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SurgSim::Physics::Fem3DElementCorotationalTetrahedron Class Reference

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

#include <SurgSim/Physics/Fem3DElementCorotationalTetrahedron.h>

Inheritance diagram for SurgSim::Physics::Fem3DElementCorotationalTetrahedron:
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Collaboration diagram for SurgSim::Physics::Fem3DElementCorotationalTetrahedron:
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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
nodeIdsAn 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
stateThe state to compute the force with
[in,out]FThe complete system force vector to add the element force into
scaleA 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
stateThe state to compute everything with
alphaMThe scaling factor for the mass contribution
alphaDThe scaling factor for the damping contribution
alphaKThe scaling factor for the stiffness contribution
xA complete system vector to use as the vector in the matrix-vector multiplication
[in,out]FThe 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
stateThe state to compute the stiffness matrix with
[in,out]KThe complete system stiffness matrix to add the element stiffness matrix into
scaleA 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
stateThe 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
stateThe 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: