GetFEM++  5.2
getfem_nonlinear_elasticity.h
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30 ===========================================================================*/
31 
32 /**@file getfem_nonlinear_elasticity.h
33  @author Yves Renard <Yves.Renard@insa-lyon.fr>,
34  @author Julien Pommier <Julien.Pommier@insa-toulouse.fr>
35  @date July 6, 2004.
36  @brief Non-linear elasticty and incompressibility bricks.
37 */
38 #ifndef GETFEM_NONLINEAR_ELASTICITY_H__
39 #define GETFEM_NONLINEAR_ELASTICITY_H__
40 
41 #include "getfem_models.h"
43 #include "getfem_derivatives.h"
44 #include "getfem_interpolation.h"
46 #include "gmm/gmm_inoutput.h"
47 
48 namespace getfem {
49 
50 
51  int check_symmetry(const base_tensor &t);
52 
53  class abstract_hyperelastic_law;
54  typedef std::shared_ptr<const abstract_hyperelastic_law> phyperelastic_law;
55 
56  /** Base class for material law.
57  Inherit from this class to define a new law.
58  */
60  public:
61  mutable int uvflag;
62  size_type nb_params_;
63  phyperelastic_law pl; /* optional reference */
64  void reset_unvalid_flag() const { uvflag = 0; }
65  void inc_unvalid_flag() const { uvflag++; }
66  int get_unvalid_flag() const { return uvflag; }
67  std::string adapted_tangent_term_assembly_fem_data; // should be filled
68  std::string adapted_tangent_term_assembly_cte_data; // to replace the
69  // default assembly
70 
71  virtual scalar_type strain_energy(const base_matrix &E,
72  const base_vector &params,
73  scalar_type det_trans) const = 0;
74  /**True Cauchy stress (for Updated Lagrangian formulation)*/
75  virtual void cauchy_updated_lagrangian(const base_matrix& F,
76  const base_matrix &E,
77  base_matrix &cauchy_stress,
78  const base_vector &params,
79  scalar_type det_trans) const;
80  virtual void sigma(const base_matrix &E, base_matrix &result,
81  const base_vector &params,
82  scalar_type det_trans) const = 0;
83  // the result of grad_sigma has to be completely symmetric.
84  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
85  const base_vector &params, scalar_type det_trans) const = 0;
86 
87  /**cauchy-truesdel tangent moduli, used in updated lagrangian*/
88  virtual void grad_sigma_updated_lagrangian(const base_matrix& F,
89  const base_matrix& E,
90  const base_vector &params,
91  scalar_type det_trans,
92  base_tensor &grad_sigma_ul)const;
93 
94  size_type nb_params() const { return nb_params_; }
95  abstract_hyperelastic_law() { nb_params_ = 0; }
96  virtual ~abstract_hyperelastic_law() {}
97  static void random_E(base_matrix &E);
98  void test_derivatives(size_type N, scalar_type h,
99  const base_vector& param) const;
100  };
101 
102  /** Saint-Venant Kirchhoff hyperelastic law.
103 
104  This is the linear law used in linear elasticity, it is not well
105  suited to large strain. (the convexes may become flat)
106  */
109  /* W = lambda*0.5*trace(E)^2 + mu*tr(E^2) */
110  virtual scalar_type strain_energy(const base_matrix &E,
111  const base_vector &params,
112  scalar_type det_trans) const;
113  /* sigma = lambda*trace(E) + 2 mu * E */
114  virtual void sigma(const base_matrix &E, base_matrix &result,
115  const base_vector &params, scalar_type det_trans) const;
116  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
117  const base_vector &params, scalar_type det_trans) const;
118  virtual void grad_sigma_updated_lagrangian(const base_matrix& F,
119  const base_matrix& E,
120  const base_vector &params,
121  scalar_type det_trans,
122  base_tensor &grad_sigma_ul)const;
124  };
125 
126 
127  /** Linear law for a membrane (plane stress), orthotropic material
128  caracterized by Ex, Ey, vYX and G, with optional orthotropic prestresses.
129  due to Jean-Yves Heddebaut <jyhed@alpino.be>
130  */
133  virtual scalar_type strain_energy(const base_matrix &E,
134  const base_vector &params,
135  scalar_type det_trans) const;
136  virtual void sigma(const base_matrix &E, base_matrix &result,
137  const base_vector &params, scalar_type det_trans) const;
138  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
139  const base_vector &params, scalar_type det_trans) const;
140  membrane_elastic_law() { nb_params_ = 6; }
141  };
142 
143 
144  /** Mooney-Rivlin hyperelastic law
145 
146  To be used for compressible and incompressible problems.
147  Following combinations are possible:
148  not compressible, not neohookean (default): 2 parameters (C1,C2)
149  not compressible, neohookean: 1 parameter (C1)
150  compressible, not neohookean: 3 parameters (C1,C2,D1)
151  compressible, neohookean: 2 parameters (C1,D1)
152  */
154  const bool compressible, neohookean;
155  virtual scalar_type strain_energy(const base_matrix &E,
156  const base_vector &params, scalar_type det_trans) const;
157  virtual void sigma(const base_matrix &E, base_matrix &result,
158  const base_vector &params, scalar_type det_trans) const;
159  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
160  const base_vector &params, scalar_type det_trans) const;
161  explicit Mooney_Rivlin_hyperelastic_law(bool compressible_=false,
162  bool neohookean_=false);
163  };
164 
165  /** Neo-Hookean hyperelastic law variants
166 
167  To be used for compressible problems.
168  For incompressible ones Mooney-Rivlin hyperelastic law can be used.
169  */
171  const bool bonet;
172  virtual scalar_type strain_energy(const base_matrix &E,
173  const base_vector &params, scalar_type det_trans) const;
174  virtual void sigma(const base_matrix &E, base_matrix &result,
175  const base_vector &params, scalar_type det_trans) const;
176  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
177  const base_vector &params, scalar_type det_trans) const;
178  explicit Neo_Hookean_hyperelastic_law(bool bonet_=true);
179  };
180 
181  /** Blatz_Ko hyperelastic law
182 
183  To be used for compressible problems.
184  */
186  virtual scalar_type strain_energy(const base_matrix &E,
187  const base_vector &params, scalar_type det_trans) const;
188  virtual void sigma(const base_matrix &E, base_matrix &result,
189  const base_vector &params, scalar_type det_trans) const;
190  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
191  const base_vector &params, scalar_type det_trans) const;
193  };
194 
195 
196  /** Ciarlet-Geymonat hyperelastic law
197  */
199  // parameters are lambda=params[0], mu=params[1], a=params[2]
200  // The parameter a has to verify a in ]0, mu/2[
201  virtual scalar_type strain_energy(const base_matrix &E,
202  const base_vector &params, scalar_type det_trans) const;
203  virtual void sigma(const base_matrix &E, base_matrix &result,
204  const base_vector &params, scalar_type det_trans) const;
205  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
206  const base_vector &params, scalar_type det_trans) const;
207  Ciarlet_Geymonat_hyperelastic_law() { nb_params_ = 3; }
208  };
209 
210  /** Plane strain hyperelastic law (takes another law as a parameter)
211  */
213  virtual scalar_type strain_energy(const base_matrix &E,
214  const base_vector &params, scalar_type det_trans) const;
215  virtual void sigma(const base_matrix &E, base_matrix &result,
216  const base_vector &params, scalar_type det_trans) const;
217  virtual void grad_sigma(const base_matrix &E, base_tensor &result,
218  const base_vector &params, scalar_type det_trans) const;
219  plane_strain_hyperelastic_law(const phyperelastic_law &pl_)
220  { pl = pl_; nb_params_ = pl->nb_params(); }
221  };
222 
223 
224 
225 
226  template<typename VECT1, typename VECT2> class elasticity_nonlinear_term
227  : public getfem::nonlinear_elem_term {
228  const mesh_fem &mf;
229  std::vector<scalar_type> U;
230  const mesh_fem *mf_data;
231  const VECT2 &PARAMS;
232  size_type N;
233  size_type NFem;
234  const abstract_hyperelastic_law &AHL;
235  base_vector params, coeff;
236  base_matrix E, Sigma, gradU;
237  base_tensor tt;
238  bgeot::multi_index sizes_;
239  int version;
240  public:
241  elasticity_nonlinear_term(const mesh_fem &mf_, const VECT1 &U_,
242  const mesh_fem *mf_data_, const VECT2 &PARAMS_,
243  const abstract_hyperelastic_law &AHL_,
244  int version_)
245  : mf(mf_), U(mf_.nb_basic_dof()), mf_data(mf_data_), PARAMS(PARAMS_),
246  N(mf_.linked_mesh().dim()), NFem(mf_.get_qdim()), AHL(AHL_),
247  params(AHL_.nb_params()), E(N, N), Sigma(N, N), gradU(NFem, N),
248  tt(N, N, N, N), sizes_(NFem, N, NFem, N),
249  version(version_) {
250  switch (version) {
251  case 0 : break; // tangent term
252  case 1 : sizes_.resize(2); break; // rhs
253  case 2 : sizes_.resize(1); sizes_[0] = 1; break; // strain energy
254  case 3 : sizes_.resize(2); break; // Id + grad(u)
255  }
256 
257  mf.extend_vector(U_, U);
258  if (gmm::vect_size(PARAMS) == AHL_.nb_params())
259  gmm::copy(PARAMS, params);
260  }
261 
262  const bgeot::multi_index &sizes(size_type) const { return sizes_; }
263 
264  virtual void compute(getfem::fem_interpolation_context& ctx,
265  bgeot::base_tensor &t) {
266  size_type cv = ctx.convex_num();
267  slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
268  ctx.pf()->interpolation_grad(ctx, coeff, gradU, mf.get_qdim());
269 
270  for (unsigned int alpha = 0; alpha < N; ++alpha)
271  gradU(alpha, alpha) += scalar_type(1);
272 
273  if (version == 3) {
274  for (size_type n = 0; n < NFem; ++n)
275  for (size_type m = 0; m < N; ++m)
276  t(n,m) = gradU(n,m);
277  return;
278  }
279 
280  gmm::mult(gmm::transposed(gradU), gradU, E);
281  for (unsigned int alpha = 0; alpha < N; ++alpha)
282  E(alpha, alpha) -= scalar_type(1);
283  gmm::scale(E, scalar_type(0.5));
284 
285  scalar_type det_trans = gmm::lu_det(gradU);
286 
287  if (version == 2) {
288  t[0] = AHL.strain_energy(E, params, det_trans);
289  return;
290  }
291 
292  AHL.sigma(E, Sigma, params, det_trans);
293 
294  if (version == 0) {
295  AHL.grad_sigma(E, tt, params, det_trans);
296  for (size_type n = 0; n < NFem; ++n)
297  for (size_type m = 0; m < N; ++m)
298  for (size_type l = 0; l < N; ++l)
299  for (size_type k = 0; k < NFem; ++k) {
300  scalar_type aux = (k == n) ? Sigma(m,l) : 0.0;
301  for (size_type j = 0; j < N; ++j)
302  for (size_type i = 0; i < N; ++i) {
303  aux += gradU(n ,j) * gradU(k, i) * tt(j, m, i, l);
304  }
305  t(n, m, k, l) = aux;
306  }
307  } else {
308  if (det_trans < scalar_type(0)) AHL.inc_unvalid_flag();
309  for (size_type i = 0; i < NFem; ++i)
310  for (size_type j = 0; j < N; ++j) {
311  scalar_type aux(0);
312  for (size_type k = 0; k < N; ++k)
313  aux += gradU(i, k) * Sigma(k, j);
314  t(i,j) = aux;
315  }
316  }
317  }
318 
319  virtual void prepare(fem_interpolation_context& ctx, size_type ) {
320  if (mf_data) {
321  size_type cv = ctx.convex_num();
322  size_type nb = AHL.nb_params();
323  coeff.resize(mf_data->nb_basic_dof_of_element(cv)*nb);
324  for (size_type i = 0; i < mf_data->nb_basic_dof_of_element(cv); ++i)
325  for (size_type k = 0; k < nb; ++k)
326  coeff[i * nb + k]
327  = PARAMS[mf_data->ind_basic_dof_of_element(cv)[i]*nb+k];
328  ctx.pf()->interpolation(ctx, coeff, params, dim_type(nb));
329  }
330  }
331 
332  };
333 
334 
335  /**
336  Tangent matrix for the non-linear elasticity
337  @ingroup asm
338  */
339  template<typename MAT, typename VECT1, typename VECT2>
341  (const MAT &K_, const mesh_im &mim, const getfem::mesh_fem &mf,
342  const VECT1 &U, const getfem::mesh_fem *mf_data, const VECT2 &PARAMS,
343  const abstract_hyperelastic_law &AHL,
344  const mesh_region &rg = mesh_region::all_convexes()) {
345  MAT &K = const_cast<MAT &>(K_);
346  GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
347  "wrong qdim for the mesh_fem");
348 
349  elasticity_nonlinear_term<VECT1, VECT2>
350  nterm(mf, U, mf_data, PARAMS, AHL, 0);
351  elasticity_nonlinear_term<VECT1, VECT2>
352  nterm2(mf, U, mf_data, PARAMS, AHL, 3);
353 
355  if (mf_data)
356  if (AHL.adapted_tangent_term_assembly_fem_data.size() > 0)
357  assem.set(AHL.adapted_tangent_term_assembly_cte_data);
358  else
359  assem.set("M(#1,#1)+=sym(comp(NonLin$1(#1,#2)(i,j,k,l).vGrad(#1)(:,i,j).vGrad(#1)(:,k,l)))");
360  else
361  if (AHL.adapted_tangent_term_assembly_cte_data.size() > 0)
362  assem.set(AHL.adapted_tangent_term_assembly_cte_data);
363  else
364  assem.set("M(#1,#1)+=sym(comp(NonLin$1(#1)(i,j,k,l).vGrad(#1)(:,i,j).vGrad(#1)(:,k,l)))");
365  assem.push_mi(mim);
366  assem.push_mf(mf);
367  if (mf_data) assem.push_mf(*mf_data);
368  assem.push_data(PARAMS);
369  assem.push_nonlinear_term(&nterm);
370  assem.push_nonlinear_term(&nterm2);
371  assem.push_mat(K);
372  assem.assembly(rg);
373  }
374 
375 
376  /**
377  @ingroup asm
378  */
379  template<typename VECT1, typename VECT2, typename VECT3>
380  void asm_nonlinear_elasticity_rhs
381  (const VECT1 &R_, const mesh_im &mim, const getfem::mesh_fem &mf,
382  const VECT2 &U, const getfem::mesh_fem *mf_data, const VECT3 &PARAMS,
383  const abstract_hyperelastic_law &AHL,
384  const mesh_region &rg = mesh_region::all_convexes()) {
385  VECT1 &R = const_cast<VECT1 &>(R_);
386  GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
387  "wrong qdim for the mesh_fem");
388 
389  elasticity_nonlinear_term<VECT2, VECT3>
390  nterm(mf, U, mf_data, PARAMS, AHL, 1);
391 
393  if (mf_data)
394  assem.set("t=comp(NonLin(#1,#2).vGrad(#1)); V(#1) += t(i,j,:,i,j)");
395  else
396  assem.set("t=comp(NonLin(#1).vGrad(#1)); V(#1) += t(i,j,:,i,j)");
397  // comp() to be optimized ?
398  assem.push_mi(mim);
399  assem.push_mf(mf);
400  if (mf_data) assem.push_mf(*mf_data);
401  assem.push_nonlinear_term(&nterm);
402  assem.push_vec(R);
403  assem.assembly(rg);
404  }
405 
406  // added by Jean-Yves Heddebaut <jyhed@alpino.be>
407  int levi_civita(int i,int j,int k);
408 
409 
410  /**@ingroup asm
411  */
412  template<typename VECT2, typename VECT3>
413  scalar_type asm_elastic_strain_energy
414  (const mesh_im &mim, const getfem::mesh_fem &mf,
415  const VECT2 &U, const getfem::mesh_fem *mf_data, const VECT3 &PARAMS,
416  const abstract_hyperelastic_law &AHL,
417  const mesh_region &rg = mesh_region::all_convexes()) {
418 
419  GMM_ASSERT1(mf.get_qdim() >= mf.linked_mesh().dim(),
420  "wrong qdim for the mesh_fem");
421 
422  elasticity_nonlinear_term<VECT2, VECT3>
423  nterm(mf, U, mf_data, PARAMS, AHL, 2);
424  std::vector<scalar_type> V(1);
425 
427  if (mf_data)
428  assem.set("V() += comp(NonLin(#1,#2))(i)");
429  else
430  assem.set("V() += comp(NonLin(#1))(i)");
431 
432  assem.push_mi(mim);
433  assem.push_mf(mf);
434  if (mf_data) assem.push_mf(*mf_data);
435  assem.push_nonlinear_term(&nterm);
436  assem.push_vec(V);
437  assem.assembly(rg);
438 
439  return V[0];
440  }
441 
442 
443 
444 
445 
446 
447 
448 
449 
450  /* ******************************************************************** */
451  /* Mixed nonlinear incompressibility assembly procedure */
452  /* ******************************************************************** */
453 
454  template<typename VECT1> class incomp_nonlinear_term
455  : public getfem::nonlinear_elem_term {
456 
457  const mesh_fem &mf;
458  std::vector<scalar_type> U;
459  size_type N;
460  base_vector coeff;
461  base_matrix gradPhi;
462  bgeot::multi_index sizes_;
463  int version;
464 
465  public:
466  incomp_nonlinear_term(const mesh_fem &mf_, const VECT1 &U_,
467  int version_)
468  : mf(mf_), U(mf_.nb_basic_dof()),
469  N(mf_.get_qdim()),
470  gradPhi(N, N), sizes_(N, N),
471  version(version_) {
472  if (version == 1) { sizes_.resize(1); sizes_[0] = 1; }
473  mf.extend_vector(U_, U);
474  }
475 
476  const bgeot::multi_index &sizes(size_type) const { return sizes_; }
477 
478  virtual void compute(getfem::fem_interpolation_context& ctx,
479  bgeot::base_tensor &t) {
480  size_type cv = ctx.convex_num();
481  slice_vector_on_basic_dof_of_element(mf, U, cv, coeff);
482  ctx.pf()->interpolation_grad(ctx, coeff, gradPhi, mf.get_qdim());
483  gmm::add(gmm::identity_matrix(), gradPhi);
484  scalar_type det = gmm::lu_inverse(gradPhi);
485 
486  if (version != 1) {
487  if (version == 2) det = sqrt(gmm::abs(det));
488  for (size_type i = 0; i < N; ++i)
489  for (size_type j = 0; j < N; ++j) {
490  t(i,j) = - det * gradPhi(j,i);
491  }
492  }
493  else t[0] = scalar_type(1) - det;
494 
495  }
496  };
497 
498  /**@ingroup asm*/
499  template<typename MAT1, typename MAT2, typename VECT1, typename VECT2>
500  void asm_nonlinear_incomp_tangent_matrix(const MAT1 &K_, const MAT2 &B_,
501  const mesh_im &mim,
502  const mesh_fem &mf_u,
503  const mesh_fem &mf_p,
504  const VECT1 &U, const VECT2 &P,
505  const mesh_region &rg = mesh_region::all_convexes()) {
506  MAT1 &K = const_cast<MAT1 &>(K_);
507  MAT2 &B = const_cast<MAT2 &>(B_);
508  GMM_ASSERT1(mf_u.get_qdim() == mf_u.linked_mesh().dim(),
509  "wrong qdim for the mesh_fem");
510 
511  incomp_nonlinear_term<VECT1> ntermk(mf_u, U, 0);
512  incomp_nonlinear_term<VECT1> ntermb(mf_u, U, 2);
514  assem("P=data(#2);"
515  "t=comp(NonLin$1(#1).vGrad(#1).Base(#2));"
516  "M$2(#1,#2)+= t(i,j,:,i,j,:);"
517  /*"w=comp(NonLin$2(#1).vGrad(#1).NonLin$2(#1).vGrad(#1).Base(#2));"
518  "M$1(#1,#1)+= w(j,i,:,j,k, m,k,:,m,i,p).P(p)"
519  "-w(i,j,:,i,j, k,l,:,k,l,p).P(p)"*/
520  /*
521  "w=comp(vGrad(#1).NonLin$2(#1).vGrad(#1).NonLin$2(#1).Base(#2));"
522  "M$1(#1,#1)+= w(:,j,k, j,i, :,m,i, m,k, p).P(p)"
523  "-w(:,j,i, j,i, :,m,l, m,l, p).P(p)"
524  */
525  "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));"
526  "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));"
527  "M$1(#1,#1)+= w1-w2"
528  );
529 
530  assem.push_mi(mim);
531  assem.push_mf(mf_u);
532  assem.push_mf(mf_p);
533  assem.push_nonlinear_term(&ntermk);
534  assem.push_nonlinear_term(&ntermb);
535  assem.push_mat(K);
536  assem.push_mat(B);
537  assem.push_data(P);
538  assem.assembly(rg);
539  }
540 
541 
542  /**@ingroup asm
543  */
544  template<typename VECT1, typename VECT2, typename VECT3>
545  void asm_nonlinear_incomp_rhs
546  (const VECT1 &R_U_, const VECT1 &R_P_, const mesh_im &mim,
547  const getfem::mesh_fem &mf_u, const getfem::mesh_fem &mf_p,
548  const VECT2 &U, const VECT3 &P,
549  const mesh_region &rg = mesh_region::all_convexes()) {
550  VECT1 &R_U = const_cast<VECT1 &>(R_U_);
551  VECT1 &R_P = const_cast<VECT1 &>(R_P_);
552  GMM_ASSERT1(mf_u.get_qdim() == mf_u.linked_mesh().dim(),
553  "wrong qdim for the mesh_fem");
554 
555  incomp_nonlinear_term<VECT2> nterm_tg(mf_u, U, 0);
556  incomp_nonlinear_term<VECT2> nterm(mf_u, U, 1);
557 
559  assem("P=data(#2); "
560  "t=comp(NonLin$1(#1).vGrad(#1).Base(#2));"
561  "V$1(#1) += t(i,j,:,i,j,k).P(k);"
562  "w=comp(NonLin$2(#1).Base(#2)); V$2(#2) += w(1,:)");
563  // assem() to be optimized ?
564 
565  assem.push_mi(mim);
566  assem.push_mf(mf_u);
567  assem.push_mf(mf_p);
568  assem.push_nonlinear_term(&nterm_tg);
569  assem.push_nonlinear_term(&nterm);
570  assem.push_vec(R_U);
571  assem.push_vec(R_P);
572  assem.push_data(P);
573  assem.assembly(rg);
574  }
575 
576 
577 
578  //===========================================================================
579  //
580  // Bricks
581  //
582  //===========================================================================
583 
584 
585  /** Add a nonlinear (large strain) elasticity term to the model with
586  respect to the variable
587  `varname` (deprecated brick, use add_finite_strain_elaticity instead).
588  Note that the constitutive law is described by `AHL` which
589  should not be freed while the model is used. `dataname` described the
590  parameters of the constitutive laws. It could be a vector of value
591  of length the number of parameter of the constitutive law or a vector
592  field described on a finite element method.
593  */
595  (model &md, const mesh_im &mim, const std::string &varname,
596  const phyperelastic_law &AHL, const std::string &dataname,
597  size_type region = size_type(-1));
598 
599 
600 
601  void compute_Von_Mises_or_Tresca
602  (model &md, const std::string &varname, const phyperelastic_law &AHL,
603  const std::string &dataname, const mesh_fem &mf_vm,
604  model_real_plain_vector &VM, bool tresca);
605 
606 
607  void compute_sigmahathat(model &md,
608  const std::string &varname,
609  const phyperelastic_law &AHL,
610  const std::string &dataname,
611  const mesh_fem &mf_sigma,
612  model_real_plain_vector &SIGMA);
613 
614 
615  /**
616  Compute the Von-Mises stress or the Tresca stress of a field
617  with respect to the constitutive elasticity law AHL (only valid in 3D).
618  */
619  template <class VECTVM> void compute_Von_Mises_or_Tresca
620  (model &md, const std::string &varname, const phyperelastic_law &AHL,
621  const std::string &dataname, const mesh_fem &mf_vm,
622  VECTVM &VM, bool tresca) {
623  model_real_plain_vector VMM(mf_vm.nb_dof());
624  compute_Von_Mises_or_Tresca
625  (md, varname, AHL, dataname, mf_vm, VMM, tresca);
626  gmm::copy(VMM, VM);
627  }
628 
629  /** Add a nonlinear incompressibility term (for large strain elasticity)
630  to the model with respect to the variable
631  `varname` (the displacement) and `multname` (the pressure).
632  */
634  (model &md, const mesh_im &mim, const std::string &varname,
635  const std::string &multname, size_type region = size_type(-1));
636 
637  //===========================================================================
638  // High-level generic assembly bricks
639  //===========================================================================
640 
641  /** Add a finite strain elasticity brick
642  to the model with respect to the variable
643  `varname` (the displacement).
644  For 2D meshes, switch automatically to plane strain elasticity.
645  High-level generic assembly version.
646  */
648  (model &md, const mesh_im &mim, const std::string &lawname,
649  const std::string &varname, const std::string &params,
650  size_type region = size_type(-1));
651 
652 
653  /** Add a finite strain incompressibility term (for large strain elasticity)
654  to the model with respect to the variable
655  `varname` (the displacement) and `multname` (the pressure).
656  High-level generic assembly version.
657  */
659  (model &md, const mesh_im &mim, const std::string &varname,
660  const std::string &multname, size_type region = size_type(-1));
661 
662  /**
663  Interpolate the Von-Mises stress of a field `varname`
664  with respect to the nonlinear elasticity constitutive law `lawname`
665  with parameters `params` (only valid in 3D).
666  */
668  (model &md, const std::string &lawname, const std::string &varname,
669  const std::string &params, const mesh_fem &mf_vm,
670  model_real_plain_vector &VM,
671  const mesh_region &rg=mesh_region::all_convexes());
672 
673  IS_DEPRECATED inline void finite_strain_elasticity_Von_Mises
674  (model &md, const std::string &varname, const std::string &lawname,
675  const std::string &params, const mesh_fem &mf_vm,
676  model_real_plain_vector &VM,
677  const mesh_region &rg=mesh_region::all_convexes()) {
678  compute_finite_strain_elasticity_Von_Mises(md, varname, lawname, params,
679  mf_vm, VM, rg);
680  }
681 
682 } /* end of namespace getfem. */
683 
684 
685 #endif /* GETFEM_NONLINEAR_ELASTICITY_H__ */
virtual size_type nb_dof() const
Return the total number of degrees of freedom.
structure used to hold a set of convexes and/or convex faces.
void slice_vector_on_basic_dof_of_element(const mesh_fem &mf, const VEC1 &vec, size_type cv, VEC2 &coeff, size_type qmult1=size_type(-1), size_type qmult2=size_type(-1))
Given a mesh_fem.
void push_data(const VEC &d)
Add a new data (dense array)
static mesh_region all_convexes()
provide a default value for the mesh_region parameters of assembly procedures etc.
size_type convex_num() const
get the current convex number
Definition: getfem_fem.cc:49
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))
Add a nonlinear incompressibility term (for large strain elasticity) to the model with respect to the...
void push_nonlinear_term(pnonlinear_elem_term net)
Add a new non-linear term.
void push_mi(const mesh_im &im_)
Add a new mesh_im.
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
True Cauchy stress (for Updated Lagrangian formulation)
Describe an integration method linked to a mesh.
void assembly(const mesh_region &region=mesh_region::all_convexes())
do the assembly on the specified region (boundary or set of convexes)
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 elasticity brick to the model with respect to the variable varname (the displacem...
void push_mf(const mesh_fem &mf_)
Add a new mesh_fem.
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())
Interpolate the Von-Mises stress of a field varname with respect to the nonlinear elasticity constitu...
Generic assembly of vectors, matrices.
``Model'' variables store the variables, the data and the description of a model. ...
size_t size_type
used as the common size type in the library
Definition: bgeot_poly.h:48
Model representation in Getfem.
Input/output on sparse matrices.
Interpolation of fields from a mesh_fem onto another.
virtual dim_type get_qdim() const
Return the Q dimension.
structure passed as the argument of fem interpolation functions.
Definition: getfem_fem.h:707
A langage for generic assembly of pde boundary value problems.
Describe a finite element method linked to a mesh.
Neo-Hookean hyperelastic law variants.
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())
Tangent matrix for the non-linear elasticity.
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))
Add a nonlinear (large strain) elasticity term to the model with respect to the variable varname (dep...
const mesh & linked_mesh() const
Return a reference to the underlying mesh.
const pfem pf() const
get the current FEM descriptor
Definition: getfem_fem.h:740
Generic assembly implementation.
Linear law for a membrane (plane stress), orthotropic material caracterized by Ex, Ey, vYX and G, with optional orthotropic prestresses.
void push_mat(const MAT &m)
Add a new output matrix (fake const version..)
abstract class for integration of non-linear terms into the mat_elem computations the nonlinear term ...
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
cauchy-truesdel tangent moduli, used in updated lagrangian
size_type alpha(short_type n, short_type d)
Return the value of which is the number of monomials of a polynomial of variables and degree ...
Definition: bgeot_poly.cc:46
Compute the gradient of a field on a getfem::mesh_fem.
void push_vec(VEC &v)
Add a new output vector.
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
cauchy-truesdel tangent moduli, used in updated lagrangian
Plane strain hyperelastic law (takes another law as a parameter)
Saint-Venant Kirchhoff hyperelastic law.
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))
Add a finite strain incompressibility term (for large strain elasticity) to the model with respect to...