NonlinearElasticitySolver< DIM > Class Template Reference

#include <NonlinearElasticitySolver.hpp>

Inheritance diagram for NonlinearElasticitySolver< DIM >:

Collaboration diagram for NonlinearElasticitySolver< DIM >:

List of all members.

Public Member Functions

NonlinearElasticitySolver (QuadraticMesh< DIM > *pQuadMesh, AbstractIncompressibleMaterialLaw< DIM > *pMaterialLaw, c_vector< double, DIM > bodyForce, double density, std::string outputDirectory, std::vector< unsigned > &fixedNodes, std::vector< c_vector< double, DIM > > *pFixedNodeLocations=NULL)

NonlinearElasticitySolver (QuadraticMesh< DIM > *pQuadMesh, std::vector< AbstractIncompressibleMaterialLaw< DIM > * > &rMaterialLaws, c_vector< double, DIM > bodyForce, double density, std::string outputDirectory, std::vector< unsigned > &fixedNodes, std::vector< c_vector< double, DIM > > *pFixedNodeLocations=NULL)

~NonlinearElasticitySolver ()

std::vector< double > & rGetPressures ()

Protected Member Functions

virtual void AssembleOnElement (Element< DIM, DIM > &rElement, c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &rAElem, c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &rAElemPrecond, c_vector< double, STENCIL_SIZE > &rBElem, bool assembleResidual, bool assembleJacobian)

virtual void AssembleOnBoundaryElement (BoundaryElement< DIM-1, DIM > &rBoundaryElement, c_matrix< double, BOUNDARY_STENCIL_SIZE, BOUNDARY_STENCIL_SIZE > &rAelem, c_vector< double, BOUNDARY_STENCIL_SIZE > &rBelem, c_vector< double, DIM > &rTraction, bool assembleResidual, bool assembleJacobian)

void FormInitialGuess ()

void AssembleSystem (bool assembleResidual, bool assembleJacobian)

virtual void ComputeStressAndStressDerivative (AbstractIncompressibleMaterialLaw< DIM > *pMaterialLaw, c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, double pressure, unsigned elementIndex, unsigned currentQuadPointGlobalIndex, c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool computeDTdE)

Protected Attributes

std::vector
< AbstractIncompressibleMaterialLaw
< DIM > * > mMaterialLaws

std::vector< double > mPressures

Static Protected Attributes

static const size_t NUM_VERTICES_PER_ELEMENT = DIM+1

static const size_t NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2

static const size_t STENCIL_SIZE = DIM*NUM_NODES_PER_ELEMENT + NUM_VERTICES_PER_ELEMENT

static const size_t NUM_NODES_PER_BOUNDARY_ELEMENT = DIM*(DIM+1)/2

static const size_t BOUNDARY_STENCIL_SIZE = DIM*NUM_NODES_PER_BOUNDARY_ELEMENT + DIM

Friends

class TestNonlinearElasticitySolver

class TestNonlinearElasticityAdjointSolver

class AdaptiveNonlinearElasticityProblem

Detailed Description

template<size_t DIM>
class NonlinearElasticitySolver< DIM >

Finite elasticity solver. Solves static *incompressible* nonlinear elasticity problems with arbitrary (incompressible) material laws and a body force.

Uses quadratic-linear bases (for displacement and pressure), and is therefore outside other assembler or solver hierarchy.

Definition at line 53 of file NonlinearElasticitySolver.hpp.

Constructor & Destructor Documentation

template<size_t DIM>

NonlinearElasticitySolver< DIM >::NonlinearElasticitySolver	(	QuadraticMesh< DIM > *	pQuadMesh,
		AbstractIncompressibleMaterialLaw< DIM > *	pMaterialLaw,
		c_vector< double, DIM >	bodyForce,
		double	density,
		std::string	outputDirectory,
		std::vector< unsigned > &	fixedNodes,
		std::vector< c_vector< double, DIM > > *	pFixedNodeLocations = `NULL`
	)			`[inline]`

Constructor for homogeneous problems.

Parameters:

	pQuadMesh	The quadratic mesh to solve on
	pMaterialLaw	A single material law to use on all elements
	bodyForce	The body force if constant. (If not constant, pass in a zero vector and call SetFunctionalBodyForce()
	density	The density (assumed constant)
	outputDirectory	The output directory
	fixedNodes	Which nodes are fixed in space (the displacement is assumed to be zero unless the next parameter is given
	pFixedNodeLocations	Optional new locations of the fixed nodes.

Definition at line 710 of file NonlinearElasticitySolver.cpp.

References NonlinearElasticitySolver< DIM >::FormInitialGuess(), AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::Initialise(), and NonlinearElasticitySolver< DIM >::mMaterialLaws.

template<size_t DIM>

NonlinearElasticitySolver< DIM >::NonlinearElasticitySolver	(	QuadraticMesh< DIM > *	pQuadMesh,
		std::vector< AbstractIncompressibleMaterialLaw< DIM > * > &	rMaterialLaws,
		c_vector< double, DIM >	bodyForce,
		double	density,
		std::string	outputDirectory,
		std::vector< unsigned > &	fixedNodes,
		std::vector< c_vector< double, DIM > > *	pFixedNodeLocations = `NULL`
	)			`[inline]`

Variant constructor taking a vector of material laws for heterogeneous problems

Parameters:

	pQuadMesh	The quadratic mesh to solve on
	rMaterialLaws	Vector of material laws for each element
	bodyForce	The body force if constant. (If not constant, pass in a zero vector and call SetFunctionalBodyForce()
	density	The density (assumed constant)
	outputDirectory	The output directory
	fixedNodes	Which nodes are fixed in space (the displacement is assumed to be zero unless the next parameter is given
	pFixedNodeLocations	Optional new locations of the fixed nodes.

Definition at line 731 of file NonlinearElasticitySolver.cpp.

References NonlinearElasticitySolver< DIM >::FormInitialGuess(), AbstractTetrahedralMesh< ELEMENT_DIM, SPACE_DIM >::GetNumElements(), AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::Initialise(), and NonlinearElasticitySolver< DIM >::mMaterialLaws.

template<size_t DIM>

NonlinearElasticitySolver< DIM >::~NonlinearElasticitySolver ( ) [inline]

Destructor.

Definition at line 757 of file NonlinearElasticitySolver.cpp.

Member Function Documentation

template<size_t DIM>

void NonlinearElasticitySolver< DIM >::AssembleOnElement	(	Element< DIM, DIM > &	rElement,
		c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &	rAElem,
		c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &	rAElemPrecond,
		c_vector< double, STENCIL_SIZE > &	rBElem,
		bool	assembleResidual,
		bool	assembleJacobian
	)			`[inline, protected, virtual]`

Assemble residual or jacobian on an element, using the current solution stored in mCurrrentSolution. The ordering assumed is (in 2d) rBElem = [u0 v0 u1 v1 .. u5 v5 p0 p1 p2].

Parameters:

	rElement	The element to assemble on.
	rAElem	The element's contribution to the LHS matrix is returned in this n by n matrix, where n is the no. of nodes in this element. There is no need to zero this matrix before calling.
	rAElemPrecond	The element's contribution to the matrix passed to PetSC in creating a preconditioner
	rBElem	The element's contribution to the RHS vector is returned in this vector of length n, the no. of nodes in this element. There is no need to zero this vector before calling.
	assembleResidual	A bool stating whether to assemble the residual vector.
	assembleJacobian	A bool stating whether to assemble the Jacobian matrix.

Definition at line 213 of file NonlinearElasticitySolver.cpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

void NonlinearElasticitySolver< DIM >::AssembleOnBoundaryElement	(	BoundaryElement< DIM-1, DIM > &	rBoundaryElement,
		c_matrix< double, BOUNDARY_STENCIL_SIZE, BOUNDARY_STENCIL_SIZE > &	rAelem,
		c_vector< double, BOUNDARY_STENCIL_SIZE > &	rBelem,
		c_vector< double, DIM > &	rTraction,
		bool	assembleResidual,
		bool	assembleJacobian
	)			`[inline, protected, virtual]`

Compute the term from the surface integral of s*phi, where s is a specified non-zero surface traction (ie Neumann boundary condition) to be added to the Rhs vector.

Parameters:

	rBoundaryElement
	rAelem	The element's contribution to the LHS matrix is returned in this n by n matrix, where n is the no. of nodes in this element. There is no need to zero this matrix before calling.
	rBelem	The element's contribution to the RHS vector is returned in this vector of length n, the no. of nodes in this element. There is no need to zero this vector before calling.
	rTraction
	assembleResidual	A bool stating whether to assemble the residual vector.
	assembleJacobian	A bool stating whether to assemble the Jacobian matrix.

Definition at line 609 of file NonlinearElasticitySolver.cpp.

References QuadraticBasisFunction< ELEMENT_DIM >::ComputeBasisFunctions(), AbstractElement< ELEMENT_DIM, SPACE_DIM >::GetIndex(), AbstractElement< ELEMENT_DIM, SPACE_DIM >::GetNodeGlobalIndex(), GaussianQuadratureRule< ELEMENT_DIM >::GetNumQuadPoints(), GaussianQuadratureRule< ELEMENT_DIM >::GetWeight(), AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mCurrentTime, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mpBoundaryQuadratureRule, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mpQuadMesh, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mpTractionBoundaryConditionFunction, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mUsingTractionBoundaryConditionFunction, NonlinearElasticitySolver< DIM >::NUM_NODES_PER_BOUNDARY_ELEMENT, and GaussianQuadratureRule< ELEMENT_DIM >::rGetQuadPoint().

Referenced by NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

void NonlinearElasticitySolver< DIM >::FormInitialGuess ( ) [inline, protected]

Set up the current guess to be the solution given no displacement. The current solution (in 2d) is order as [u1 v1 u2 v2 ... uN vN p1 p2 .. pM] (where there are N total nodes and M vertices) so the initial guess is [0 0 0 0 ... 0 0 p1 p2 .. pM] where p_i are such that T is zero (depends on material law).

In a homogeneous problem, all p_i are the same. In a heterogeneous problem, p for a given vertex is the zero-strain-pressure for ONE of the elements containing that vertex (which element containing the vertex is reached LAST). In this case the initial guess will be close but not exactly the solution given zero body force.

Definition at line 673 of file NonlinearElasticitySolver.cpp.

References AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mCurrentSolution, NonlinearElasticitySolver< DIM >::mMaterialLaws, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mNumDofs, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mpQuadMesh, and NonlinearElasticitySolver< DIM >::NUM_VERTICES_PER_ELEMENT.

Referenced by NonlinearElasticitySolver< DIM >::NonlinearElasticitySolver().

template<size_t DIM>

void NonlinearElasticitySolver< DIM >::AssembleSystem	(	bool	assembleResidual,
		bool	assembleJacobian
	)			`[inline, protected, virtual]`

Assemble the residual vector (using the current solution stored in mCurrentSolution, output going to mpLinearSystem->rGetRhsVector), or Jacobian matrix (using the current solution stored in mCurrentSolution, output going to mpLinearSystem->rGetLhsMatrix).

Parameters:

	assembleResidual	A bool stating whether to assemble the residual vector.
	assembleJacobian	A bool stating whether to assemble the Jacobian matrix.

Implements AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >.

Definition at line 48 of file NonlinearElasticitySolver.cpp.

Referenced by ImplicitCardiacMechanicsSolver< DIM >::Solve(), and ExplicitCardiacMechanicsSolver< DIM >::Solve().

template<size_t DIM>

void NonlinearElasticitySolver< DIM >::ComputeStressAndStressDerivative	(	AbstractIncompressibleMaterialLaw< DIM > *	pMaterialLaw,
		c_matrix< double, DIM, DIM > &	rC,
		c_matrix< double, DIM, DIM > &	rInvC,
		double	pressure,
		unsigned	elementIndex,
		unsigned	currentQuadPointGlobalIndex,
		c_matrix< double, DIM, DIM > &	rT,
		FourthOrderTensor< DIM, DIM, DIM, DIM > &	rDTdE,
		bool	computeDTdE
	)			`[inline, protected, virtual]`

Simple (one-line function which just calls ComputeStressAndStressDerivative() on the material law, using C, inv(C), and p as the input and with rT and rDTdE as the output. Overloaded by other assemblers (eg cardiac mechanics) which need to add extra terms to the stress.

Parameters:

	pMaterialLaw	The material law for this element
	rC	The Lagrangian deformation tensor (F^T F)
	rInvC	The inverse of C. Should be computed by the user.
	pressure	The current pressure
	elementIndex	Index of the current element
	currentQuadPointGlobalIndex	The index (assuming an outer loop over elements and an inner loop over quadrature points), of the current quadrature point.
	rT	The stress will be returned in this parameter
	rDTdE	the stress derivative will be returned in this parameter, assuming the final parameter is true
	computeDTdE	A boolean flag saying whether the stress derivative is required or not.

Reimplemented in AbstractCardiacMechanicsSolver< DIM >.

Definition at line 593 of file NonlinearElasticitySolver.cpp.

References AbstractMaterialLaw< DIM >::ComputeStressAndStressDerivative().

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnElement().

template<size_t DIM>

std::vector< double > & NonlinearElasticitySolver< DIM >::rGetPressures ( ) [inline]

Get pressures for each vertex

Definition at line 796 of file NonlinearElasticitySolver.cpp.

References AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mCurrentSolution, AbstractNonlinearElasticitySolver< INCOMPRESSIBLE, DIM >::mpQuadMesh, and NonlinearElasticitySolver< DIM >::mPressures.

Member Data Documentation

template<size_t DIM>

const size_t NonlinearElasticitySolver< DIM >::NUM_VERTICES_PER_ELEMENT = DIM+1 [static, protected]

Number of vertices per element

Reimplemented in AbstractCardiacMechanicsSolver< DIM >.

Definition at line 62 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnElement(), NonlinearElasticitySolver< DIM >::AssembleSystem(), and NonlinearElasticitySolver< DIM >::FormInitialGuess().

template<size_t DIM>

const size_t NonlinearElasticitySolver< DIM >::NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2 [static, protected]

Number of nodes per element

Reimplemented in AbstractCardiacMechanicsSolver< DIM >.

Definition at line 64 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnElement(), and NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

const size_t NonlinearElasticitySolver< DIM >::STENCIL_SIZE = DIM*NUM_NODES_PER_ELEMENT + NUM_VERTICES_PER_ELEMENT [static, protected]

Stencil size - number of unknowns per element (DIM*NUM_NODES_PER_ELEMENT displacement unknowns, NUM_VERTICES_PER_ELEMENT pressure unknowns

Reimplemented in AbstractCardiacMechanicsSolver< DIM >.

Definition at line 67 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnElement(), and NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

const size_t NonlinearElasticitySolver< DIM >::NUM_NODES_PER_BOUNDARY_ELEMENT = DIM*(DIM+1)/2 [static, protected]

Number of nodes per boundary element

Definition at line 69 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnBoundaryElement(), and NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

const size_t NonlinearElasticitySolver< DIM >::BOUNDARY_STENCIL_SIZE = DIM*NUM_NODES_PER_BOUNDARY_ELEMENT + DIM [static, protected]

Boundary stencil size

Definition at line 71 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleSystem().

template<size_t DIM>

std::vector<AbstractIncompressibleMaterialLaw<DIM>*> NonlinearElasticitySolver< DIM >::mMaterialLaws [protected]

The material laws for each element. This will either be of size 1 (same material law for all elements, ie homogeneous), or size num_elem.

Definition at line 79 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::AssembleOnElement(), NonlinearElasticitySolver< DIM >::FormInitialGuess(), NonlinearElasticitySolver< DIM >::NonlinearElasticitySolver(), and AbstractCardiacMechanicsSolver< DIM >::~AbstractCardiacMechanicsSolver().

template<size_t DIM>

std::vector<double> NonlinearElasticitySolver< DIM >::mPressures [protected]

The solution pressures. mPressures[i] = pressure at node i (ie vertex i).

Definition at line 84 of file NonlinearElasticitySolver.hpp.

Referenced by NonlinearElasticitySolver< DIM >::rGetPressures().

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

pde/src/solver/NonlinearElasticitySolver.hpp
pde/src/solver/NonlinearElasticitySolver.cpp


Public Member Functions
	NonlinearElasticitySolver (QuadraticMesh< DIM > pQuadMesh, AbstractIncompressibleMaterialLaw< DIM > pMaterialLaw, c_vector< double, DIM > bodyForce, double density, std::string outputDirectory, std::vector< unsigned > &fixedNodes, std::vector< c_vector< double, DIM > > *pFixedNodeLocations=NULL)
	NonlinearElasticitySolver (QuadraticMesh< DIM > pQuadMesh, std::vector< AbstractIncompressibleMaterialLaw< DIM > > &rMaterialLaws, c_vector< double, DIM > bodyForce, double density, std::string outputDirectory, std::vector< unsigned > &fixedNodes, std::vector< c_vector< double, DIM > > *pFixedNodeLocations=NULL)
	~NonlinearElasticitySolver ()
std::vector< double > &	rGetPressures ()
Protected Member Functions
virtual void	AssembleOnElement (Element< DIM, DIM > &rElement, c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &rAElem, c_matrix< double, STENCIL_SIZE, STENCIL_SIZE > &rAElemPrecond, c_vector< double, STENCIL_SIZE > &rBElem, bool assembleResidual, bool assembleJacobian)
virtual void	AssembleOnBoundaryElement (BoundaryElement< DIM-1, DIM > &rBoundaryElement, c_matrix< double, BOUNDARY_STENCIL_SIZE, BOUNDARY_STENCIL_SIZE > &rAelem, c_vector< double, BOUNDARY_STENCIL_SIZE > &rBelem, c_vector< double, DIM > &rTraction, bool assembleResidual, bool assembleJacobian)
void	FormInitialGuess ()
void	AssembleSystem (bool assembleResidual, bool assembleJacobian)
virtual void	ComputeStressAndStressDerivative (AbstractIncompressibleMaterialLaw< DIM > *pMaterialLaw, c_matrix< double, DIM, DIM > &rC, c_matrix< double, DIM, DIM > &rInvC, double pressure, unsigned elementIndex, unsigned currentQuadPointGlobalIndex, c_matrix< double, DIM, DIM > &rT, FourthOrderTensor< DIM, DIM, DIM, DIM > &rDTdE, bool computeDTdE)
Protected Attributes
std::vector < AbstractIncompressibleMaterialLaw < DIM > * >	mMaterialLaws
std::vector< double >	mPressures
Static Protected Attributes
static const size_t	NUM_VERTICES_PER_ELEMENT = DIM+1
static const size_t	NUM_NODES_PER_ELEMENT = (DIM+1)*(DIM+2)/2
static const size_t	STENCIL_SIZE = DIM*NUM_NODES_PER_ELEMENT + NUM_VERTICES_PER_ELEMENT
static const size_t	NUM_NODES_PER_BOUNDARY_ELEMENT = DIM*(DIM+1)/2
static const size_t	BOUNDARY_STENCIL_SIZE = DIM*NUM_NODES_PER_BOUNDARY_ELEMENT + DIM
Friends
class	TestNonlinearElasticitySolver
class	TestNonlinearElasticityAdjointSolver
class	AdaptiveNonlinearElasticityProblem

NonlinearElasticitySolver< DIM > Class Template Reference

Public Member Functions

Protected Member Functions

Protected Attributes

Static Protected Attributes

Friends

Detailed Description

template<size_t DIM> class NonlinearElasticitySolver< DIM >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<size_t DIM>
class NonlinearElasticitySolver< DIM >