getfem_nonlinear_elasticity.h

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/* -*- c++ -*- (enables emacs c++ mode) */
/*===========================================================================
 
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/**@file getfem_nonlinear_elasticity.h
   @author  Yves Renard <Yves.Renard@insa-lyon.fr>,
   @author  Julien Pommier <Julien.Pommier@insa-toulouse.fr>
   @date July 6, 2004.
   @brief Non-linear elasticty and incompressibility bricks.
*/
#ifndef GETFEM_NONLINEAR_ELASTICITY_H__
#define GETFEM_NONLINEAR_ELASTICITY_H__
 
#include "getfem_models.h"
#include "getfem_assembling_tensors.h"
#include "getfem_derivatives.h"
#include "getfem_interpolation.h"
#include "getfem_generic_assembly.h"
#include "gmm/gmm_inoutput.h"
 
namespace getfem {
 
 
  int check_symmetry(const base_tensor &t);
 
  class abstract_hyperelastic_law;
  typedef std::shared_ptr<const abstract_hyperelastic_law> phyperelastic_law;
 
  /** Base class for material law.
      Inherit from this class to define a new law.
  */
  class abstract_hyperelastic_law {
  public:
    mutable int uvflag;
    size_type nb_params_;
    phyperelastic_law pl; /* optional reference */
    void reset_unvalid_flag() const { uvflag = 0; }
    void inc_unvalid_flag() const { uvflag++; }
    int get_unvalid_flag() const { return uvflag; }
    std::string adapted_tangent_term_assembly_fem_data; // should be filled
    std::string adapted_tangent_term_assembly_cte_data; // to replace the
                                                        // default assembly
 
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params,
                                      scalar_type det_trans) const = 0;
        /**True Cauchy stress (for Updated Lagrangian formulation)*/
        virtual void cauchy_updated_lagrangian(const base_matrix& F,
                        const base_matrix &E,
                        base_matrix &cauchy_stress,
                        const base_vector &params,
                        scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params,
                       scalar_type det_trans) const = 0;
    // the result of grad_sigma has to be completely symmetric.
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                 const base_vector &params, scalar_type det_trans) const = 0;
 
        /**cauchy-truesdel tangent moduli, used in updated lagrangian*/
        virtual void grad_sigma_updated_lagrangian(const base_matrix& F,
                        const base_matrix& E,
                        const base_vector &params,
                        scalar_type det_trans,
                        base_tensor &grad_sigma_ul)const;
 
    size_type nb_params() const { return nb_params_; }
    abstract_hyperelastic_law() { nb_params_ = 0; }
    virtual ~abstract_hyperelastic_law() {}
    static void random_E(base_matrix &E);
    void test_derivatives(size_type N, scalar_type h,
                          const base_vector& param) const;
  };
 
  /** Saint-Venant Kirchhoff hyperelastic law.
 
      This is the linear law used in linear elasticity, it is not well
      suited to large strain. (the convexes may become flat)
  */
  struct SaintVenant_Kirchhoff_hyperelastic_law :
    public abstract_hyperelastic_law {
    /* W = lambda*0.5*trace(E)^2 + mu*tr(E^2) */
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params,
                                      scalar_type det_trans) const;
    /* sigma = lambda*trace(E) + 2 mu * E */
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                      const base_vector &params, scalar_type det_trans) const;
        virtual void grad_sigma_updated_lagrangian(const base_matrix& F,
                                const base_matrix& E,
                                const base_vector &params,
                                scalar_type det_trans,
                                base_tensor &grad_sigma_ul)const;
    SaintVenant_Kirchhoff_hyperelastic_law();
  };
 
 
  /** Linear law for a membrane (plane stress), orthotropic material
      caracterized by Ex, Ey, vYX and G, with optional orthotropic prestresses.
      due to Jean-Yves Heddebaut <jyhed@alpino.be>
  */
  struct membrane_elastic_law :
    public abstract_hyperelastic_law {
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params,
                                      scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                       const base_vector &params, scalar_type det_trans) const;
    membrane_elastic_law() { nb_params_ = 6; }
  };
 
 
  /** Mooney-Rivlin hyperelastic law
 
      To be used for compressible and incompressible problems.
      Following combinations are possible:
        not compressible, not neohookean (default): 2 parameters (C1,C2)
        not compressible, neohookean: 1 parameter (C1)
        compressible, not neohookean: 3 parameters (C1,C2,D1)
        compressible, neohookean: 2 parameters (C1,D1)
  */
  struct Mooney_Rivlin_hyperelastic_law : public abstract_hyperelastic_law {
    const bool compressible, neohookean;
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params, scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                            const base_vector &params, scalar_type det_trans) const;
    explicit Mooney_Rivlin_hyperelastic_law(bool compressible_=false,
                                            bool neohookean_=false);
  };
 
  /** Neo-Hookean hyperelastic law variants
 
      To be used for compressible problems.
      For incompressible ones Mooney-Rivlin hyperelastic law can be used.
  */
  struct Neo_Hookean_hyperelastic_law : public abstract_hyperelastic_law {
    const bool bonet;
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params, scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                            const base_vector &params, scalar_type det_trans) const;
    explicit Neo_Hookean_hyperelastic_law(bool bonet_=true);
  };
 
  /** Blatz_Ko hyperelastic law
 
      To be used for compressible problems.
  */
  struct generalized_Blatz_Ko_hyperelastic_law : public abstract_hyperelastic_law {
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params, scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                            const base_vector &params, scalar_type det_trans) const;
    generalized_Blatz_Ko_hyperelastic_law();
  };
 
 
  /** Ciarlet-Geymonat hyperelastic law
   */
  struct Ciarlet_Geymonat_hyperelastic_law : public abstract_hyperelastic_law {
    // parameters are lambda=params[0], mu=params[1], a=params[2]
    // The parameter a has to verify a in ]0, mu/2[
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params, scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                            const base_vector &params, scalar_type det_trans) const;
    Ciarlet_Geymonat_hyperelastic_law() { nb_params_ = 3; }
  };
 
  /** Plane strain hyperelastic law (takes another law as a parameter)
   */
  struct plane_strain_hyperelastic_law : public abstract_hyperelastic_law {
    virtual scalar_type strain_energy(const base_matrix &E,
                                      const base_vector &params, scalar_type det_trans) const;
    virtual void sigma(const base_matrix &E, base_matrix &result,
                       const base_vector &params, scalar_type det_trans) const;
    virtual void grad_sigma(const base_matrix &E, base_tensor &result,
                            const base_vector &params, scalar_type det_trans) const;
    plane_strain_hyperelastic_law(const phyperelastic_law &pl_)
    { pl = pl_; nb_params_ = pl->nb_params(); }
  };
 
 
 
 
  template<typename VECT1, typename VECT2> class elasticity_nonlinear_term
    : public getfem::nonlinear_elem_term {
    const mesh_fem &mf;
    std::vector<scalar_type> U;
    const mesh_fem *mf_data;
    const VECT2 &PARAMS;
    size_type N;
    size_type NFem;
    const abstract_hyperelastic_law &AHL;
    base_vector params, coeff;
    base_matrix E, Sigma, gradU;
    base_tensor tt;
    bgeot::multi_index sizes_;
    int version;
  public:
    elasticity_nonlinear_term(const mesh_fem &mf_, const VECT1 &U_,
                              const mesh_fem *mf_data_, const VECT2 &PARAMS_,
                              const abstract_hyperelastic_law &AHL_,
                              int version_)
      : mf(mf_), U(mf_.nb_basic_dof()), mf_data(mf_data_), PARAMS(PARAMS_),
        N(mf_.linked_mesh().dim()), NFem(mf_.get_qdim()), AHL(AHL_),
        params(AHL_.nb_params()), E(N, N), Sigma(N, N), gradU(NFem, N),
        tt(N, N, N, N), sizes_(NFem, N, NFem, N),
        version(version_) {
      switch (version) {
      case 0 : break; // tangent term
      case 1 : sizes_.resize(2); break; // rhs
      case 2 : sizes_.resize(1); sizes_[0] = 1; break; // strain energy
      case 3 : sizes_.resize(2); break; // Id + grad(u)
      }
 
      mf.extend_vector(U_, U);
      if (gmm::vect_size(PARAMS) == AHL_.nb_params())
        gmm::copy(PARAMS, params);
    }
 
    const bgeot::multi_index &sizes(size_type) const {  return sizes_; }
 
    virtual void compute(getfem::fem_interpolation_context& ctx,
                         bgeot::base_tensor &t) {
      size_type cv = ctx.convex_num();
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
      ctx.pf()->interpolation_grad(ctx, coeff, gradU, mf.get_qdim());
 
      for (unsigned int alpha = 0; alpha < N; ++alpha)
        gradU(alpha, alpha) += scalar_type(1);
 
      if (version == 3) {
        for (size_type n = 0; n < NFem; ++n)
          for (size_type m = 0; m < N; ++m)
            t(n,m) = gradU(n,m);
        return;
      }
 
      gmm::mult(gmm::transposed(gradU), gradU, E);
      for (unsigned int alpha = 0; alpha < N; ++alpha)
        E(alpha, alpha) -= scalar_type(1);
      gmm::scale(E, scalar_type(0.5));
 
      scalar_type det_trans = gmm::lu_det(gradU);
 
      if (version == 2) {
        t[0] = AHL.strain_energy(E, params, det_trans);
        return;
      }
 
      AHL.sigma(E, Sigma, params, det_trans);
 
      if (version == 0) {
        AHL.grad_sigma(E, tt, params, det_trans);
        for (size_type n = 0; n < NFem; ++n)
          for (size_type m = 0; m < N; ++m)
            for (size_type l = 0; l < N; ++l)
              for (size_type k = 0; k < NFem; ++k) {
                scalar_type aux = (k == n) ? Sigma(m,l) : 0.0;
                for (size_type j = 0; j < N; ++j)
                  for (size_type i = 0; i < N; ++i) {
                    aux += gradU(n ,j) * gradU(k, i) * tt(j, m, i, l);
                  }
                t(n, m, k, l) = aux;
              }
      } else {
        if (det_trans < scalar_type(0)) AHL.inc_unvalid_flag();
        for (size_type i = 0; i < NFem; ++i)
          for (size_type j = 0; j < N; ++j) {
            scalar_type aux(0);
            for (size_type k = 0; k < N; ++k)
              aux += gradU(i, k) * Sigma(k, j);
            t(i,j) = aux;
          }
      }
    }
 
    virtual void prepare(fem_interpolation_context& ctx, size_type ) {
      if (mf_data) {
        size_type cv = ctx.convex_num();
        size_type nb = AHL.nb_params();
        coeff.resize(mf_data->nb_basic_dof_of_element(cv)*nb);
        for (size_type i = 0; i < mf_data->nb_basic_dof_of_element(cv); ++i)
          for (size_type k = 0; k < nb; ++k)
            coeff[i * nb + k]
              = PARAMS[mf_data->ind_basic_dof_of_element(cv)[i]*nb+k];
        ctx.pf()->interpolation(ctx, coeff, params, dim_type(nb));
      }
    }
 
  };
 
 
  /**
      Tangent matrix for the non-linear elasticity
      @ingroup asm
  */
  template<typename MAT, typename VECT1, typename VECT2>
  void asm_nonlinear_elasticity_tangent_matrix
  (const MAT &K_, const mesh_im &mim, const getfem::mesh_fem &mf,
   const VECT1 &U, const getfem::mesh_fem *mf_data, const VECT2 &PARAMS,
   const abstract_hyperelastic_law &AHL,
   const mesh_region &rg = mesh_region::all_convexes()) {
    MAT &K = const_cast<MAT &>(K_);
    GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
                "wrong qdim for the mesh_fem");
 
    elasticity_nonlinear_term<VECT1, VECT2>
      nterm(mf, U, mf_data, PARAMS, AHL, 0);
    elasticity_nonlinear_term<VECT1, VECT2>
      nterm2(mf, U, mf_data, PARAMS, AHL, 3);
 
    getfem::generic_assembly assem;
    if (mf_data)
      if (AHL.adapted_tangent_term_assembly_fem_data.size() > 0)
        assem.set(AHL.adapted_tangent_term_assembly_cte_data);
      else
        assem.set("M(#1,#1)+=sym(comp(NonLin$1(#1,#2)(i,j,k,l).vGrad(#1)(:,i,j).vGrad(#1)(:,k,l)))");
    else
      if (AHL.adapted_tangent_term_assembly_cte_data.size() > 0)
        assem.set(AHL.adapted_tangent_term_assembly_cte_data);
      else
        assem.set("M(#1,#1)+=sym(comp(NonLin$1(#1)(i,j,k,l).vGrad(#1)(:,i,j).vGrad(#1)(:,k,l)))");
    assem.push_mi(mim);
    assem.push_mf(mf);
    if (mf_data) assem.push_mf(*mf_data);
    assem.push_data(PARAMS);
    assem.push_nonlinear_term(&nterm);
    assem.push_nonlinear_term(&nterm2);
    assem.push_mat(K);
    assem.assembly(rg);
  }
 
 
  /**
     @ingroup asm
  */
  template<typename VECT1, typename VECT2, typename VECT3>
  void asm_nonlinear_elasticity_rhs
  (const VECT1 &R_, const mesh_im &mim, const getfem::mesh_fem &mf,
   const VECT2 &U, const getfem::mesh_fem *mf_data, const VECT3 &PARAMS,
   const abstract_hyperelastic_law &AHL,
   const mesh_region &rg = mesh_region::all_convexes()) {
    VECT1 &R = const_cast<VECT1 &>(R_);
    GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
                "wrong qdim for the mesh_fem");
 
    elasticity_nonlinear_term<VECT2, VECT3>
      nterm(mf, U, mf_data, PARAMS, AHL, 1);
 
    getfem::generic_assembly assem;
    if (mf_data)
      assem.set("t=comp(NonLin(#1,#2).vGrad(#1)); V(#1) += t(i,j,:,i,j)");
    else
      assem.set("t=comp(NonLin(#1).vGrad(#1)); V(#1) += t(i,j,:,i,j)");
    // comp() to be optimized ?
    assem.push_mi(mim);
    assem.push_mf(mf);
    if (mf_data) assem.push_mf(*mf_data);
    assem.push_nonlinear_term(&nterm);
    assem.push_vec(R);
    assem.assembly(rg);
  }
 
  // added by Jean-Yves Heddebaut <jyhed@alpino.be>
  int levi_civita(int i,int j,int k);
 
 
  /**@ingroup asm
   */
  template<typename VECT2, typename VECT3>
  scalar_type asm_elastic_strain_energy
  (const mesh_im &mim, const getfem::mesh_fem &mf,
   const VECT2 &U, const getfem::mesh_fem *mf_data, const VECT3 &PARAMS,
   const abstract_hyperelastic_law &AHL,
   const mesh_region &rg = mesh_region::all_convexes()) {
 
    GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
                "wrong qdim for the mesh_fem");
 
    elasticity_nonlinear_term<VECT2, VECT3>
      nterm(mf, U, mf_data, PARAMS, AHL, 2);
    std::vector<scalar_type> V(1);
 
    getfem::generic_assembly assem;
    if (mf_data)
      assem.set("V() += comp(NonLin(#1,#2))(i)");
    else
      assem.set("V() += comp(NonLin(#1))(i)");
 
    assem.push_mi(mim);
    assem.push_mf(mf);
    if (mf_data) assem.push_mf(*mf_data);
    assem.push_nonlinear_term(&nterm);
    assem.push_vec(V);
    assem.assembly(rg);
 
    return V[0];
  }
 
 
 
 
 
 
 
 
 
  /* ******************************************************************** */
  /*                Mixed nonlinear incompressibility assembly procedure      */
  /* ******************************************************************** */
 
  template<typename VECT1> class incomp_nonlinear_term
    : public getfem::nonlinear_elem_term {
 
    const mesh_fem &mf;
    std::vector<scalar_type> U;
    size_type N;
    base_vector coeff;
    base_matrix gradPhi;
    bgeot::multi_index sizes_;
    int version;
 
  public:
    incomp_nonlinear_term(const mesh_fem &mf_, const VECT1 &U_,
                          int version_)
      : mf(mf_), U(mf_.nb_basic_dof()),
        N(mf_.get_qdim()),
        gradPhi(N, N), sizes_(N, N),
        version(version_) {
      if (version == 1) { sizes_.resize(1); sizes_[0] = 1; }
      mf.extend_vector(U_, U);
    }
 
    const bgeot::multi_index &sizes(size_type) const { return sizes_; }
 
    virtual void compute(getfem::fem_interpolation_context& ctx,
                         bgeot::base_tensor &t) {
      size_type cv = ctx.convex_num();
      slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
      ctx.pf()->interpolation_grad(ctx, coeff, gradPhi, mf.get_qdim());
      gmm::add(gmm::identity_matrix(), gradPhi);
      scalar_type det = gmm::lu_inverse(gradPhi);
 
      if (version != 1) {
        if (version == 2) det = sqrt(gmm::abs(det));
        for (size_type i = 0; i < N; ++i)
          for (size_type j = 0; j < N; ++j) {
            t(i,j) = - det * gradPhi(j,i);
          }
      }
      else t[0] = scalar_type(1) - det;
 
    }
  };
 
  /**@ingroup asm*/
  template<typename MAT1, typename MAT2, typename VECT1, typename VECT2>
  void asm_nonlinear_incomp_tangent_matrix(const MAT1 &K_, const MAT2 &B_,
                                           const mesh_im &mim,
                                           const mesh_fem &mf_u,
                                           const mesh_fem &mf_p,
                                           const VECT1 &U, const VECT2 &P,
                                           const mesh_region &rg = mesh_region::all_convexes()) {
    MAT1 &K = const_cast<MAT1 &>(K_);
    MAT2 &B = const_cast<MAT2 &>(B_);
    GMM_ASSERT1(mf_u.get_qdim() == mf_u.linked_mesh().dim(),
                "wrong qdim for the mesh_fem");
 
    incomp_nonlinear_term<VECT1> ntermk(mf_u, U, 0);
    incomp_nonlinear_term<VECT1> ntermb(mf_u, U, 2);
    getfem::generic_assembly
      assem("P=data(#2);"
            "t=comp(NonLin$1(#1).vGrad(#1).Base(#2));"
            "M$2(#1,#2)+= t(i,j,:,i,j,:);"
             /*"w=comp(NonLin$2(#1).vGrad(#1).NonLin$2(#1).vGrad(#1).Base(#2));"
              "M$1(#1,#1)+= w(j,i,:,j,k, m,k,:,m,i,p).P(p)"
              "-w(i,j,:,i,j, k,l,:,k,l,p).P(p)"*/
            /*
              "w=comp(vGrad(#1).NonLin$2(#1).vGrad(#1).NonLin$2(#1).Base(#2));"
              "M$1(#1,#1)+= w(:,j,k, j,i, :,m,i, m,k, p).P(p)"
              "-w(:,j,i, j,i, :,m,l, m,l, p).P(p)"
            */
            "w1=comp(vGrad(#1)(:,j,k).NonLin$2(#1)(j,i).vGrad(#1)(:,m,i).NonLin$2(#1)(m,k).Base(#2)(p).P(p));"
            "w2=comp(vGrad(#1)(:,j,i).NonLin$2(#1)(j,i).vGrad(#1)(:,m,l).NonLin$2(#1)(m,l).Base(#2)(p).P(p));"
            "M$1(#1,#1)+= w1-w2"
            );
 
    assem.push_mi(mim);
    assem.push_mf(mf_u);
    assem.push_mf(mf_p);
    assem.push_nonlinear_term(&ntermk);
    assem.push_nonlinear_term(&ntermb);
    assem.push_mat(K);
    assem.push_mat(B);
    assem.push_data(P);
    assem.assembly(rg);
  }
 
 
  /**@ingroup asm
   */
  template<typename VECT1, typename VECT2, typename VECT3>
  void asm_nonlinear_incomp_rhs
  (const VECT1 &R_U_, const VECT1 &R_P_, const mesh_im &mim,
   const getfem::mesh_fem &mf_u, const getfem::mesh_fem &mf_p,
   const VECT2 &U, const VECT3 &P,
   const mesh_region &rg = mesh_region::all_convexes()) {
    VECT1 &R_U = const_cast<VECT1 &>(R_U_);
    VECT1 &R_P = const_cast<VECT1 &>(R_P_);
    GMM_ASSERT1(mf_u.get_qdim() == mf_u.linked_mesh().dim(),
                "wrong qdim for the mesh_fem");
 
    incomp_nonlinear_term<VECT2> nterm_tg(mf_u, U, 0);
    incomp_nonlinear_term<VECT2> nterm(mf_u, U, 1);
 
    getfem::generic_assembly
      assem("P=data(#2); "
            "t=comp(NonLin$1(#1).vGrad(#1).Base(#2));"
            "V$1(#1) += t(i,j,:,i,j,k).P(k);"
            "w=comp(NonLin$2(#1).Base(#2)); V$2(#2) += w(1,:)");
    // assem() to be optimized ?
 
    assem.push_mi(mim);
    assem.push_mf(mf_u);
    assem.push_mf(mf_p);
    assem.push_nonlinear_term(&nterm_tg);
    assem.push_nonlinear_term(&nterm);
    assem.push_vec(R_U);
    assem.push_vec(R_P);
    assem.push_data(P);
    assem.assembly(rg);
  }
 
 
 
  //===========================================================================
  //
  //  Bricks
  //
  //===========================================================================
 
 
  /** Add a nonlinear (large strain) elasticity term to the model with
      respect to the variable
      `varname` (deprecated brick, use add_finite_strain_elaticity instead).
      Note that the constitutive law is described by `AHL` which
      should not be freed while the model is used. `dataname` described the
      parameters of the constitutive laws. It could be a vector of value
      of length the number of parameter of the constitutive law or a vector
      field described on a finite element method.
  */
  size_type add_nonlinear_elasticity_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const phyperelastic_law &AHL, const std::string &dataname,
   size_type region = size_type(-1));
 
 
 
  void compute_Von_Mises_or_Tresca
  (model &md, const std::string &varname, const phyperelastic_law &AHL,
   const std::string &dataname, const mesh_fem &mf_vm,
   model_real_plain_vector &VM, bool tresca);
 
 
  void compute_sigmahathat(model &md,
                           const std::string &varname,
                           const phyperelastic_law &AHL,
                           const std::string &dataname,
                           const mesh_fem &mf_sigma,
                           model_real_plain_vector &SIGMA);
 
 
  /**
     Compute the Von-Mises stress or the Tresca stress of a field
     with respect to the constitutive elasticity law AHL (only valid in 3D).
  */
  template <class VECTVM> void compute_Von_Mises_or_Tresca
  (model &md, const std::string &varname, const phyperelastic_law &AHL,
   const std::string &dataname, const mesh_fem &mf_vm,
   VECTVM &VM, bool tresca) {
    model_real_plain_vector VMM(mf_vm.nb_dof());
    compute_Von_Mises_or_Tresca
      (md, varname, AHL, dataname, mf_vm, VMM, tresca);
    gmm::copy(VMM, VM);
  }
 
  /** Add a nonlinear incompressibility term (for large strain elasticity)
      to the model with respect to the variable
      `varname` (the displacement) and `multname` (the pressure).
  */
  size_type add_nonlinear_incompressibility_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname, size_type region = size_type(-1));
 
  //===========================================================================
  //  High-level generic assembly bricks
  //===========================================================================
 
  /** Add a finite strain elasticity brick
      to the model with respect to the variable
      `varname` (the displacement).
      For 2D meshes, switch automatically to plane strain elasticity.
      High-level generic assembly version.
  */
  size_type add_finite_strain_elasticity_brick
  (model &md, const mesh_im &mim, const std::string &lawname,
   const std::string &varname, const std::string &params,
   size_type region = size_type(-1));
 
 
  /** Add a finite strain incompressibility term (for large strain elasticity)
      to the model with respect to the variable
      `varname` (the displacement) and `multname` (the pressure).
      High-level generic assembly version.
  */
  size_type add_finite_strain_incompressibility_brick
  (model &md, const mesh_im &mim, const std::string &varname,
   const std::string &multname, size_type region = size_type(-1));
 
  /**
     Interpolate the Von-Mises stress of a field `varname`
     with respect to the nonlinear elasticity constitutive law `lawname`
     with parameters `params` (only valid in 3D).
  */
  void compute_finite_strain_elasticity_Von_Mises
  (model &md, const std::string &lawname, const std::string &varname,
   const std::string &params, const mesh_fem &mf_vm,
   model_real_plain_vector &VM,
   const mesh_region &rg=mesh_region::all_convexes());
 
  IS_DEPRECATED inline void finite_strain_elasticity_Von_Mises
  (model &md, const std::string &varname, const std::string &lawname,
   const std::string &params, const mesh_fem &mf_vm,
   model_real_plain_vector &VM,
   const mesh_region &rg=mesh_region::all_convexes()) {
    compute_finite_strain_elasticity_Von_Mises(md, varname, lawname, params,
                                               mf_vm, VM, rg);
  }
 
}  /* end of namespace getfem.                                             */
 
 
#endif /* GETFEM_NONLINEAR_ELASTICITY_H__ */