType(1e-2),
		int	s = 1 )

inline

Set the BDF (backward differentiation formula) time integration scheme.

Parameters

dt	Time step size
s	Step of the BDF scheme

Member Data Documentation

◆ dbc

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Vector<IndexType, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::dbc

◆ dmask

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Vector<bool, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::dmask

|# nodes| x 1 mask of Dirichlet boundary conditions s.t. dmask(i) == true if node i is constrained

◆ egU

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Vector<IndexType, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::egU

|# quad.pts.| x 1 vector of element indices for quadrature points of elastic potential

◆ GgU

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Matrix<ScalarType, kDims * ElementType::kNodes, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::GgU

|# dims * # elem nodes| x |# quad.pts.| matrix of element elastic gradient vectors at quadrature points

◆ GNegU

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Matrix<ScalarType, Eigen::Dynamic, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::GNegU

|ElementType::kNodes| x |kDims * # quad.pts.| matrix of shape function gradients at quadrature points

◆ HgU

template<fem::CElement TElement, int Dims, physics::CHyperElasticEnergy THyperElasticEnergy, common::CFloatingPoint TScalar = Scalar, common::CIndex TIndex = Index>

Eigen::Matrix<ScalarType, kDims * ElementType::kNodes, Eigen::Dynamic> pbat::sim::dynamics::FemElastoDynamics< TElement, Dims, THyperElasticEnergy, TScalar, TIndex >::HgU

|# dims * # elem nodes| x |# dims * # elem nodes * # quad.pts.| matrix of element elastic hessian matrices at quadrature points

The documentation for this struct was generated from the following file:

C:/git/PhysicsBasedAnimationToolkit/source/pbat/sim/dynamics/FemElastoDynamics.h

Public Types

Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ FemElastoDynamics()

Member Function Documentation

◆ aext()

◆ ComputeElasticEnergy()

◆ Constrain()

◆ Construct()

◆ Deserialize()

◆ DirichletCoordinates() [1/2]

◆ DirichletCoordinates() [2/2]

◆ DirichletNodes()

◆ DirichletVelocities() [1/2]

◆ DirichletVelocities() [2/2]

◆ FreeCoordinates() [1/2]

◆ FreeCoordinates() [2/2]

◆ FreeNodes()

◆ FreeVelocities() [1/2]

◆ FreeVelocities() [2/2]

◆ IsDirichletDof()

◆ IsDirichletNode()

◆ M()

◆ Serialize()

◆ SetElasticEnergy() [1/2]

◆ SetElasticEnergy() [2/2]

◆ SetExternalLoad() [1/2]

◆ SetExternalLoad() [2/2]

◆ SetInitialConditions()

◆ SetMassMatrix() [1/2]

◆ SetMassMatrix() [2/2]

◆ SetTimeIntegrationScheme()

Member Data Documentation

◆ dbc

◆ dmask

◆ egU

◆ GgU

◆ GNegU

◆ HgU