NeoHookean.hpp

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/** \file NeoHookean.hpp
 * \ingroup nonlinear_elastic_elem
 * \brief Implementation of Neo-Hookean elastic material
 * \example NeoHookean.hpp
 */
 
 
 
#ifndef __NEOHOOKEAN_HPP__
#define __NEOHOOKEAN_HPP__
 
/** \brief NeoHookan equation
 * \ingroup nonlinear_elastic_elem
 */
template <typename TYPE>
struct NeoHookean
    : public NonlinearElasticElement::FunctionsToCalculatePiolaKirchhoffI<
          TYPE> {
 
  using PiolaKirchoffI =
      NonlinearElasticElement::FunctionsToCalculatePiolaKirchhoffI<TYPE>;
 
  NeoHookean()
      : NonlinearElasticElement::FunctionsToCalculatePiolaKirchhoffI<TYPE>(),
        t_invC(PiolaKirchoffI::resizeAndSet(invC)) {}
 
  TYPE detC;
  TYPE logJ;
  MatrixBoundedArray<TYPE, 9> invC;
  FTensor::Tensor2<FTensor::PackPtr<TYPE *, 0>, 3, 3> t_invC;
 
  FTensor::Index<'i', 3> i;
  FTensor::Index<'j', 3> j;
  FTensor::Index<'k', 3> k;
 
  /** \brief calculate second Piola Kirchhoff
    *
    * \f$\mathbf{S} =
    \mu(\mathbf{I}-\mathbf{C}^{-1})+\lambda(\ln{J})\mathbf{C}^{-1}\f$
 
    For details look to: <br>
    NONLINEAR CONTINUUM MECHANICS FOR FINITE ELEMENT ANALYSIS, Javier Bonet,
    Richard D. Wood
 
    */
  MoFEMErrorCode NeoHooke_PiolaKirchhoffII() {
    MoFEMFunctionBeginHot;
 
    detC = determinantTensor3by3(this->C);
    CHKERR invertTensor3by3(this->C, detC, invC);
    this->J = determinantTensor3by3(this->F);
 
    logJ = log(sqrt(this->J * this->J));
    constexpr auto t_kd = FTensor::Kronecker_Delta<double>();
 
    this->t_S(i, j) = this->mu * (t_kd(i, j) - t_invC(i, j)) +
                      (this->lambda * logJ) * t_invC(i, j);
 
    MoFEMFunctionReturnHot(0);
  }
 
  virtual MoFEMErrorCode calculateP_PiolaKirchhoffI(
      const NonlinearElasticElement::BlockData block_data,
      boost::shared_ptr<const NumeredEntFiniteElement> fe_ptr) {
    MoFEMFunctionBegin;
 
    this->lambda = LAMBDA(block_data.E, block_data.PoissonRatio);
    this->mu = MU(block_data.E, block_data.PoissonRatio);
    CHKERR this->calculateC_CauchyDeformationTensor();
    CHKERR this->NeoHooke_PiolaKirchhoffII();
 
    this->t_P(i, j) = this->t_F(i, k) * this->t_S(k, j);
 
    MoFEMFunctionReturn(0);
  }
 
  /** \brief calculate elastic energy density
   *
 
   For details look to: <br>
   NONLINEAR CONTINUUM MECHANICS FOR FINITE ELEMENT ANALYSIS, Javier Bonet,
   Richard D. Wood
 
   */
  MoFEMErrorCode NeoHookean_ElasticEnergy() {
    MoFEMFunctionBegin;
    this->eNergy = this->t_C(i, i);
    this->eNergy = 0.5 * this->mu * (this->eNergy - 3);
    logJ = log(sqrt(this->J * this->J));
    this->eNergy += -this->mu * logJ + 0.5 * this->lambda * pow(logJ, 2);
    MoFEMFunctionReturn(0);
  }
 
  MoFEMErrorCode calculateElasticEnergy(
      const NonlinearElasticElement::BlockData block_data,
      boost::shared_ptr<const NumeredEntFiniteElement> fe_ptr) {
    MoFEMFunctionBegin;
 
    this->lambda = LAMBDA(block_data.E, block_data.PoissonRatio);
    this->mu = MU(block_data.E, block_data.PoissonRatio);
    CHKERR this->calculateC_CauchyDeformationTensor();
    this->J = determinantTensor3by3(this->F);
    CHKERR this->NeoHookean_ElasticEnergy();
 
    MoFEMFunctionReturn(0);
  }
};
 
#endif