Small strain plasticity with paraboloidal yield criterion (Isotropic Hardening) More...

#include <users_modules/small_strain_plasticity/src/SmallStrainPlasticityMaterialModels.hpp>

Inheritance diagram for SmallStrainParaboloidalPlasticity:

Collaboration diagram for SmallStrainParaboloidalPlasticity:

Public Member Functions
	SmallStrainParaboloidalPlasticity ()

virtual PetscErrorCode	freeHemholtzEnergy ()
	Available energy. More...

PetscErrorCode	evalF ()

virtual PetscErrorCode	yieldFunction ()
	Evaluate yield function. More...

virtual PetscErrorCode	flowPotential ()
	Flow potential. More...

Public Member Functions inherited from SmallStrainPlasticity::ClosestPointProjection
	ClosestPointProjection ()

virtual PetscErrorCode	setActiveVariablesW ()

virtual PetscErrorCode	setActiveVariablesYH ()

virtual PetscErrorCode	rEcordW ()

virtual PetscErrorCode	rEcordY ()

virtual PetscErrorCode	rEcordH ()

virtual PetscErrorCode	pLayW ()

virtual PetscErrorCode	pLayW_NoHessian ()

virtual PetscErrorCode	pLayY ()

virtual PetscErrorCode	pLayY_NoGradient ()

virtual PetscErrorCode	pLayH ()

virtual PetscErrorCode	createMatAVecR ()

virtual PetscErrorCode	destroyMatAVecR ()

virtual PetscErrorCode	evaluatePotentials ()

virtual PetscErrorCode	cAlculateR (Vec R)

virtual PetscErrorCode	cAlculateA ()

PetscErrorCode	snesCreate ()

PetscErrorCode	snesDestroy ()

PetscErrorCode	solveColasetProjection ()

PetscErrorCode	consistentTangent ()

Public Attributes
double	mu

double	lambda

double	nup

double	Ht

double	Hc

double	sIgma_yt

double	sIgma_yc

double	nt

double	nc

adouble	I1
	Auxiliary function. More...

adouble	J2

Public Attributes inherited from SmallStrainPlasticity::ClosestPointProjection
VectorDouble	sTrain

VectorDouble	internalVariables

VectorDouble	internalVariables0

VectorDouble	plasticStrain0

VectorDouble	plasticStrain

double	deltaGamma

double	tOl

int	gG

VectorAdaptor	sTress

VectorAdaptor	internalFluxes

ublas::symmetric_matrix< double, ublas::lower >	C

ublas::symmetric_matrix< double, ublas::lower >	D

MatrixDouble	partialWStrainPlasticStrain

VectorAdaptor	partialYSigma

VectorAdaptor	partialYFlux

VectorAdaptor	partialHSigma

VectorAdaptor	partialHFlux

ublas::symmetric_matrix< double, ublas::lower >	partial2HSigma

ublas::symmetric_matrix< double, ublas::lower >	partial2HFlux

MatrixDouble	partial2HSigmaFlux

vector< int >	tAgs

VectorDouble	activeVariablesW

VectorDouble	activeVariablesYH

double	w

double	y

double	h

ublas::vector< adouble >	a_sTrain

ublas::vector< adouble >	a_plasticStrain

ublas::vector< adouble >	a_internalVariables

ublas::vector< adouble >	a_sTress

ublas::vector< adouble >	a_internalFluxes

adouble	a_w

adouble	a_y

adouble	a_h

VectorDouble	gradientW

MatrixDouble	hessianW

VectorDouble	gradientY

VectorDouble	gradientH

MatrixDouble	hessianH

Mat	A

ublas::matrix< double, ublas::column_major >	dataA

Vec	R

Vec	Chi

Vec	dChi

SNES	sNes

KSP	kSp

PC	pC

SNESLineSearch	lineSearch

MatrixDouble	Ep

MatrixDouble	Lp

MatrixDouble	Cp

MatrixDouble	Cep

VectorDouble	Yp

Detailed Description

Small strain plasticity with paraboloidal yield criterion (Isotropic Hardening)

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 162 of file SmallStrainPlasticityMaterialModels.hpp.

Constructor & Destructor Documentation

◆ SmallStrainParaboloidalPlasticity()

SmallStrainParaboloidalPlasticity::SmallStrainParaboloidalPlasticity ( )

inline

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 164 of file SmallStrainPlasticityMaterialModels.hpp.

                                      :
   SmallStrainPlasticity::ClosestPointProjection() {
     internalVariables.resize(2,false);
     internalVariables.clear();
   }

Member Function Documentation

◆ evalF()

PetscErrorCode SmallStrainParaboloidalPlasticity::evalF ( )

inline

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 269 of file SmallStrainPlasticityMaterialModels.hpp.

                          {
     PetscFunctionBegin;
     adouble tR = 0;
     for(int dd = 0;dd<3;dd++) {
       tR += a_sTress[dd];
     }
     I1=tR;
  
     tR /= 3.;
     J2 = 0;
     adouble t;
     for(int dd = 0;dd<3;dd++) {
       t = (a_sTress[dd]-tR);
       J2 += t*t;
     }
    for(int dd = 3;dd<6;dd++) {
       J2 += 2.*a_sTress[dd]*a_sTress[dd]; // s:s off diagonal terms need to go twice
     }
     J2=0.5*J2;
  
     PetscFunctionReturn(0);
   }

◆ flowPotential()

virtual PetscErrorCode SmallStrainParaboloidalPlasticity::flowPotential ( )

inlinevirtual

Flow potential.

\[ \Psi = 6J_2 + 2\alpha I_1 \left(\overline{\alpha_1}-\overline{\alpha_0}\right) - 2\overline{\alpha_0} \,\overline{\alpha_1} \]

\[ \alpha= \frac{1-2\nu_p}{1+\nu_p} \]

Reimplemented from SmallStrainPlasticity::ClosestPointProjection.

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 327 of file SmallStrainPlasticityMaterialModels.hpp.

                                          {
     PetscFunctionBegin;
     ierr = evalF(); CHKERRQ(ierr);
     double alpha= (1-2*nup)/(1+nup); //relation between alpha and plastic Poission's ratio
     a_h =6*J2 + 2*alpha*I1*(a_internalFluxes[1]-a_internalFluxes[0]) - 2*a_internalFluxes[0]*a_internalFluxes[1];
     PetscFunctionReturn(0);
   }

◆ freeHemholtzEnergy()

virtual PetscErrorCode SmallStrainParaboloidalPlasticity::freeHemholtzEnergy ( )

inlinevirtual

Available energy.

\[ \psi = \frac{1}{2} \lambda \textrm{tr}[\varepsilon]^2 + \mu \varepsilon : \varepsilon + \sigma_{yt}\alpha_0 + \frac{1}{2} H_t \alpha_0^2 + \sigma_{yc}\alpha_1 + \frac{1}{2} H_c \alpha_1^2 \]

Energy with linear hardening

Reimplemented from SmallStrainPlasticity::ClosestPointProjection.

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 224 of file SmallStrainPlasticityMaterialModels.hpp.

                                               {
     PetscFunctionBegin;
     //elastic part
     adouble tR = 0;
     for(int dd = 0;dd<3;dd++) {
       tR += a_sTrain[dd]-a_plasticStrain[dd];
     }
     a_w = 0.5*lambda*tR*tR;
     adouble t;
     int dd = 0;
     for(;dd<3;dd++) {
       t = a_sTrain[dd]-a_plasticStrain[dd];
       a_w += mu*t*t;
     }
     for(;dd<6;dd++) {
       t = a_sTrain[dd]-a_plasticStrain[dd];
       a_w += 0.5*mu*t*t;
     }
     //plastic part
     //isotropic
 //    a_w += a_internalVariables[0]*sIgma_yt + 0.5*Ht*a_internalVariables[0]*a_internalVariables[0];
 //    a_w += a_internalVariables[1]*sIgma_yc + 0.5*Hc*a_internalVariables[1]*a_internalVariables[1];
     a_w +=(sIgma_yt+Ht)*a_internalVariables[0] + (Ht/nt)*exp(-nt*a_internalVariables[0]);
     a_w +=(sIgma_yc+Hc)*a_internalVariables[1] + (Hc/nc)*exp(-nc*a_internalVariables[1]);
  
     PetscFunctionReturn(0);
   }

◆ yieldFunction()

virtual PetscErrorCode SmallStrainParaboloidalPlasticity::yieldFunction ( )

inlinevirtual

Evaluate yield function.

\[ y = 6J_2 + 2I_1\left(\overline{\alpha_1}-\overline{\alpha_0}\right) - 2\overline{\alpha_0} \,\overline{\alpha_1} \]

where

\[ \overline{\alpha_0}=\frac{\partial \psi}{\partial \alpha_0}=\sigma_{yt} + H_t \alpha_0 \]

\[ \overline{\alpha_1}=\frac{\partial \psi}{\partial \alpha_1}=\sigma_{yc} + H_c \alpha_1 \]

Reimplemented from SmallStrainPlasticity::ClosestPointProjection.

Examples: SmallStrainPlasticityMaterialModels.hpp.

Definition at line 309 of file SmallStrainPlasticityMaterialModels.hpp.

                                          {
     PetscFunctionBegin;
     ierr = evalF(); CHKERRQ(ierr);
     a_y = 6*J2 + 2*I1*(a_internalFluxes[1]-a_internalFluxes[0]) - 2*a_internalFluxes[0]*a_internalFluxes[1];
     PetscFunctionReturn(0);
   }