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BoyceAndArruda.h
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BoyceAndArruda.h
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/******************************************************************************
* SOFA, Simulation Open-Framework Architecture *
* (c) 2006 INRIA, USTL, UJF, CNRS, MGH *
* *
* This program is free software; you can redistribute it and/or modify it *
* under the terms of the GNU Lesser General Public License as published by *
* the Free Software Foundation; either version 2.1 of the License, or (at *
* your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, but WITHOUT *
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or *
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License *
* for more details. *
* *
* You should have received a copy of the GNU Lesser General Public License *
* along with this program. If not, see <http://www.gnu.org/licenses/>. *
*******************************************************************************
* Authors: The SOFA Team and external contributors (see Authors.txt) *
* *
* Contact information: contact@sofa-framework.org *
******************************************************************************/
#pragma once
#include <sofa/component/solidmechanics/fem/hyperelastic/config.h>
#include <sofa/component/solidmechanics/fem/hyperelastic/material/HyperelasticMaterial.h>
#include <sofa/type/Vec.h>
#include <sofa/type/Mat.h>
#include <string>
namespace sofa::component::solidmechanics::fem::hyperelastic::material
{
/** a Class that describe a generic hyperelastic material : exemple of Boyce and Arruda
The material is described based on continuum mechanics and the description is independent
to any discretization method like the finite element method.
A material is generically described by a strain energy function and its first and second derivatives.
In practice the energy is the sum of several energy terms which depends on 2 quantities :
the determinant of the deformation gradient J and the right Cauchy Green deformation tensor */
template<class DataTypes>
class BoyceAndArruda : public HyperelasticMaterial<DataTypes>{
public:
static constexpr std::string_view Name = "ArrudaBoyce";
typedef typename DataTypes::Coord::value_type Real;
typedef type::Mat<3,3,Real> Matrix3;
typedef type::Mat<6,6,Real> Matrix6;
typedef type::MatSym<3,Real> MatrixSym;
virtual Real getStrainEnergy(StrainInformation<DataTypes> *sinfo, const MaterialParameters<DataTypes> ¶m) {
Real I1=sinfo->trC;
Real mu=param.parameterArray[0];
Real k0=param.parameterArray[1];
return (Real)mu*((Real)(1.0/2.0)*(pow(sinfo->J,(Real)(-2.0/3.0))*I1-3)+(Real)(1.0/160.0)*(pow(sinfo->J,(Real)(-4.0/3.0))*I1*I1-9)+(Real)(11.0/(1050.0*8*8))*(pow(sinfo->J,(Real)-(Real)2.0)*I1*I1*I1-27)
+(Real)(19.0/(7000.0*8.0*8.0*8.0))*(pow(sinfo->J,(Real)(-8.0/3.0))*pow(I1,(Real)4.0)-pow((Real)3,(Real)4))+(Real)(519.0/(673750.0*8.0*8.0*8.0*8.0))*(pow(sinfo->J,(Real)(-10.0/3.0))*pow(I1,(Real)5.0)-pow((Real)3,(Real)5)))
+k0*log(sinfo->J)*log(sinfo->J)/2;
}
virtual void deriveSPKTensor(StrainInformation<DataTypes> *sinfo, const MaterialParameters<DataTypes> ¶m,MatrixSym &SPKTensorGeneral){
MatrixSym inversematrix;
MatrixSym C=sinfo->deformationTensor;
invertMatrix(inversematrix,C);
Real I1=sinfo->trC;
Real mu=param.parameterArray[0];
Real k0=param.parameterArray[1];
MatrixSym ID;
ID.identity();
SPKTensorGeneral=((inversematrix*(Real)(-1.0/3.0)*I1+ID)*(Real)(1.0/2.0)*pow(sinfo->J,(Real)(-2.0/3.0))+(inversematrix*(Real)(-2.0/3.0)*I1*I1+ID*(Real)2.0*I1)*(Real)(1.0/160.0)*pow(sinfo->J,(Real)(-4.0/3.0))+(ID*(Real)3.0*I1*I1-inversematrix*I1*I1*I1)*(Real)(11.0/(1050.0*8*8))*pow(sinfo->J,(Real)(-2.0))
+(inversematrix*(Real)(-4.0/3.0)*pow(I1,(Real)4.0)+ID*(Real)4.0*pow(I1,(Real)3.0))*(Real)(19.0/(7000.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-8.0/3.0))+(inversematrix*(Real)(-5.0/3.0)*pow(I1,(Real)5.0)+ID*(Real)5.0*pow(I1,(Real)4.0))*(Real)(519.0/(673750.0*8.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-10.0/3.0)))*2.0*mu
+inversematrix*k0*log(sinfo->J);
}
virtual void applyElasticityTensor(StrainInformation<DataTypes> *sinfo, const MaterialParameters<DataTypes> ¶m,const MatrixSym& inputTensor, MatrixSym &outputTensor) {
MatrixSym inversematrix;
MatrixSym C=sinfo->deformationTensor;
invertMatrix(inversematrix,C);
Real I1=sinfo->trC;
Real mu=param.parameterArray[0];
Real k0=param.parameterArray[1];
MatrixSym ID;
ID.identity();
// C-1:H
Real _trHC=inputTensor[0]*inversematrix[0]+inputTensor[2]*inversematrix[2]+inputTensor[5]*inversematrix[5]
+2*inputTensor[1]*inversematrix[1]+2*inputTensor[3]*inversematrix[3]+2*inputTensor[4]*inversematrix[4];
MatrixSym Firstmatrix;
//C-1HC-1 convert to sym matrix
Firstmatrix.Mat2Sym(inversematrix.SymMatMultiply(inputTensor.SymSymMultiply(inversematrix)),Firstmatrix);
//trH
Real trH=inputTensor[0]+inputTensor[2]+inputTensor[5];
outputTensor=(((inversematrix*(Real)(-1.0/3.0)*I1+ID)*(Real)(-1.0/3.0)*_trHC-inversematrix*(Real)(1.0/3.0)*trH+Firstmatrix*(Real)(1.0/3.0)*I1)*(Real)(1.0/2.0)*pow(sinfo->J,(Real)(-2.0/3.0))
+((inversematrix*(Real)(-2.0/3.0)*I1*I1+ID*(Real)2.0*I1)*(Real)(-2.0/3.0)*_trHC-inversematrix*(Real)(4.0/3.0)*I1*trH+Firstmatrix*(Real)(2.0/3.0)*I1*I1+ID*(Real)(2.0)*trH)*(Real)(1.0/160.0)*pow(sinfo->J,(Real)(-4.0/3.0))
+((inversematrix*(Real)(-I1)*I1*I1+ID*(Real)3.0*I1*I1)*(-_trHC)-inversematrix*(Real)3.0*I1*I1*trH+Firstmatrix*I1*I1*I1+ID*(Real)6.0*I1*trH)*(Real)(11.0/(1050.0*8.0*8.0))*pow(sinfo->J,(Real)-2.0)
+((inversematrix*(Real)(-4.0/3.0)*pow(I1,(Real)4.0)+ID*(Real)4.0*pow(I1,(Real)3))*(Real)(-4.0/3.0)*_trHC-inversematrix*(Real)(16.0/3.0)*pow(I1,(Real)3.0)*trH+Firstmatrix*(Real)(4.0/3.0)*pow(I1,(Real)4.0)+ID*(Real)12.0*I1*I1*trH)*(Real)(19.0/(7000.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-8.0/3.0))+
((inversematrix*(Real)(-5.0/3.0)*pow(I1,(Real)5.0)+ID*(Real)5.0*pow(I1,(Real)4))*(Real)(-5.0/3.0)*_trHC-inversematrix*(Real)(25.0/3.0)*pow(I1,(Real)4.0)*trH+Firstmatrix*(Real)(5.0/3.0)*pow(I1,(Real)5.0)+ID*(Real)20.0*pow(I1,(Real)3.0)*trH)*(Real)(519.0/(673750.0*8.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-10.0/3.0)))*2.0*mu
+inversematrix*(Real)(k0/(Real)2.0)*_trHC-Firstmatrix*(Real)(k0*log(sinfo->J));
}
virtual void ElasticityTensor(StrainInformation<DataTypes> *sinfo, const MaterialParameters<DataTypes> ¶m,Matrix6 &outputTensor) {
MatrixSym ID;
ID.identity();
MatrixSym _C;
invertMatrix(_C,sinfo->deformationTensor);
MatrixSym CC;
CC=_C;
CC[1]+=_C[1];CC[3]+=_C[3];CC[4]+=_C[4];
Matrix6 C_H_C;
C_H_C[0][0]=_C[0]*_C[0]; C_H_C[1][1]=_C[1]*_C[1]+_C[0]*_C[2]; C_H_C[2][2]=_C[2]*_C[2]; C_H_C[3][3]=_C[3]*_C[3]+_C[0]*_C[5]; C_H_C[4][4]=_C[4]*_C[4]+_C[2]*_C[5];
C_H_C[5][5]=_C[5]*_C[5];
C_H_C[1][0]=_C[0]*_C[1];C_H_C[0][1]=2*C_H_C[1][0];
C_H_C[2][0]=C_H_C[0][2]=_C[1]*_C[1]; C_H_C[5][0]=C_H_C[0][5]=_C[3]*_C[3];
C_H_C[3][0]=_C[0]*_C[3];C_H_C[0][3]=2*C_H_C[3][0]; C_H_C[4][0]=_C[1]*_C[3];C_H_C[0][4]=2*C_H_C[4][0];
C_H_C[1][2]=_C[2]*_C[1];C_H_C[2][1]=2*C_H_C[1][2]; C_H_C[1][5]=_C[3]*_C[4];C_H_C[5][1]=2*C_H_C[1][5];
C_H_C[3][1]=C_H_C[1][3]=_C[0]*_C[4]+_C[1]*_C[3]; C_H_C[1][4]=C_H_C[4][1]=_C[1]*_C[4]+_C[2]*_C[3];
C_H_C[3][2]=_C[4]*_C[1];C_H_C[2][3]=2*C_H_C[3][2]; C_H_C[4][2]=_C[4]*_C[2];C_H_C[2][4]=2*C_H_C[4][2];
C_H_C[2][5]=C_H_C[5][2]=_C[4]*_C[4];
C_H_C[3][5]=_C[3]*_C[5];C_H_C[5][3]=2*C_H_C[3][5];
C_H_C[4][3]=C_H_C[3][4]=_C[3]*_C[4]+_C[5]*_C[1];
C_H_C[4][5]=_C[4]*_C[5];C_H_C[5][4]=2*C_H_C[4][5];
Matrix6 trC_HC_;
trC_HC_[0]=_C[0]*CC;
trC_HC_[1]=_C[1]*CC;
trC_HC_[2]=_C[2]*CC;
trC_HC_[3]=_C[3]*CC;
trC_HC_[4]=_C[4]*CC;
trC_HC_[5]=_C[5]*CC;
Matrix6 trID_HC_;
trID_HC_[0]=ID[0]*CC;
trID_HC_[1]=ID[1]*CC;
trID_HC_[2]=ID[2]*CC;
trID_HC_[3]=ID[3]*CC;
trID_HC_[4]=ID[4]*CC;
trID_HC_[5]=ID[5]*CC;
Matrix6 trC_HID;
trC_HID[0]=_C[0]*ID;
trC_HID[1]=_C[1]*ID;
trC_HID[2]=_C[2]*ID;
trC_HID[3]=_C[3]*ID;
trC_HID[4]=_C[4]*ID;
trC_HID[5]=_C[5]*ID;
Matrix6 trIDHID;
trIDHID[0]=ID[0]*ID;
trIDHID[1]=ID[1]*ID;
trIDHID[2]=ID[2]*ID;
trIDHID[3]=ID[3]*ID;
trIDHID[4]=ID[4]*ID;
trIDHID[5]=ID[5]*ID;
Real I1=sinfo->trC;
Real mu=param.parameterArray[0];
Real k0=param.parameterArray[1];
outputTensor=((((trC_HC_*(Real)(1.0/3.0)*I1-trID_HC_)*(Real)(1.0/3.0)-trC_HID*(Real)(1.0/3.0)+C_H_C*(Real)(1.0/3.0)*I1)*(Real)(1.0/2.0)*pow(sinfo->J,(Real)(-2.0/3.0))
+((trC_HC_*(Real)(2.0/3.0)*I1*I1-trID_HC_*(Real)2.0*I1)*(Real)(2.0/3.0)-trC_HID*(Real)(4.0/3.0)*I1+C_H_C*(Real)(2.0/3.0)*I1*I1+trIDHID*(Real)2.0)*(Real)(1.0/160.0)*pow(sinfo->J,(Real)(-4.0/3.0))
+(trC_HC_*I1*I1*I1-trID_HC_*(Real)3.0*I1*I1-trC_HID*(Real)3.0*I1*I1+C_H_C*I1*I1*I1+trIDHID*(Real)6.0*I1)*(Real)(11.0/(1050.0*8.0*8.0))*pow(sinfo->J,(Real)-2.0)
+((trC_HC_*(Real)(4.0/3.0)*pow(I1,(Real)4.0)-trID_HC_*(Real)4.0*pow(I1,(Real)3.0))*(Real)(4.0/3.0)-trC_HID*(Real)(16.0/3.0)*pow(I1,(Real)3.0)+C_H_C*(Real)(4.0/3.0)*pow(I1,(Real)4.0)+trIDHID*(Real)12.0*I1*I1)*(Real)(19.0/(7000.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-8.0/3.0))
+((trC_HC_*(Real)(5.0/3.0)*pow(I1,(Real)5.0)-trID_HC_*(Real)5*pow(I1,(Real)4.0))*(Real)(5.0/3.0)-trC_HID*(Real)(25.0/3.0)*pow(I1,(Real)4.0)+C_H_C*(Real)(5.0/3.0)*pow(I1,(Real)5.0)+trIDHID*(Real)20.0*pow(I1,(Real)3.0))*(Real)(519.0/(673750.0*8.0*8.0*8.0*8.0))*pow(sinfo->J,(Real)(-10.0/3.0)))*2.0*mu
+trC_HC_*(Real)k0/(Real)2.0-C_H_C*k0*log(sinfo->J))*2.0;
}
};
} // namespace sofa::component::solidmechanics::fem::hyperelastic::material