Defines an Isotropic Elasticity Tensor. More...

#include <IsotropicElasticityTensor.h>

Inheritance diagram for IsotropicElasticityTensor:

Public Member Functions
	IsotropicElasticityTensor (const bool constant=true)

void	setLambda (const Real lambda)
	Set the first Lame Coefficient. More...

void	setMu (const Real mu)
	Set the second Lame Coefficient. More...

void	setYoungsModulus (const Real E)
	Set the Young's Modulus. More...

void	setPoissonsRatio (const Real nu)
	Set Poissons Ratio. More...

void	setBulkModulus (const Real k)
	Set the Bulk Modulus. More...

void	setShearModulus (const Real k)
	Set the shear modulus... More...

virtual	~IsotropicElasticityTensor ()

void	calculate (unsigned int qp)
	Public function that will be called whenever the values for this matrix need to be filled in. More...

virtual ColumnMajorMatrix	calculateDerivative (unsigned int qp, unsigned int i)

Protected Member Functions
virtual void	calculateEntries (unsigned int qp)
	Fill in the matrix. More...

void	calculateLameCoefficients ()
	Calculates lambda and mu based on what has been set. More...

Real	isotropicEntry (const unsigned int i, const unsigned j, const unsigned k, const unsigned l)
	Computes a single entry of C_ijkl. More...

Protected Attributes
bool	_lambda_set

bool	_mu_set

bool	_E_set

bool	_nu_set

bool	_k_set

Real	_lambda

Real	_mu

Real	_E

Real	_nu

Real	_k

bool	_constant
	Whether or not the matrix is constant for all of time and space. More...

bool	_values_computed
	Whether or not the values have been computed once. More...

Detailed Description

Defines an Isotropic Elasticity Tensor.

The input is any two of the following:

Youngs Modulus Poissons Ration First and Second Lame Coefficients (lambda and mu) Bulk Modulus

Internally this class uses the Lame Coefficients. Everything is is transformed to these coefficients.

Note that by default this tensor is constant... meaning that it never changes after the first time it is computed.

If you want to modify this behavior you can pass in false to the constructor.

Definition at line 33 of file IsotropicElasticityTensor.h.

Constructor & Destructor Documentation

◆ IsotropicElasticityTensor()

IsotropicElasticityTensor::IsotropicElasticityTensor ( const bool constant = true )

Definition at line 12 of file IsotropicElasticityTensor.C.

   : ElasticityTensor(constant),
     _lambda_set(false),
     _mu_set(false),
     _nu_set(false),
     _k_set(false),
     _lambda(0),
     _mu(0),
     _nu(0),
     _k(0)
 {
 }

◆ ~IsotropicElasticityTensor()

virtual IsotropicElasticityTensor::~IsotropicElasticityTensor ( )

inlinevirtual

Definition at line 68 of file IsotropicElasticityTensor.h.

68 {}

Member Function Documentation

◆ calculate()

void ElasticityTensor::calculate ( unsigned int qp )

inherited

Public function that will be called whenever the values for this matrix need to be filled in.

Definition at line 18 of file ElasticityTensor.C.

 {
   if (!_constant || !_values_computed)
   {
     calculateEntries(qp);
     _values_computed = true;
   }
 }

◆ calculateDerivative()

ColumnMajorMatrix ElasticityTensor::calculateDerivative	(	unsigned int	qp,
		unsigned int	i
	)

virtualinherited

Definition at line 28 of file ElasticityTensor.C.

 {
   ColumnMajorMatrix m(9, 9);
   return m;
 }

◆ calculateEntries()

void IsotropicElasticityTensor::calculateEntries ( unsigned int qp )

protectedvirtual

Fill in the matrix.

Implements ElasticityTensor.

Reimplemented in IsotropicElasticityTensorRZ.

Definition at line 113 of file IsotropicElasticityTensor.C.

 {
   calculateLameCoefficients();
  
   unsigned int i, j, k, l;
   i = j = k = l = 0;
  
   // Walk down the columns of the 9x9 matrix
   for (unsigned int q = 0; q < 81; ++q)
   {
     // This algorithm was developed by Derek Gaston and Cody Permann
     // it's based on page 29 of Michael Tonk's notes
     j += i / 3;
     k += j / 3;
     l += k / 3;
  
     i %= 3;
     j %= 3;
     k %= 3;
     l %= 3;
  
     _values[q] = isotropicEntry(i, j, k, l);
  
     ++i;
   }
 }

◆ calculateLameCoefficients()

void IsotropicElasticityTensor::calculateLameCoefficients ( )

protected

Calculates lambda and mu based on what has been set.

These are based on Michael Tonks's's notes

Definition at line 67 of file IsotropicElasticityTensor.C.

 {
   if (_lambda_set && _mu_set) // First and second Lame
     return;
   else if (_lambda_set && _nu_set)
     _mu = (_lambda * (1.0 - 2.0 * _nu)) / (2.0 * _nu);
   else if (_lambda_set && _k_set)
     _mu = (3.0 * (_k - _lambda)) / 2.0;
   else if (_lambda_set && _E_set)
     _mu = ((_E - 3.0 * _lambda) / 4.0) +
           (std::sqrt((_E - 3.0 * _lambda) * (_E - 3.0 * _lambda) + 8.0 * _lambda * _E) / 4.0);
   else if (_mu_set && _nu_set)
     _lambda = (2.0 * _mu * _nu) / (1.0 - 2.0 * _nu);
   else if (_mu_set && _k_set)
     _lambda = (3.0 * _k - 2.0 * _mu) / 3.0;
   else if (_mu_set && _E_set)
     _lambda = ((2.0 * _mu - _E) * _mu) / (_E - 3.0 * _mu);
   else if (_nu_set && _k_set)
   {
     _lambda = (3.0 * _k * _nu) / (1.0 + _nu);
     _mu = (3.0 * _k * (1.0 - 2.0 * _nu)) / (2.0 * (1.0 + _nu));
   }
   else if (_E_set && _nu_set) // Young's Modulus and Poisson's Ratio
   {
     _lambda = (_nu * _E) / ((1.0 + _nu) * (1 - 2.0 * _nu));
     _mu = _E / (2.0 * (1.0 + _nu));
   }
   else if (_E_set && _k_set)
   {
     _lambda = (3.0 * _k * (3.0 * _k - _E)) / (9.0 * _k - _E);
     _mu = (3.0 * _E * _k) / (9.0 * _k - _E);
   }
   _lambda_set = true;
   _mu_set = true;
 }

Referenced by calculateEntries(), and IsotropicElasticityTensorRZ::calculateLameCoefficients().

◆ isotropicEntry()

Real IsotropicElasticityTensor::isotropicEntry	(	const unsigned int	i,
		const unsigned	j,
		const unsigned	k,
		const unsigned	l
	)

protected

Computes a single entry of C_ijkl.

Note that the formula for this came from Michael Tonks on page 234 of his notes.

Definition at line 104 of file IsotropicElasticityTensor.C.

 {
   return _lambda * (i == j) * (k == l) + _mu * ((i == k) * (j == l) + (i == l) * (j == k));
 }

Referenced by calculateEntries().

◆ setBulkModulus()

void IsotropicElasticityTensor::setBulkModulus ( const Real k )

Set the Bulk Modulus.

Definition at line 54 of file IsotropicElasticityTensor.C.

 {
   _k = k;
   _k_set = true;
 }

◆ setLambda()

void IsotropicElasticityTensor::setLambda ( const Real lambda )

Set the first Lame Coefficient.

Definition at line 26 of file IsotropicElasticityTensor.C.

 {
   _lambda = lambda;
   _lambda_set = true;
 }

◆ setMu()

void IsotropicElasticityTensor::setMu ( const Real mu )

Set the second Lame Coefficient.

Definition at line 33 of file IsotropicElasticityTensor.C.

 {
   _mu = mu;
   _mu_set = true;
 }

Referenced by setShearModulus().

◆ setPoissonsRatio()

void IsotropicElasticityTensor::setPoissonsRatio ( const Real nu )

Set Poissons Ratio.

Definition at line 47 of file IsotropicElasticityTensor.C.

 {
   _nu = nu;
   _nu_set = true;
 }

◆ setShearModulus()

void IsotropicElasticityTensor::setShearModulus ( const Real k )

Set the shear modulus...

same thing as Mu

Definition at line 61 of file IsotropicElasticityTensor.C.

 {
   setMu(k);
 }

◆ setYoungsModulus()

void IsotropicElasticityTensor::setYoungsModulus ( const Real E )

Set the Young's Modulus.

Definition at line 40 of file IsotropicElasticityTensor.C.

 {
   _E = E;
   _E_set = true;
 }

Member Data Documentation

◆ _constant

bool ElasticityTensor::_constant

protectedinherited

Whether or not the matrix is constant for all of time and space.

Definition at line 48 of file ElasticityTensor.h.

Referenced by ElasticityTensor::calculate().

◆ _E

Real IsotropicElasticityTensor::_E

protected

Definition at line 73 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateEntries(), IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setYoungsModulus().

◆ _E_set

bool IsotropicElasticityTensor::_E_set

protected

Definition at line 71 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setYoungsModulus().

◆ _k

Real IsotropicElasticityTensor::_k

protected

Definition at line 73 of file IsotropicElasticityTensor.h.

Referenced by calculateLameCoefficients(), and setBulkModulus().

◆ _k_set

bool IsotropicElasticityTensor::_k_set

protected

Definition at line 71 of file IsotropicElasticityTensor.h.

Referenced by calculateLameCoefficients(), and setBulkModulus().

◆ _lambda

Real IsotropicElasticityTensor::_lambda

protected

Definition at line 73 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), isotropicEntry(), and setLambda().

◆ _lambda_set

bool IsotropicElasticityTensor::_lambda_set

protected

Definition at line 71 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setLambda().

◆ _mu

Real IsotropicElasticityTensor::_mu

protected

Definition at line 73 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), isotropicEntry(), and setMu().

◆ _mu_set

bool IsotropicElasticityTensor::_mu_set

protected

Definition at line 71 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setMu().

◆ _nu

Real IsotropicElasticityTensor::_nu

protected

Definition at line 73 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateEntries(), IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setPoissonsRatio().

◆ _nu_set

bool IsotropicElasticityTensor::_nu_set

protected

Definition at line 71 of file IsotropicElasticityTensor.h.

Referenced by IsotropicElasticityTensorRZ::calculateLameCoefficients(), calculateLameCoefficients(), and setPoissonsRatio().

◆ _values_computed

bool ElasticityTensor::_values_computed

protectedinherited

Whether or not the values have been computed once.

Definition at line 53 of file ElasticityTensor.h.

Referenced by ElasticityTensor::calculate().

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

solid_mechanics/include/materials/IsotropicElasticityTensor.h
solid_mechanics/src/materials/IsotropicElasticityTensor.C

Public Member Functions

Protected Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ IsotropicElasticityTensor()

◆ ~IsotropicElasticityTensor()

Member Function Documentation

◆ calculate()

◆ calculateDerivative()

◆ calculateEntries()

◆ calculateLameCoefficients()

◆ isotropicEntry()

◆ setBulkModulus()

◆ setLambda()

◆ setMu()

◆ setPoissonsRatio()

◆ setShearModulus()

◆ setYoungsModulus()

Member Data Documentation

◆ _constant

◆ _E

◆ _E_set

◆ _k

◆ _k_set

◆ _lambda

◆ _lambda_set

◆ _mu

◆ _mu_set

◆ _nu

◆ _nu_set

◆ _values_computed