libgetfem++-dev 4.2.1~beta1~svn4482~dfsg-2build1 / usr / include / getfem / getfem_nonlinear_elasticity.h

/* -*- 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_modeling.h"
#include "getfem_models.h"
#include "getfem_assembling_tensors.h"
#include "getfem_derivatives.h"
#include "getfem_interpolation.h"
#include "gmm/gmm_inoutput.h"

namespace getfem {


  int check_symmetry(const base_tensor &t);

  /** 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_;
    getfem::abstract_hyperelastic_law *pl; /* optional reference */
    void reset_unvalid_flag(void) const { uvflag = 0; }
    void inc_unvalid_flag(void) const { uvflag++; }
    int get_unvalid_flag(void) 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(void) const { return nb_params_; }
    abstract_hyperelastic_law() { nb_params_ = 0; pl = 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(void);
  };


  /** 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(void) { 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;
    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;
    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(void);
  };


  /** 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(void) { 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(getfem::abstract_hyperelastic_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      */
  /* ******************************************************************** */

# define MDBRICK_NONLINEAR_INCOMP 964552

  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`. Note that the constitutive law is described by `AHL` which
      should not be freed since 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 abstract_hyperelastic_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 abstract_hyperelastic_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 abstract_hyperelastic_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 abstract_hyperelastic_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));












  //===========================================================================
  //
  //  Bricks for the old brick system (DEPRECATED)
  //
  //===========================================================================


# define MDBRICK_NONLINEAR_ELASTICITY 821357

  /** Non-linear elasticity brick  ( @f$ \int (I+\nabla u)\hat{\hat{\sigma}}:\nabla v = l(v)  @f$ ).
      
      @f$ \hat{\hat{\sigma}} @f$ is known as the second Piola-Kirchhoff stress tensor, and is given by \f[ \hat{\hat{\sigma}} = -\frac{\partial}{\partial L}W(L) \f],
      with @f$W@f$ the strain energy of the material, and @f$L=\frac{1}{2}\left(\nabla u^t\nabla u + \nabla u^t + \nabla u\right)@f$ is the Green-Lagrange strain tensor.

      This brick handle the computation of the tangent matrix and the
      right hand side for large strain problems, with hyperelastic
      material laws.
  
      @ingroup bricks
  */
    template<typename MODEL_STATE = standard_model_state>
    class mdbrick_nonlinear_elasticity : public mdbrick_abstract<MODEL_STATE> {

      TYPEDEF_MODEL_STATE_TYPES;

      const abstract_hyperelastic_law &AHL;
      const mesh_im &mim;
      const mesh_fem &mf_u;
      mdbrick_parameter<VECTOR> PARAMS_;

      virtual void proper_update(void) {}

    public :

      virtual void do_compute_tangent_matrix(MODEL_STATE &MS, size_type i0,
					     size_type) {
	gmm::sub_interval SUBI(i0, mf_u.nb_dof());
	gmm::clear(gmm::sub_matrix(MS.tangent_matrix(), SUBI));
	asm_nonlinear_elasticity_tangent_matrix
	  (gmm::sub_matrix(MS.tangent_matrix(), SUBI), mim, mf_u,
	   gmm::sub_vector(MS.state(), SUBI), &(params().mf()), params().get(),
	   AHL, this->mf_u.linked_mesh().get_mpi_region());
      }
      virtual void do_compute_residual(MODEL_STATE &MS, size_type i0, size_type) {
	gmm::sub_interval SUBI(i0, mf_u.nb_dof());
	gmm::clear(gmm::sub_vector(MS.residual(), SUBI));
	asm_nonlinear_elasticity_rhs(gmm::sub_vector(MS.residual(), SUBI), mim,
				     mf_u, gmm::sub_vector(MS.state(), SUBI), 
				     &(params().mf()), params().get(), AHL,
				     this->mf_u.linked_mesh().get_mpi_region());
      }

      mdbrick_parameter<VECTOR> &params() { 
	PARAMS_.reshape(AHL.nb_params()); return PARAMS_; 
      }

      SUBVECTOR get_solution(MODEL_STATE &MS) {
	gmm::sub_interval SUBU(this->first_index(), mf_u.nb_dof());
	return gmm::sub_vector(MS.state(), SUBU);
      }



      /* modified by Jean-Yves Heddebaut <jyhed@alpino.be> sep08, to handle
	 cases where mesh dim <> fem qdim.

	 For the membrane case, the cauchy stresses are calculated starting
	 from the 2X2 lagrange tensor.
	 To compute the jacobian in case of 2D mesh with 3D displacements,
	 a 3th column is added to gradphi, expressing that the  unit vector
	 perpendicular to the reference surface eZ' (0,0,1), is transformed
	 in a  unit vector perpendicular to the deformed surface. (eZ is the
	 vector eX X eY, with eX and eY = images of eX' and eY')
	 (to be validated!)
      */

      template <class VECTVM>
      void compute_Von_Mises_or_Tresca(MODEL_STATE &MS, const mesh_fem &mf_vm,
				       VECTVM &VM, bool tresca) {
	unsigned N = unsigned(mf_u.linked_mesh().dim());
	unsigned NP = unsigned(AHL.nb_params()), NFem = mf_u.get_qdim();
	VECTOR GRAD(mf_vm.nb_dof()*NFem*N), PARAMS(mf_vm.nb_dof()*NP);      
	interpolation(PARAMS_.mf(), mf_vm, PARAMS_.get(), PARAMS);
	compute_gradient(mf_u, mf_vm, get_solution(MS), GRAD);
	GMM_ASSERT1(gmm::vect_size(VM) == mf_vm.nb_dof(),
		    "The vector has not the good size");
	base_matrix E(N, N), gradphi(NFem,N),gradphit(N,NFem), Id(N, N),
	  sigmahathat(N,N),aux(NFem,N), sigma(NFem,NFem),
	  IdNFem(NFem, NFem);
	base_vector p(NP);
	base_vector eig(NFem);
	base_vector ez(NFem);	// vector normal at deformed surface, (ex X ey)
	double normEz(0);		//norm of ez
	gmm::copy(gmm::identity_matrix(), Id);
	gmm::copy(gmm::identity_matrix(), IdNFem);
	for (size_type i = 0; i < mf_vm.nb_dof(); ++i) {
	  gmm::resize(gradphi,NFem,N);
	  std::copy(GRAD.begin()+i*NFem*N, GRAD.begin()+(i+1)*NFem*N,
		    gradphit.begin());
	  gmm::copy(gmm::transposed(gradphit),gradphi);
	  for (unsigned int alpha = 0; alpha <N; ++alpha)
	    gradphi(alpha, alpha)+=1;
	  gmm::mult(gmm::transposed(gradphi), gradphi, E);
	  gmm::add(gmm::scaled(Id, -scalar_type(1)), E);
	  gmm::scale(E, scalar_type(1)/scalar_type(2));
	  gmm::copy(gmm::sub_vector(PARAMS, gmm::sub_interval(i*NP,NP)), p);
	  AHL.sigma(E, sigmahathat, p, scalar_type(1));
	  if (NFem == 3 && N == 2) {
	    //jyh : compute ez, normal on deformed surface
	    for (unsigned int l = 0; l <NFem; ++l)  {
	      ez[l]=0;
	      for (unsigned int m = 0; m <NFem; ++m) 
		for (unsigned int n = 0; n <NFem; ++n){
		  ez[l]+=levi_civita(l,m,n)*gradphi(m,0)*gradphi(n,1);
		}
	      normEz= gmm::vect_norm2(ez);
	    }
	    //jyh : end compute ez
	  }
	  gmm::mult(gradphi, sigmahathat, aux);
	  gmm::mult(aux, gmm::transposed(gradphi), sigma);
	
	  /* jyh : complete gradphi for virtual 3rd dim (perpendicular to
	     deformed surface, same thickness) */
	  if (NFem == 3 && N == 2) {
	    gmm::resize(gradphi,NFem,NFem);
	    for (unsigned int ll = 0; ll <NFem; ++ll) 
	      for (unsigned int ii = 0; ii <NFem; ++ii) 
		for (unsigned int jj = 0; jj <NFem; ++jj) 
		  gradphi(ll,2)+=(levi_civita(ll,ii,jj)*gradphi(ii,0)
				  *gradphi(jj,1))/normEz;
	    //jyh : end complete graphi
	  }
	
	  gmm::scale(sigma, scalar_type(1) / gmm::lu_det(gradphi));
	
	  if (!tresca) {
	    /* von mises: norm(deviator(sigma)) */
	    gmm::add(gmm::scaled(IdNFem, -gmm::mat_trace(sigma) / NFem), sigma);
	  
	    //jyh : von mises stress=sqrt(3/2)* norm(sigma) ?
	    VM[i] = sqrt(3.0/2)*gmm::mat_euclidean_norm(sigma);
	  } else {
	    /* else compute the tresca criterion */
	    //jyh : to be adapted for membrane if necessary
	    gmm::symmetric_qr_algorithm(sigma, eig);
	    std::sort(eig.begin(), eig.end());
	    VM[i] = eig.back() - eig.front();
	  }
	}
      }

      mdbrick_nonlinear_elasticity(const abstract_hyperelastic_law &AHL_,
				   const mesh_im &mim_,
				   const mesh_fem &mf_u_,
				   const VECTOR &PARAMS)
	: AHL(AHL_), mim(mim_), mf_u(mf_u_),
	  PARAMS_("params", mf_u.linked_mesh(), this) {
	params().set(PARAMS);
	this->add_proper_mesh_fem(mf_u, MDBRICK_NONLINEAR_ELASTICITY);
	this->add_proper_mesh_im(mim);
	this->proper_is_linear_ = false;
	this->proper_is_coercive_ = this->proper_is_symmetric_ = true;
	this->force_update();
      }
    };


  /* ******************************************************************** */
  /*		Mixed nonlinear incompressible condition brick.           */
  /* ******************************************************************** */

  /** Incompressible non-linear elasticity brick.
      @ingroup bricks
  */
  template<typename MODEL_STATE = standard_model_state>
  class mdbrick_nonlinear_incomp : public mdbrick_abstract<MODEL_STATE>  {
    
    TYPEDEF_MODEL_STATE_TYPES;
   
    mdbrick_abstract<MODEL_STATE> &sub_problem;
    const mesh_fem &mf_p;
    size_type num_fem;

    virtual void proper_update(void) {
      this->proper_mixed_variables.clear();
      this->proper_mixed_variables.add(sub_problem.nb_dof(), mf_p.nb_dof());
    }

  public :

    SUBVECTOR get_pressure(MODEL_STATE &MS) {
      gmm::sub_interval SUBU(this->first_index() + sub_problem.nb_dof(),
			     mf_p.nb_dof());
      return gmm::sub_vector(MS.state(), SUBU);
    }
    
    template<typename MATRIX> void get_B(MODEL_STATE &MS, MATRIX B) {
      const mesh_fem &mf_u = *(this->mesh_fems[num_fem]);
      gmm::sub_interval SUBI(this->first_index()+sub_problem.nb_dof(), mf_p.nb_dof()); /* P */
      gmm::sub_interval SUBJ(this->first_index()+this->mesh_fem_positions[num_fem], mf_u.nb_dof());           /* U */
      gmm::copy(gmm::sub_matrix(MS.tangent_matrix(), SUBJ, SUBI), B);
    }


    virtual void do_compute_tangent_matrix(MODEL_STATE &MS, size_type i0,
					   size_type) {
      const mesh_fem &mf_u = *(this->mesh_fems[num_fem]);
      size_type i1 = this->mesh_fem_positions[num_fem];
      gmm::sub_interval SUBI(i0+sub_problem.nb_dof(), mf_p.nb_dof()); /* P */
      gmm::sub_interval SUBJ(i0+i1, mf_u.nb_dof());           /* U */
      T_MATRIX B(mf_u.nb_dof(), mf_p.nb_dof());
      asm_nonlinear_incomp_tangent_matrix(gmm::sub_matrix(MS.tangent_matrix(),
							  SUBJ, SUBJ), B,
					  *(this->mesh_ims[0]), mf_u, mf_p, 
					  gmm::sub_vector(MS.state(), SUBJ), 
					  gmm::sub_vector(MS.state(), SUBI),
					  mf_u.linked_mesh().get_mpi_region());
      gmm::copy(B, gmm::sub_matrix(MS.tangent_matrix(), SUBJ, SUBI));
      gmm::copy(gmm::transposed(B),
		gmm::sub_matrix(MS.tangent_matrix(), SUBI, SUBJ));
      gmm::clear(gmm::sub_matrix(MS.tangent_matrix(), SUBI, SUBI));
    }

    virtual void do_compute_residual(MODEL_STATE &MS, size_type i0, size_type) {
      const mesh_fem &mf_u = *(this->mesh_fems[num_fem]);
      size_type i1 = this->mesh_fem_positions[num_fem];
      gmm::sub_interval SUBI(i0 + sub_problem.nb_dof(), mf_p.nb_dof());
      gmm::sub_interval SUBJ(i0+i1, mf_u.nb_dof());
      gmm::clear(gmm::sub_vector(MS.residual(), SUBI));
      asm_nonlinear_incomp_rhs(gmm::sub_vector(MS.residual(), SUBJ),
			       gmm::sub_vector(MS.residual(), SUBI),
			       *(this->mesh_ims[0]), mf_u, mf_p, 
			       gmm::sub_vector(MS.state(), SUBJ),
			       gmm::sub_vector(MS.state(), SUBI),
			       mf_u.linked_mesh().get_mpi_region());
    }

    mdbrick_nonlinear_incomp(mdbrick_abstract<MODEL_STATE> &problem,
			     const mesh_fem &mf_p_, size_type num_fem_=0)
      : sub_problem(problem), mf_p(mf_p_), num_fem(num_fem_) {
      this->add_proper_mesh_fem(mf_p, MDBRICK_NONLINEAR_INCOMP);
      this->add_sub_brick(sub_problem);
      this->proper_is_linear_ = this->proper_is_coercive_ = false;
      this->proper_is_symmetric_ = true;
      this->force_update();
    }
  };



}  /* end of namespace getfem.                                             */


#endif /* GETFEM_NONLINEAR_ELASTICITY_H__ */