Fem Element 3D co-rotational based on a tetrahedron volume discretization. More...

#include <SurgSim/Physics/Fem3DElementCorotationalTetrahedron.h>

Inheritance diagram for SurgSim::Physics::Fem3DElementCorotationalTetrahedron:

Public Member Functions
	Fem3DElementCorotationalTetrahedron (std::array< size_t, 4 > nodeIds)
	Constructor. More...

virtual void	initialize (const SurgSim::Math::OdeState &state) override
	Initialize the FemElement once everything has been set. More...

virtual void	addForce (const SurgSim::Math::OdeState &state, SurgSim::Math::Vector *F, double scale=1.0) override
	Adds the element force (computed for a given state) to a complete system force vector F (assembly) More...

virtual void	addStiffness (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *K, double scale=1.0) override
	Adds the element stiffness matrix K (= -df/dx) (computed for a given state) to a complete system stiffness matrix K (assembly) More...

virtual void	addMatVec (const SurgSim::Math::OdeState &state, double alphaM, double alphaD, double alphaK, const SurgSim::Math::Vector &vector, SurgSim::Math::Vector *result) override
	Adds the element matrix-vector contribution F += (alphaM.M + alphaD.D + alphaK.K).x (computed for a given state) into a complete system data structure F (assembly) More...

virtual bool	update (const SurgSim::Math::OdeState &state) override
	Update the element co-rotational frame. More...

Public Member Functions inherited from SurgSim::Physics::Fem3DElementTetrahedron
	Fem3DElementTetrahedron (std::array< size_t, 4 > nodeIds)
	Constructor. More...

virtual double	getVolume (const SurgSim::Math::OdeState &state) const override
	Get the element volume based on the input state. More...

virtual void	addMass (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *M, double scale=1.0) override
	Adds the element mass matrix M (computed for a given state) to a complete system mass matrix M (assembly) More...

virtual void	addDamping (const SurgSim::Math::OdeState &state, SurgSim::Math::Matrix *D, double scale=1.0) override
	Adds the element damping matrix D (= -df/dv) (comuted for a given state) to a complete system damping matrix D (assembly) More...

virtual void	addFMDK (const SurgSim::Math::OdeState &state, SurgSim::Math::Vector F, SurgSim::Math::Matrix M, SurgSim::Math::Matrix D, SurgSim::Math::Matrix K) override
	Adds the element force vector, mass, stiffness and damping matrices (computed for a given state) into a complete system data structure F, M, D, K (assembly) More...

virtual SurgSim::Math::Vector	computeCartesianCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &naturalCoordinate) const override
	Computes a given natural coordinate in cartesian coordinates. More...

virtual SurgSim::Math::Vector	computeNaturalCoordinate (const SurgSim::Math::OdeState &state, const SurgSim::Math::Vector &cartesianCoordinate) const override
	Computes a natural coordinate given a global coordinate. More...

Public Member Functions inherited from SurgSim::Physics::FemElement
	FemElement ()
	Constructor. More...

virtual	~FemElement ()
	Virtual destructor. More...

size_t	getNumDofPerNode () const
	Gets the number of degree of freedom per node. More...

size_t	getNumNodes () const
	Gets the number of nodes connected by this element. More...

size_t	getNodeId (size_t elementNodeId) const
	Gets the elementNodeId-th node id. More...

const std::vector< size_t > &	getNodeIds () const
	Gets the node ids for this element. More...

void	setYoungModulus (double E)
	Sets the Young modulus (in N.m-2) More...

double	getYoungModulus () const
	Gets the Young modulus (in N.m-2) More...

void	setPoissonRatio (double nu)
	Sets the Poisson ratio (unitless) More...

double	getPoissonRatio () const
	Gets the Poisson ratio (unitless) More...

void	setMassDensity (double rho)
	Sets the mass density (in Kg.m-3) More...

double	getMassDensity () const
	Gets the mass density (in Kg.m-3) More...

double	getMass (const SurgSim::Math::OdeState &state) const
	Gets the element mass based on the input state (in Kg) More...

bool	isValidCoordinate (const SurgSim::Math::Vector &naturalCoordinate) const
	Determines whether a given natural coordinate is valid. More...

Protected Attributes
SurgSim::Math::Matrix33d	m_rotation
	The element rigid rotation. More...

Eigen::Matrix< double, 12, 12 >	m_corotationalStiffnessMatrix
	The co-rotational stiffness matrix. More...

SurgSim::Math::Matrix44d	m_Vinverse
	The constant inverse matrix of the undeformed tetrahedron homogeneous 4 points coordinates. More...

Protected Attributes inherited from SurgSim::Physics::Fem3DElementTetrahedron
double	m_restVolume
	Shape functions: Tetrahedron rest volume. More...

std::array< double, 4 >	m_ai
	Shape functions coefficients Ni(x,y,z) = 1/6V ( ai + x.bi + y.ci + z.di ) More...

std::array< double, 4 >	m_bi

std::array< double, 4 >	m_ci

std::array< double, 4 >	m_di

Eigen::Matrix< double, 12, 1 >	m_x0
	The tetrahedon rest state. More...

Eigen::Matrix< double, 6, 6 >	m_Em
	Elasticity material matrix (contains the elastic properties of the material) More...

Eigen::Matrix< double, 6, 12 >	m_strain
	Strain matrix. More...

Eigen::Matrix< double, 6, 12 >	m_stress
	Stress matrix. More...

Eigen::Matrix< double, 12, 12 >	m_M
	Mass matrix. More...

Eigen::Matrix< double, 12, 12 >	m_K
	Stiffness matrix. More...

Protected Attributes inherited from SurgSim::Physics::FemElement
size_t	m_numDofPerNode
	Number of degree of freedom per node for this element. More...

std::vector< size_t >	m_nodeIds
	Node ids connected by this element. More...

double	m_rho
	Mass density (in Kg.m-3) More...

double	m_E
	Young modulus (in N.m-2) More...

double	m_nu
	Poisson ratio (unitless) More...

Additional Inherited Members
Protected Member Functions inherited from SurgSim::Physics::Fem3DElementTetrahedron
void	computeShapeFunctions (const SurgSim::Math::OdeState &state, double volume, std::array< double, 4 > ai, std::array< double, 4 > bi, std::array< double, 4 > ci, std::array< double, 4 > *di) const
	Computes the tetrahedron shape functions. More...

void	computeStiffness (const SurgSim::Math::OdeState &state, Eigen::Matrix< double, 12, 12 > *k)
	Computes the tetrahedron stiffness matrix. More...

void	computeMass (const SurgSim::Math::OdeState &state, Eigen::Matrix< double, 12, 12 > *m)
	Computes the tetrahedron mass matrix. More...

void	addForce (const SurgSim::Math::OdeState &state, const Eigen::Matrix< double, 12, 12 > &k, SurgSim::Math::Vector *F, double scale=1.0)
	Adds the element force (computed for a given state) to a complete system force vector F (assembly) This method relies on a given stiffness matrix and does not evaluate it from the state. More...

Protected Member Functions inherited from SurgSim::Physics::FemElement
void	setNumDofPerNode (size_t numDofPerNode)
	Sets the number of degrees of freedom per node. More...

Detailed Description

Fem Element 3D co-rotational based on a tetrahedron volume discretization.

Note: This class derives from the linear version of the FEM 3D element tetrahedron, adding a rigid frame; attached to the tetrahedron element to follow its rigid motion. Therefore it computes deformation in the; local coordinate system of the tetrahedron. This class is based on 2 papers:; "Interactive Virtual Materials", Muller, Gross. Graphics Interface 2004; "Exact Corotational Linear FEM Stiffness Matrix", Jernej Barbic. Technical Report USC 2012.; Only the force and stiffness calculation are different, involving some changes as well in addMatVec; (it uses the updated stiffness matrix).; The update method takes care of extracting the rigid motion of the element.; This element is updating its stiffness matrix at each new time step, which means that it cannot; be used with any OdeSolverLinearXXX, it needs an ode solver that recomputes the data at each iteration.

Constructor & Destructor Documentation

SurgSim::Physics::Fem3DElementCorotationalTetrahedron::Fem3DElementCorotationalTetrahedron ( std::array< size_t, 4 > nodeIds )

explicit

Constructor.

Parameters

nodeIds An array of 4 node (A, B, C, D) ids defining this tetrahedron element in a overall mesh

Note: It is required that the triangle ABC is CCW looking from D (i.e. dot(cross(AB, AC), AD) > 0); This is required from the signed volume calculation method getVolume(); A warning will be logged when the initialize function is called if this condition is not met, but the simulation will keep running. Behavior will be undefined because of possible negative volume terms.

Member Function Documentation

void SurgSim::Physics::Fem3DElementCorotationalTetrahedron::addForce	(	const SurgSim::Math::OdeState &	state,
		SurgSim::Math::Vector *	F,
		double	scale = `1.0`
	)

overridevirtual

Adds the element force (computed for a given state) to a complete system force vector F (assembly)

Parameters

	state	The state to compute the force with
[in,out]	F	The complete system force vector to add the element force into
	scale	A factor to scale the added force with

Note: The element force is of size (getNumDofPerNode() x getNumNodes()); This method supposes that the incoming state contains information with the same number of dof; per node as getNumDofPerNode()

Reimplemented from SurgSim::Physics::Fem3DElementTetrahedron.

void SurgSim::Physics::Fem3DElementCorotationalTetrahedron::addMatVec	(	const SurgSim::Math::OdeState &	state,
		double	alphaM,
		double	alphaD,
		double	alphaK,
		const SurgSim::Math::Vector &	x,
		SurgSim::Math::Vector *	F
	)

overridevirtual

Adds the element matrix-vector contribution F += (alphaM.M + alphaD.D + alphaK.K).x (computed for a given state) into a complete system data structure F (assembly)

Parameters

	state	The state to compute everything with
	alphaM	The scaling factor for the mass contribution
	alphaD	The scaling factor for the damping contribution
	alphaK	The scaling factor for the stiffness contribution
	x	A complete system vector to use as the vector in the matrix-vector multiplication
[in,out]	F	The complete system force vector to add the element matrix-vector contribution into

Note: This method supposes that the incoming state contains information with the same number of dof; per node as getNumDofPerNode()

Reimplemented from SurgSim::Physics::Fem3DElementTetrahedron.

void SurgSim::Physics::Fem3DElementCorotationalTetrahedron::addStiffness	(	const SurgSim::Math::OdeState &	state,
		SurgSim::Math::Matrix *	K,
		double	scale = `1.0`
	)

overridevirtual

Adds the element stiffness matrix K (= -df/dx) (computed for a given state) to a complete system stiffness matrix K (assembly)

Parameters

	state	The state to compute the stiffness matrix with
[in,out]	K	The complete system stiffness matrix to add the element stiffness matrix into
	scale	A factor to scale the added stiffness matrix with

Note: The element stiffness matrix is square of size getNumDofPerNode() x getNumNodes(); This method supposes that the incoming state contains information with the same number of; dof per node as getNumDofPerNode()

Reimplemented from SurgSim::Physics::Fem3DElementTetrahedron.

void SurgSim::Physics::Fem3DElementCorotationalTetrahedron::initialize ( const SurgSim::Math::OdeState & state )

overridevirtual

Initialize the FemElement once everything has been set.

Parameters

state The state to initialize the FemElement with

Note: We use the theory of linear elasticity, so this method pre-compute the stiffness and mass matrices; It is required that the triangle ABC is CCW looking from D (i.e. dot(cross(AB, AC), AD) > 0); This is required from the signed volume calculation method getVolume(); A warning will be logged in if this condition is not met, but the simulation will keep running. Behavior will be undefined because of possible negative volume terms.

Reimplemented from SurgSim::Physics::Fem3DElementTetrahedron.

bool SurgSim::Physics::Fem3DElementCorotationalTetrahedron::update ( const SurgSim::Math::OdeState & state )

overridevirtual

Update the element co-rotational frame.

Updating as well the stiffness matrix.

Parameters

state The state from which the element rigid transformation needs to be computed

Returns: True if the update was successful, false otherwise, in which case the representation should be deactivated (invalid data).

Reimplemented from SurgSim::Physics::FemElement.

Member Data Documentation

Eigen::Matrix<double, 12, 12> SurgSim::Physics::Fem3DElementCorotationalTetrahedron::m_corotationalStiffnessMatrix

protected

The co-rotational stiffness matrix.

SurgSim::Math::Matrix33d SurgSim::Physics::Fem3DElementCorotationalTetrahedron::m_rotation

protected

The element rigid rotation.

SurgSim::Math::Matrix44d SurgSim::Physics::Fem3DElementCorotationalTetrahedron::m_Vinverse

protected

The constant inverse matrix of the undeformed tetrahedron homogeneous 4 points coordinates.

This is useful to compute the deformation gradient from which the element rotation is extracted.

The documentation for this class was generated from the following files:

SurgSim/Physics/Fem3DElementCorotationalTetrahedron.h
SurgSim/Physics/Fem3DElementCorotationalTetrahedron.cpp

Public Member Functions

Protected Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation