linear_elasticity/elasticity_tensor.h

Go to the documentation of this file.

//LIC// ====================================================================
//LIC// This file forms part of oomph-lib, the object-oriented, 
//LIC// multi-physics finite-element library, available 
//LIC// at http://www.oomph-lib.org.
//LIC// 
//LIC//    Version 1.0; svn revision $LastChangedRevision$
//LIC//
//LIC// $LastChangedDate$
//LIC// 
//LIC// Copyright (C) 2006-2016 Matthias Heil and Andrew Hazel
//LIC// 
//LIC// This library is free software; you can redistribute it and/or
//LIC// modify it under the terms of the GNU Lesser General Public
//LIC// License as published by the Free Software Foundation; either
//LIC// version 2.1 of the License, or (at your option) any later version.
//LIC// 
//LIC// This library is distributed in the hope that it will be useful,
//LIC// but WITHOUT ANY WARRANTY; without even the implied warranty of
//LIC// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
//LIC// Lesser General Public License for more details.
//LIC// 
//LIC// You should have received a copy of the GNU Lesser General Public
//LIC// License along with this library; if not, write to the Free Software
//LIC// Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
//LIC// 02110-1301  USA.
//LIC// 
//LIC// The authors may be contacted at oomph-lib@maths.man.ac.uk.
//LIC// 
//LIC//====================================================================
//Header file for objects representing the fourth-rank elasticity tensor
//for linear elasticity problems

//Include guards to prevent multiple inclusion of the header
#ifndef OOMPH_ELASTICITY_TENSOR_HEADER
#define OOMPH_ELASTICITY_TENSOR_HEADER

// Config header generated by autoconfig
#ifdef HAVE_CONFIG_H
  #include <oomph-lib-config.h>
#endif

#include "../generic/oomph_utilities.h"

namespace oomph
{
 //=====================================================================
 /// A base class that represents the fourth-rank elasticity tensor
 /// \f$E_{ijkl}\f$ defined such that
 /// \f[\tau_{ij} = E_{ijkl} e_{kl},\f]
 /// where \f$e_{ij}\f$ is the infinitessimal (Cauchy) strain tensor
 /// and \f$\tau_{ij}\f$ is the stress tensor. The symmetries of the 
 /// tensor are such that
 /// \f[E_{ijkl} = E_{jikl} = E_{ijlk} = E_{klij}\f]
 /// and thus there are relatively few independent components. These
 /// symmetries are included in the definition of the object so that
 /// non-physical symmetries cannot be accidentally imposed.
 //=====================================================================
class ElasticityTensor
 {

   protected:
  
  ///\short Translation table from the four indices to the corresponding
  ///independent component
  static const unsigned Index[3][3][3][3];

  ///Member function that returns the i-th independent component of the
  ///elasticity tensor
  virtual inline double independent_component(const unsigned &i) const 
   {return 0.0;}

  ///\short Helper range checking function 
  /// (Note that this only captures over-runs in 3D but
  /// errors are likely to be caught in evaluation of the
  /// stress and strain tensors anyway...)
  void range_check(const unsigned &i, const unsigned &j,
                   const unsigned &k, const unsigned &l) const
   {
    if((i > 2) || (j > 2) || (k> 2) || (l>2))
     {
      std::ostringstream error_message;
      if(i > 2)
       {
        error_message << "Range Error : Index 1 " << i 
                      << " is not in the range (0,2)";
       }
      if(j > 2)
       {
        error_message << "Range Error : Index 2 " << j 
                      << " is not in the range (0,2)";
       }

      if(k > 2)
       {
        error_message << "Range Error : Index 2 " << k 
                      << " is not in the range (0,2)";
       }

      if(l > 2)
       {
        error_message << "Range Error : Index 4 " << l 
                      << " is not in the range (0,2)";
       }
      
      //Throw the error
      throw OomphLibError(error_message.str(),
                          OOMPH_CURRENT_FUNCTION,
                          OOMPH_EXCEPTION_LOCATION);
     }
   }

  ///Empty Constructor
  ElasticityTensor() {}

 public:

  ///Empty virtual Destructor 
  virtual ~ElasticityTensor() {}

   public:
  
  ///\short Return the appropriate independent component
  ///via the index translation scheme (const version).
  double operator()(const unsigned &i, const unsigned &j,
                    const unsigned &k, const unsigned &l) const
   {
    //Range check
#ifdef PARANOID
    range_check(i,j,k,l);
#endif
    return independent_component(Index[i][j][k][l]);
   } 

 /// \short Allow the values to be set (virtual function that must be
 /// overloaded if values can be set directly
  virtual void set_value(const unsigned &i, const unsigned &j, 
                         const unsigned &k, const unsigned &l, 
                         const double &value)
  {
   std::stringstream error_stream;
   error_stream << "Broken base implementation.\n"
                << "Must be overloaded for specific storage schemes.\n";
   throw OomphLibError(error_stream.str().c_str(),
                       OOMPH_CURRENT_FUNCTION,
                       OOMPH_EXCEPTION_LOCATION);
  }
  
 };


//===================================================================
/// An isotropic elasticity tensor defined in terms of Young's modulus
/// and Poisson's ratio. The elasticity tensor is assumed to be
/// non-dimensionalised on some reference value for Young's modulus
/// so the value provided to the constructor (if any) is to be
/// interpreted as the ratio of the actual Young's modulus to the
/// Young's modulus used to non-dimensionalise the stresses/tractions
/// in the governing equations.
//===================================================================
 class IsotropicElasticityTensor : public ElasticityTensor
  {
   //Storage for the independent components of the elasticity tensor
  double C[4];

  //Translation scheme between the 21 independent components of the general
  //elasticity tensor and the isotropic case
  static const unsigned StaticIndex[21];
  
    public:
  
  /// \short Constructor. Passing in the values of the Poisson's ratio 
  /// and Young's modulus (interpreted as the ratio of the actual 
  /// Young's modulus to the Young's modulus (or other reference stiffness)
  /// used to non-dimensionalise stresses and tractions in the governing
  /// equations).
  IsotropicElasticityTensor(const double &nu,
                            const double &E) : ElasticityTensor()
   {
    //Set the three indepdent components
    C[0] = 0.0;
    double lambda=E*nu/((1.0+nu)*(1.0-2.0*nu));
    double mu=E/(2.0*(1.0+nu));
    this->set_lame_coefficients(lambda,mu);
   }

  /// \short Constructor. Passing in the value of the Poisson's ratio.
  /// Stresses and tractions in the governing equations are assumed
  /// to have been non-dimensionalised on Young's modulus.
  IsotropicElasticityTensor(const double &nu) : ElasticityTensor()
   {
    //Set the three indepdent components
    C[0] = 0.0;
    
    // reference value
    double E=1.0;
    double lambda=E*nu/((1.0+nu)*(1.0-2.0*nu));
    double mu=E/(2.0*(1.0+nu));
    this->set_lame_coefficients(lambda,mu);
   }    

  /// \short Constructur. Passing in the values of the two lame
  /// coefficients directly (interpreted as the ratios of these
  /// quantities to a reference stiffness used to non-dimensionalised
  IsotropicElasticityTensor(const Vector<double> &lame)
   {
    //Set the three independent componens
    C[0] = 0.0;
    this->set_lame_coefficients(lame[0],lame[1]);
   }

  /// \short Update parameters: Specify values of the Poisson's ratio 
  /// and (optionally) Young's modulus (interpreted as the ratio of the actual 
  /// Young's modulus to the Young's modulus (or other reference stiffness)
  /// used to non-dimensionalise stresses and tractions in the governing
  /// equations).
  void update_constitutive_parameters(const double &nu,
                                      const double &E=1.0)
   {
    //Set the three indepdent components
    C[0] = 0.0;
    double lambda=E*nu/((1.0+nu)*(1.0-2.0*nu));
    double mu=E/(2.0*(1.0+nu));
    this->set_lame_coefficients(lambda,mu);
   }


  ///Overload the independent coefficient function
  inline double independent_component(const unsigned &i) const
   {return C[StaticIndex[i]];}
    

    private:
  
  //Set the values of the lame coefficients
  void set_lame_coefficients(const double &lambda, const double &mu)
   {
    C[1] = lambda + 2.0*mu;
    C[2] = lambda;
    C[3] = mu;
   }

 };



//========================================================================
/// A general elasticity tensor that provides storage for all 21 independent
/// components
//===================================================================
class GeneralElasticityTensor : public ElasticityTensor
{
 //Storage for the independent components of the elasticity tensor
 double C[21];
 
  public:
 
 /// \short Empy Constructor. 
  GeneralElasticityTensor() : ElasticityTensor() 
  {
   //Initialise all independent components to zero
   for(unsigned i=0;i<21;i++) {C[i] = 0.0;}
  }
 
 ///Overload the independent coefficient function
 inline double independent_component(const unsigned &i) const
 {return C[i];}

 /// \short Allow the values to be set
 void set_value(const unsigned &i, const unsigned &j, 
                const unsigned &k, const unsigned &l, const double &value)
 {
  C[this->Index[i][j][k][l]] = value;
 }


 };





}
#endif