/**
 * @file   material_mazars_inline_impl.cc
 *
 * @author Marion Estelle Chambart <marion.chambart@epfl.ch>
 * @author Nicolas Richart <nicolas.richart@epfl.ch>
 *
 * @date creation: Wed Apr 06 2011
 * @date last modification: Tue Aug 04 2015
 *
 * @brief  Implementation of the inline functions of the material damage
 *
 * @section LICENSE
 *
 * Copyright (©)  2010-2012, 2014,  2015 EPFL  (Ecole Polytechnique  Fédérale de
 * Lausanne)  Laboratory (LSMS  -  Laboratoire de  Simulation  en Mécanique  des
 * Solides)
 *
 * Akantu 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 3 of the License, or (at your option) any
 * later version.
 *
 * Akantu 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 Akantu. If not, see <http://www.gnu.org/licenses/>.
 *
 */

/* -------------------------------------------------------------------------- */


/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void
MaterialMazars<spatial_dimension>::computeStressOnQuad(const Matrix<Real> & grad_u,
						       Matrix<Real> & sigma,
						       Real & dam,
						       Real & Ehat) {
  Matrix<Real> epsilon(3, 3);
  epsilon.clear();

  for (UInt i = 0; i < spatial_dimension; ++i)
    for (UInt j = 0; j < spatial_dimension; ++j)
      epsilon(i,j) = .5*(grad_u(i,j) + grad_u(j,i));

  Vector<Real> Fdiag(3);
  Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

  Ehat = 0.;
  for (UInt i = 0; i < 3; ++i) {
    Real epsilon_p = std::max(Real(0.), Fdiag(i));
    Ehat += epsilon_p * epsilon_p;
  }
  Ehat = sqrt(Ehat);

  MaterialElastic<spatial_dimension>::computeStressOnQuad(grad_u, sigma);

  if(damage_in_compute_stress) {
    computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
  }

  if(!this->is_non_local) {
    computeDamageAndStressOnQuad(grad_u, sigma, dam, Ehat);
  }
}

/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void
MaterialMazars<spatial_dimension>::computeDamageAndStressOnQuad(const Matrix<Real> & grad_u,
								Matrix<Real> & sigma,
								Real & dam,
								Real & Ehat) {
  if(!damage_in_compute_stress) {
    Vector<Real> Fdiag(3);
    Fdiag.clear();

    Matrix<Real> epsilon(3, 3);
    epsilon.clear();
    for (UInt i = 0; i < spatial_dimension; ++i)
      for (UInt j = 0; j < spatial_dimension; ++j)
	epsilon(i,j) = .5*(grad_u(i,j) + grad_u(j,i));

    Math::matrixEig(3, epsilon.storage(), Fdiag.storage());

    computeDamageOnQuad(Ehat, sigma, Fdiag, dam);
  }

  sigma *= 1 - dam;
}

/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
inline void
MaterialMazars<spatial_dimension>::computeDamageOnQuad(const Real & epsilon_equ,
						       __attribute__((unused)) const Matrix<Real> & sigma,
						       const Vector<Real> & epsilon_princ,
						       Real & dam) {
  Real Fs = epsilon_equ - K0;
  if (Fs > 0.) {
    Real dam_t;
    Real dam_c;
    dam_t = 1 - K0*(1 - At)/epsilon_equ - At*(exp(-Bt*(epsilon_equ - K0)));
    dam_c = 1 - K0*(1 - Ac)/epsilon_equ - Ac*(exp(-Bc*(epsilon_equ - K0)));

    Real Cdiag;
    Cdiag = this->E*(1-this->nu)/((1+this->nu)*(1-2*this->nu));

    Vector<Real> sigma_princ(3);
    sigma_princ(0) = Cdiag*epsilon_princ(0) + this->lambda*(epsilon_princ(1) + epsilon_princ(2));
    sigma_princ(1) = Cdiag*epsilon_princ(1) + this->lambda*(epsilon_princ(0) + epsilon_princ(2));
    sigma_princ(2) = Cdiag*epsilon_princ(2) + this->lambda*(epsilon_princ(1) + epsilon_princ(0));

    Vector<Real> sigma_p(3);
    for (UInt i = 0; i < 3; i++) sigma_p(i) = std::max(Real(0.), sigma_princ(i));
    sigma_p *= 1. - dam;

    Real trace_p = this->nu / this->E * (sigma_p(0) + sigma_p(1) + sigma_p(2));

    Real alpha_t = 0;
    for (UInt i = 0; i < 3; ++i) {
      Real epsilon_t = (1 + this->nu)/this->E * sigma_p(i) - trace_p;
      Real epsilon_p = std::max(Real(0.), epsilon_princ(i));
      alpha_t += epsilon_t * epsilon_p;
    }

    alpha_t /= epsilon_equ * epsilon_equ;
    alpha_t = std::min(alpha_t, Real(1.));

    Real alpha_c = 1. - alpha_t;

    alpha_t = std::pow(alpha_t, beta);
    alpha_c = std::pow(alpha_c, beta);

    Real damtemp;
    damtemp = alpha_t * dam_t + alpha_c * dam_c;

    dam = std::max(damtemp, dam);
    dam = std::min(dam, Real(1.));
  }
}


/* -------------------------------------------------------------------------- */
// template<UInt spatial_dimension>
// inline void MaterialMazars<spatial_dimension>::computeTangentModuliOnQuad(Matrix<Real> & tangent) {
//   MaterialElastic<spatial_dimension>::computeTangentModuliOnQuad(tangent);

//   tangent *= (1-dam);
// }