Class for creating an triaxial plastic bounding surface material for three-dimensional elements. More...

#include <Plastic3DBA.hpp>

Inheritance diagram for Plastic3DBA:

Collaboration diagram for Plastic3DBA:

Public Member Functions
	Plastic3DBA (const double K, const double G, const double rho, const double H0, const double h, const double m, const double Su, const double beta)
	Creates a Plastic3DBA material to be specified at a Gauss-point in an Element. More...

	~Plastic3DBA ()
	Destroys this Plastic3DBA material. More...

std::unique_ptr< Material >	CopyMaterial ()

double	GetDensity () const
	Access material density. More...

double	GetPoissonRatio () const
	Returns the Poisson's ratio. More...

double	GetBulkModulus () const
	Access bulk modulus. More...

double	GetShearModulus () const
	Access shear modulus. More...

double	GetElasticityModulus () const
	Access modulus of elasticity. More...

double	GetEnergy () const
	Access the material's energy at current strain. More...

Eigen::MatrixXd	GetDamping () const
	Returns the material viscous damping. More...

Eigen::VectorXd	GetStrain () const
	Returns the material strain. More...

Eigen::VectorXd	GetStress () const
	Returns the material stress. More...

Eigen::VectorXd	GetStrainRate () const
	Returns the material strain rate. More...

Eigen::VectorXd	GetTotalStress () const
	Computes the material total stress. More...

Eigen::MatrixXd	GetTangentStiffness () const
	Returns the material stiffness. More...

Eigen::MatrixXd	GetInitialTangentStiffness () const
	Returns the initial material stiffness. More...

void	CommitState ()
	Perform converged material state update. More...

void	ReverseState ()
	Reverse the material states to previous converged state. More...

void	InitialState ()
	Brings the material states to its initial state in the element. More...

void	UpdateState (const Eigen::VectorXd strain, const unsigned int cond)
	Update the material state for this iteration. More...

Public Member Functions inherited from Material
	Material (std::string name, bool model)
	Creates a Material to be specified at a Gauss-point in an Element. More...

virtual	~Material ()=0
	Destroys this Material object. More...

std::string	GetName ()
	Gets material information. More...

bool	IsViscous ()
	Gets material stress model. More...

Protected Member Functions
Eigen::VectorXd	ComputeIdentityVector () const
	Constructs a Second Order Identity Tensor. More...

Eigen::MatrixXd	ComputeDeviatoricTensor () const
	Constructs deviatoric tensor. More...

Eigen::MatrixXd	ComputeIdentityTensor () const
	Constructs fourth-rank identity tensor. More...

Eigen::MatrixXd	ComputeIdentityOperator () const
	Constructs fourth-rank symmetric identity operator. More...

double	ComputeTensorTrace (const Eigen::VectorXd &T)
	Computes the trace of a tensor of second-rank. More...

double	ComputeTensorNorm (const Eigen::VectorXd &T)
	Computes the norm of a tensor of second-rank. More...

double	ComputeInnerProduct (const Eigen::VectorXd &V1, const Eigen::VectorXd &V2)
	Compute inner product of two tensor of first-rank. More...

Eigen::VectorXd	ComputeHardening (Eigen::VectorXd const &DeviatoricIncrStrain, const Eigen::VectorXd &DeviatoricStress)
	Compute hardening using the Newton-Rhapson method. More...

Eigen::VectorXd	ComputeHardeningBisection (Eigen::VectorXd const &DeviatoricIncrStrain, const Eigen::VectorXd &DeviatoricStress)
	Compute hardening using the bi-section method. More...

Private Attributes
double	K
	Bulk modulus. More...

double	G
	Shear modulus. More...

double	Rho
	Material density. More...

double	H0
	Bounding surface hardening. More...

double	h
	Exponential hardening parameter. More...

double	m
	Exponential hardening parameter. More...

double	Su
	Undrained soil strength. More...

double	R
	Bounding surface radius. More...

double	beta
	The integration factor. More...

double	psi
	Internal hardening parameters. More...

double	kappa
	Internal hardening parameters. More...

double	psi_n
	Internal hardening parameter at time n. More...

double	kappa_n
	Internal hardening parameter at time n. More...

Eigen::VectorXd	Strain
	Strain vector. More...

Eigen::VectorXd	Strain_n
	Strain at time n. More...

Eigen::VectorXd	Stress
	Trial stress vector. More...

Eigen::VectorXd	Stress_n
	Stress vector at time n. More...

Eigen::VectorXd	DeviatoricStress0
	Stress tensor at F0. More...

Eigen::VectorXd	DeviatoricStress0_n
	Stress tensor at F0 at time n. More...

Eigen::MatrixXd	TangentStiffness
	Consistent tangent stiffness. More...

Eigen::MatrixXd	TangentStiffness_n
	Consistent tangent stiffness at time n. More...

int	FirstLoadFlag
	First loading flag. More...

int	FirstLoadFlag_n
	First loading flag at time n. More...

int	rootFlag
	Flag to control the linear system solution. More...

int	rootFlag_n
	Flag to control the linear system solution at time n. More...

double	Hn
	The hardening function. More...

Detailed Description

Class for creating an triaxial plastic bounding surface material for three-dimensional elements.

See also: Material.hpp

Constructor & Destructor Documentation

◆ Plastic3DBA()

Plastic3DBA::Plastic3DBA	(	const double	K,
		const double	G,
		const double	rho,
		const double	H0,
		const double	h,
		const double	m,
		const double	Su,
		const double	beta
	)

Creates a Plastic3DBA material to be specified at a Gauss-point in an Element.

Parameters

K	The material bulk modulus.
G	The material shear modulus.
rho	The material density.
H0	The bounding surface hardening.
h	The hardening parameter.
m	The exponential hardening parameter.
Su	Undrained soil strength.
beta	The integration factor.

See also: Plastic3DBA::K, Plastic3DBA::G, Plastic3DBA::Rho, Plastic3DBA::H0, Plastic3DBA::h, Plastic3DBA::m, Plastic3DBA::Su, Plastic3DBA::R, Plastic3DBA::beta.

◆ ~Plastic3DBA()

Plastic3DBA::~Plastic3DBA ( )

Destroys this Plastic3DBA material.

Member Function Documentation

◆ CommitState()

void Plastic3DBA::CommitState ( )

virtual

Perform converged material state update.

Note: This function sets the trail stress and strain as converged.

See also: Plastic3DBA::Strain_n, Plastic3DBA::Stress_n.

Implements Material.

◆ ComputeDeviatoricTensor()

Eigen::MatrixXd Plastic3DBA::ComputeDeviatoricTensor ( ) const

protected

Constructs deviatoric tensor.

Returns: The deviatoric tensor.

◆ ComputeHardening()

Eigen::VectorXd Plastic3DBA::ComputeHardening	(	Eigen::VectorXd const &	DeviatoricIncrStrain,
		const Eigen::VectorXd &	DeviatoricStress
	)

protected

Compute hardening using the Newton-Rhapson method.

Parameters

DeviatoricIncrStrain	The deviatoric incremental strain.
DeviatoricStress	The deviatoric stress.

Returns: Vector that contains kappa and psi using Newton-Rhapson method.

◆ ComputeHardeningBisection()

Eigen::VectorXd Plastic3DBA::ComputeHardeningBisection	(	Eigen::VectorXd const &	DeviatoricIncrStrain,
		const Eigen::VectorXd &	DeviatoricStress
	)

protected

Compute hardening using the bi-section method.

Parameters

DeviatoricIncrStrain	The deviatoric incremental strain.
DeviatoricStress	The deviatoric stress.

Returns: Vector that contains kappa and psi using bisection method.

◆ ComputeIdentityOperator()

Eigen::MatrixXd Plastic3DBA::ComputeIdentityOperator ( ) const

protected

Constructs fourth-rank symmetric identity operator.

Returns: A rank-four tensor.

◆ ComputeIdentityTensor()

Eigen::MatrixXd Plastic3DBA::ComputeIdentityTensor ( ) const

protected

Constructs fourth-rank identity tensor.

Returns: A rank-four tensor.

◆ ComputeIdentityVector()

Eigen::VectorXd Plastic3DBA::ComputeIdentityVector ( ) const

protected

Constructs a Second Order Identity Tensor.

Returns: The identity second-rank tensor.

◆ ComputeInnerProduct()

double Plastic3DBA::ComputeInnerProduct	(	const Eigen::VectorXd &	V1,
		const Eigen::VectorXd &	V2
	)

protected

Compute inner product of two tensor of first-rank.

Parameters

V1	A first-rank tensor.
V2	A first-rank tensor.

Returns: An scalar with the inner product.

◆ ComputeTensorNorm()

double Plastic3DBA::ComputeTensorNorm ( const Eigen::VectorXd & T )

protected

Computes the norm of a tensor of second-rank.

Parameters

T	A second-rank tensor.

Returns: An scalar with the norm.

◆ ComputeTensorTrace()

double Plastic3DBA::ComputeTensorTrace ( const Eigen::VectorXd & T )

protected

Computes the trace of a tensor of second-rank.

Parameters

T	A second-rank tensor.

Returns: An scalar with the trace.

◆ CopyMaterial()

std::unique_ptr<Material> Plastic3DBA::CopyMaterial ( )

virtual

Returns: A Material pointer to the Plastic3DBA derived class.

See also: Material, Plastic3DBA.

Implements Material.

◆ GetBulkModulus()

double Plastic3DBA::GetBulkModulus ( ) const

virtual

Access bulk modulus.

Returns: The material bulk's modulus.

See also: Plastic3DBA::K.

Implements Material.

◆ GetDamping()

Eigen::MatrixXd Plastic3DBA::GetDamping ( ) const

virtual

Returns the material viscous damping.

Returns: Vector with the material damping components.

Implements Material.

◆ GetDensity()

double Plastic3DBA::GetDensity ( ) const

virtual

Access material density.

Returns: The material density value.

See also: Plastic3DBA::Rho.

Implements Material.

◆ GetElasticityModulus()

double Plastic3DBA::GetElasticityModulus ( ) const

virtual

Access modulus of elasticity.

Returns: The material Elasticity's modulus.

Implements Material.

◆ GetEnergy()

double Plastic3DBA::GetEnergy ( ) const

virtual

Access the material's energy at current strain.

Returns: Scalar with the material energy value.

Implements Material.

◆ GetInitialTangentStiffness()

Eigen::MatrixXd Plastic3DBA::GetInitialTangentStiffness ( ) const

virtual

Returns the initial material stiffness.

Returns: Matrix with the initial material tangent stiffness matrix.

Note: The initial tangent stiffness matrix is computed when the strain vector is zero.

Implements Material.

◆ GetPoissonRatio()

double Plastic3DBA::GetPoissonRatio ( ) const

virtual

Returns the Poisson's ratio.

Returns: The material poisson's ratio.

Implements Material.

◆ GetShearModulus()

double Plastic3DBA::GetShearModulus ( ) const

virtual

Access shear modulus.

Returns: The material shear's modulus.

See also: Plastic3DBA::G.

Implements Material.

◆ GetStrain()

Eigen::VectorXd Plastic3DBA::GetStrain ( ) const

virtual

Returns the material strain.

Returns: Vector with the material strain components.

Note: The strain can be revisited in Plastic3DBA.

See also: Plastic3DBA::Strain.

Implements Material.

◆ GetStrainRate()

Eigen::VectorXd Plastic3DBA::GetStrainRate ( ) const

virtual

Returns the material strain rate.

Returns: Vector with the material strain-rate components.

Note: The strain can be revisited in Plastic3DBA.

Implements Material.

◆ GetStress()

Eigen::VectorXd Plastic3DBA::GetStress ( ) const

virtual

Returns the material stress.

Returns: Vector with the material stress components.

Note: The strain can be revisited in Plastic3DBA.

See also: Plastic3DBA::Stress.

Implements Material.

◆ GetTangentStiffness()

Eigen::MatrixXd Plastic3DBA::GetTangentStiffness ( ) const

virtual

Returns the material stiffness.

Returns: Matrix with the material consistent tangent stiffness matrix.

Note: The stiffness matrix can be revisited in Plastic3DBA.

See also: Plastic3DBA::TangentStiffness.

Implements Material.

◆ GetTotalStress()

Eigen::VectorXd Plastic3DBA::GetTotalStress ( ) const

virtual

Computes the material total stress.

Returns: Vector with the material total stress components.

See also: Plastic3DBA::Stress.

Implements Material.

◆ InitialState()

void Plastic3DBA::InitialState ( )

virtual

Brings the material states to its initial state in the element.

Note: This funtion returns the material states to the beginning.

Implements Material.

◆ ReverseState()

void Plastic3DBA::ReverseState ( )

virtual

Reverse the material states to previous converged state.

Note: This funtion returns the material states to previous converged states.

Implements Material.

◆ UpdateState()

void Plastic3DBA::UpdateState	(	const Eigen::VectorXd	strain,
		const unsigned int	cond
	)

virtual

Update the material state for this iteration.

Parameters

strain	Vector with the strain components at this Gauss-point.
cond	If the the elastic/plastic material components will be updated.

Note: This function computes the strain and tanget stiffness matrix once the trial strain converged.

Implements Material.

Member Data Documentation

◆ beta

double Plastic3DBA::beta

private

The integration factor.

◆ DeviatoricStress0

Eigen::VectorXd Plastic3DBA::DeviatoricStress0

private

Stress tensor at F0.

◆ DeviatoricStress0_n

Eigen::VectorXd Plastic3DBA::DeviatoricStress0_n

private

Stress tensor at F0 at time n.

◆ FirstLoadFlag

int Plastic3DBA::FirstLoadFlag

private

First loading flag.

◆ FirstLoadFlag_n

int Plastic3DBA::FirstLoadFlag_n

private

First loading flag at time n.

◆ G

double Plastic3DBA::G

private

Shear modulus.

◆ h

double Plastic3DBA::h

private

Exponential hardening parameter.

◆ H0

double Plastic3DBA::H0

private

Bounding surface hardening.

◆ Hn

double Plastic3DBA::Hn

private

The hardening function.

◆ K

double Plastic3DBA::K

private

Bulk modulus.

◆ kappa

double Plastic3DBA::kappa

private

Internal hardening parameters.

◆ kappa_n

double Plastic3DBA::kappa_n

private

Internal hardening parameter at time n.

◆ m

double Plastic3DBA::m

private

Exponential hardening parameter.

◆ psi

double Plastic3DBA::psi

private

Internal hardening parameters.

◆ psi_n

double Plastic3DBA::psi_n

private

Internal hardening parameter at time n.

◆ R

double Plastic3DBA::R

private

Bounding surface radius.

◆ Rho

double Plastic3DBA::Rho

private

Material density.

◆ rootFlag

int Plastic3DBA::rootFlag

private

Flag to control the linear system solution.

◆ rootFlag_n

int Plastic3DBA::rootFlag_n

private

Flag to control the linear system solution at time n.

◆ Strain

Eigen::VectorXd Plastic3DBA::Strain

private

Strain vector.

◆ Strain_n

Eigen::VectorXd Plastic3DBA::Strain_n

private

Strain at time n.

◆ Stress

Eigen::VectorXd Plastic3DBA::Stress

private

Trial stress vector.

◆ Stress_n

Eigen::VectorXd Plastic3DBA::Stress_n

private

Stress vector at time n.

◆ Su

double Plastic3DBA::Su

private

Undrained soil strength.

◆ TangentStiffness

Eigen::MatrixXd Plastic3DBA::TangentStiffness

private

Consistent tangent stiffness.

◆ TangentStiffness_n

Eigen::MatrixXd Plastic3DBA::TangentStiffness_n

private

Consistent tangent stiffness at time n.

Public Member Functions

Protected Member Functions

Private Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Plastic3DBA()

◆ ~Plastic3DBA()

Member Function Documentation

◆ CommitState()

◆ ComputeDeviatoricTensor()

◆ ComputeHardening()

◆ ComputeHardeningBisection()

◆ ComputeIdentityOperator()

◆ ComputeIdentityTensor()

◆ ComputeIdentityVector()

◆ ComputeInnerProduct()

◆ ComputeTensorNorm()

◆ ComputeTensorTrace()

◆ CopyMaterial()

◆ GetBulkModulus()

◆ GetDamping()

◆ GetDensity()

◆ GetElasticityModulus()

◆ GetEnergy()

◆ GetInitialTangentStiffness()

◆ GetPoissonRatio()

◆ GetShearModulus()

◆ GetStrain()

◆ GetStrainRate()

◆ GetStress()

◆ GetTangentStiffness()

◆ GetTotalStress()

◆ InitialState()

◆ ReverseState()

◆ UpdateState()

Member Data Documentation

◆ beta

◆ DeviatoricStress0

◆ DeviatoricStress0_n

◆ FirstLoadFlag

◆ FirstLoadFlag_n

◆ G

◆ h

◆ H0

◆ Hn

◆ K

◆ kappa

◆ kappa_n

◆ m

◆ psi

◆ psi_n

◆ R

◆ Rho

◆ rootFlag

◆ rootFlag_n

◆ Strain

◆ Strain_n

◆ Stress

◆ Stress_n

◆ Su

◆ TangentStiffness

◆ TangentStiffness_n