PolynomialMaterialLaw3d Class Reference

#include <PolynomialMaterialLaw3d.hpp>

Inherits AbstractIsotropicIncompressibleMaterialLaw< 3 >.

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List of all members.

Public Member Functions

double Get_dW_dI1 (double I1, double I2)
double Get_dW_dI2 (double I1, double I2)
double Get_d2W_dI1 (double I1, double I2)
double Get_d2W_dI2 (double I1, double I2)
double Get_d2W_dI1I2 (double I1, double I2)
double GetAlpha (unsigned i, unsigned j)
 PolynomialMaterialLaw3d (unsigned n, std::vector< std::vector< double > > alpha)

Static Public Member Functions

static std::vector
< std::vector< double > > 		GetZeroedAlpha (unsigned n)

Private Attributes

unsigned mN
std::vector< std::vector
< double > > 		mAlpha

Detailed Description

PolynomialMaterialLaw3d

An incompressible, isotropic, hyperelastic material law with a polynomial form

W(I_1,I_2) = Sigma_{0<p+q<=N} alpha_{pq} (I_1-3)^p (I_2-3)^q - (pressure/2) C^{-1}

For example, if N=1, this reduces to the Mooney Rivlin law W(I_1,I_2) = alpha_{10} (I_1-3) + alpha_{01} (I_2-3) - (pressure/2) C^{-1} ie the matrix alpha has the form [ 0 c1 ] [ c2 0 ] where c1 and c2 is the usual notation for the Mooney-Rivlin constants

The polynomial is specified by passing in N and the matrix (actually a std::vector of std::vector<double>s) alpha. alpha should be of size N+1 by N+1, with the bottom right hand block (ie the components such that p+q>N) all zero. alpha[0][0] should really also be 0, but, being since alpha[0][0] (I1_3)^0 (I2-3)^0 is a constant and disappears when the strain energy W is differentiated to obtain the stress, it is not used. An exception is thrown if alpha[p][q]!=0 for p+q > N though.

Definition at line 57 of file PolynomialMaterialLaw3d.hpp.

Constructor & Destructor Documentation

PolynomialMaterialLaw3d::PolynomialMaterialLaw3d ( unsigned  n,
std::vector< std::vector< double > >  alpha 
)

Constructor.

Parameters:
n the parameter n
alpha the matrix of parameters alpha

Definition at line 123 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

Member Function Documentation

double PolynomialMaterialLaw3d::Get_d2W_dI1 ( double  I1,
double  I2 
) [virtual]

Get the second derivative d^2W/dI1^2.

Todo:
The name of this method should not include underscores.
Parameters:
I1 first principal invariant of C
I2 second principal invariant of C

Implements AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Definition at line 64 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

double PolynomialMaterialLaw3d::Get_d2W_dI1I2 ( double  I1,
double  I2 
) [virtual]

Get the second derivative d^2W/dI1dI2.

Todo:
The name of this method should not include underscores.
Parameters:
I1 first principal invariant of C
I2 second principal invariant of C

Implements AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Definition at line 98 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

double PolynomialMaterialLaw3d::Get_d2W_dI2 ( double  I1,
double  I2 
) [virtual]

Get the second derivative d^2W/dI2^2.

Todo:
The name of this method should not include underscores.
Parameters:
I1 first principal invariant of C
I2 second principal invariant of C

Implements AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Definition at line 81 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

double PolynomialMaterialLaw3d::Get_dW_dI1 ( double  I1,
double  I2 
) [virtual]

Get the first derivative dW/dI1.

Todo:
The name of this method should not include underscores.
Parameters:
I1 first principal invariant of C
I2 second principal invariant of C

Implements AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Definition at line 31 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

double PolynomialMaterialLaw3d::Get_dW_dI2 ( double  I1,
double  I2 
) [virtual]

Get the first derivative dW/dI2.

Todo:
The name of this method should not include underscores.
Parameters:
I1 first principal invariant of C
I2 second principal invariant of C

Implements AbstractIsotropicIncompressibleMaterialLaw< 3 >.

Definition at line 48 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

double PolynomialMaterialLaw3d::GetAlpha ( unsigned  i,
unsigned  j 
)

Get the parameter alpha_{ij}.

Parameters:
i index i
j index j

Definition at line 115 of file PolynomialMaterialLaw3d.cpp.

References mAlpha, and mN.

std::vector< std::vector< double > > PolynomialMaterialLaw3d::GetZeroedAlpha ( unsigned  n  )  [static]

Resize the matrix alpha to be of size (n+1)*(n+1) and zero all entries.

Parameters:
n the parameter n

Definition at line 154 of file PolynomialMaterialLaw3d.cpp.

Member Data Documentation

std::vector< std::vector<double> > PolynomialMaterialLaw3d::mAlpha [private]

Matrix of parameters alpha.

Definition at line 65 of file PolynomialMaterialLaw3d.hpp.

Referenced by Get_d2W_dI1(), Get_d2W_dI1I2(), Get_d2W_dI2(), Get_dW_dI1(), Get_dW_dI2(), GetAlpha(), and PolynomialMaterialLaw3d().

unsigned PolynomialMaterialLaw3d::mN [private]

Parameter N.

Definition at line 62 of file PolynomialMaterialLaw3d.hpp.

Referenced by Get_d2W_dI1(), Get_d2W_dI1I2(), Get_d2W_dI2(), Get_dW_dI1(), Get_dW_dI2(), GetAlpha(), and PolynomialMaterialLaw3d().

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