[Getfem-commits] r4852 - /trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m

[farshid . dabaghi]

Author: fdabaghi
Date: Fri Feb  6 09:34:23 2015
New Revision: 4852

URL: http://svn.gna.org/viewcvs/getfem?rev=4852&view=rev
Log:
modification

Added:
    trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m

Added: trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m
URL: 
http://svn.gna.org/viewcvs/getfem/trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m?rev=4852&view=auto
==============================================================================
--- trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m   
(added)
+++ trunk/getfem/interface/tests/matlab/demo_dynamic_plasticity_with_contac.m   
Fri Feb  6 09:34:23 2015
@@ -0,0 +1,444 @@
+% Copyright (C) 2010-2014  Yves Renard, Farshid Dabaghi.
+%
+% This file is a part of GETFEM++
+%
+% Getfem++  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 along with the GCC Runtime Library
+% Exception either version 3.1 or (at your option) any later version.
+% This program  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 and GCC Runtime Library Exception for more details.
+% You  should  have received a copy of the GNU Lesser General Public License
+% along  with  this program;  if not, write to the Free Software Foundation,
+% Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301, USA.
+
+
+
+
+
+% We compute a dynamic plasticity problem with a Von Mises criterion with or
+% without kinematic hardening and with unilateral contact with a rigid 
obstacle.
+% For convenience we consider an homogenous Dirichlet condition on the top
+% of the domain. 
+
+
+
+clear all;
+gf_workspace('clear all');
+clc;
+
+with_hardening = 1;
+bi_material = false;
+test_tangent_matrix = 0;
+do_plot = true;
+plot_mesh = true;
+% Initialize used data
+LX = 20;
+LY = 100;
+NX = 20;
+NY = 50;
+
+
+% alpha is parametr of the generalized integration algorithms The
+% The choice alpha = 1/2 yields the mid point method and alpha = 1 leads to
+% backward Euler integration
+alpha_method = false;
+alpha = 1.0;
+
+
+f = [0 15000]';
+dirichlet_val = 20;
+
+
+% transient part.
+T = pi/4;
+dt = 0.01;
+theta= 1;
+
+
+
+
+
+% Create the mesh
+% m = gfMesh('triangles grid', [0:(LX/NX):LX], [0:(LY/NY):LY]);
+m = 
gfMesh('import','structured',sprintf('GT="GT_PK(2,1)";SIZES=[%d,%d];NOISED=0;NSUBDIV=[%d,%d];',
 LX, LY, NX, NY));
+N = gf_mesh_get(m, 'dim');
+
+
+r = 10;                  % Augmentation parameter
+
+% Signed distance representing the obstacle
+if (N == 1) obstacle = 'x'; elseif (N == 2) obstacle = 'y'; else obstacle = 
'z'; end;
+  
+% Plotting
+% gf_plot_mesh(m, 'vertices', 'on', 'convexes', 'on');
+% return;
+
+%lambda_degree =1;
+
+% Define used MeshIm
+mim=gfMeshIm(m);  set(mim, 'integ', gfInteg('IM_TRIANGLE(6)')); % Gauss 
methods on triangles
+
+% Define used MeshFem
+mf_u=gfMeshFem(m,2); set(mf_u, 'fem',gfFem('FEM_PK(2,2)'));
+mf_data=gfMeshFem(m); set(mf_data, 'fem', gfFem('FEM_PK_DISCONTINUOUS(2,0)'));
+% mf_sigma=gfMeshFem(m,4); set(mf_sigma, 
'fem',gfFem('FEM_PK_DISCONTINUOUS(2,1)'));
+mf_sigma=gfMeshFem(m,4); set(mf_sigma, 
'fem',gfFem('FEM_PK_DISCONTINUOUS(2,0)'));
+mf_vm = gfMeshFem(m); set(mf_vm, 'fem', gfFem('FEM_PK_DISCONTINUOUS(2,1)'));
+
+
+%mfflambda = gf_mesh_fem(mesh1, N);  gf_mesh_fem_set(mfflambda, 'classical 
fem', 1);
+mflambda=gfMeshFem(m,1); set(mflambda, 'fem',gfFem('FEM_PK(2,1)'));
+
+
+GAMMAD = 1; GAMMAC = 2;
+% Find the border of the domain
+% P=get(m, 'pts');
+% pidleft=find(abs(P(1,:))<1e-6); % Retrieve index of points which x near to 0
+% pidright=find(abs(P(1,:) - LX)<1e-6); % Retrieve index of points which x 
near to L
+% fleft =get(m,'faces from pid',pidleft); 
+% fright=get(m,'faces from pid',pidright);
+% %set(m,'boundary',1,fleft); % for Dirichlet condition
+% set(m,'region',GAMMAD,fleft);
+% %set(m,'boundary',2,fright); % for Contact condition
+% set(m,'region',GAMMAC,fright);
+P=get(m, 'pts');
+border = gf_mesh_get(m,'outer faces');
+normals = gf_mesh_get(m, 'normal of faces', border);
+contact_boundary=border(:, find(normals(N, :) < -0.01));
+gf_mesh_set(m, 'region', GAMMAC, contact_boundary);
+contact_boundary=border(:, find(normals(N, :) > 0.01));
+gf_mesh_set(m, 'region', GAMMAD, contact_boundary);
+
+if (plot_mesh)
+ gf_plot_mesh(m, 'regions', [GAMMAC],'vertices', 'off', 'convexes', 'off');
+ title('Mesh and contact boundary (in red)');
+ pause(0.1);
+
+end
+
+% Decomposed the mesh into 2 regions with different values of Lamé coeff
+if (bi_material) separation = LY/2; else separation = 0; end
+pidtop    = find(P(2,:)>=separation-1E-6); % Retrieve index of points of the 
top part
+pidbottom = find(P(2,:)<=separation+1E-6); % Retrieve index of points of the 
bottom part
+cvidtop   = get(m, 'cvid from pid', pidtop);
+cvidbottom= get(m, 'cvid from pid', pidbottom);
+CVtop     = sort(get(mf_data, 'basic dof from cvid', cvidtop));
+CVbottom  = sort(get(mf_data, 'basic dof from cvid', cvidbottom));
+
+% Definition of Lame coeff
+lambda(CVbottom,1) = 121150; % Steel
+lambda(CVtop,1) = 84605; % Iron
+mu(CVbottom,1) = 80769; %Steel
+mu(CVtop,1) = 77839; % Iron
+% Definition of plastic threshold
+von_mises_threshold(CVbottom) = 7000;
+von_mises_threshold(CVtop) = 8000;
+rho = 0.1;
+% Definition of hardening parameter
+if (with_hardening)
+  H = mu(1)/5;
+else
+  H = 0;
+end
+
+% Create the model
+md = gfModel('real');
+
+% Declare that u is the unknown of the system on mf_u
+% 2 is the number of version of the data stored, for the time integration 
scheme 
+set(md, 'add fem variable', 'u', mf_u, 2);
+
+
+
+% Time integration scheme and inertia term
+if(alpha_method) 
+ nbdofu = gf_mesh_fem_get(mf_u, 'nbdof');
+ M = gf_asm('mass matrix', mim, mf_u);
+ gf_model_set(md, 'add fem data', 'Previous_u', mf_u);
+ set(md, 'add initialized data', 'rho', rho);
+% % gf_model_set(md, 'add mass brick', mim, string varname[, string 
dataname_rho[, int region]]);
+% gf_model_set(md, 'add mass brick', mim,'u' ,'rho');
+ 
+else
+
+gf_model_set(md, 'add theta method for second order', 'u',theta);
+gf_model_set(md, 'set time step', dt);
+
+
+set(md, 'add initialized data', 'rho', rho);
+gf_model_set(md, 'add mass brick', mim, 'Dot2_u', 'rho');
+
+end
+
+
+
+
+% Declare that lambda is a data of the system on mf_data
+set(md, 'add initialized fem data', 'lambda', mf_data, lambda);
+
+% Declare that mu is a data of the system on mf_data
+set(md, 'add initialized fem data', 'mu', mf_data, mu);
+
+% Declare that von_mises_threshold is a data of the system on mf_data
+set(md, 'add initialized fem data', 'von_mises_threshold', mf_data, 
von_mises_threshold);
+
+N = gf_mesh_get(m, 'dim');
+% gf_model_set(md, 'add fem data', 'Previous_u', mf_u);
+mim_data = gf_mesh_im_data(mim, -1, [N, N]);
+gf_model_set(md, 'add im data', 'sigma', mim_data);
+
+
+ % Declare that alpha is a data of the system 
+ 
+set(md, 'add initialized data', 'alpha', [alpha]);
+
+set(md, 'add initialized data', 'H', [H]);
+
+Is = 'Reshape(Id(meshdim*meshdim),meshdim,meshdim,meshdim,meshdim)';
+IxI = 'Id(meshdim)@Id(meshdim)';
+coeff_long = '((lambda)*(H))/((2*(mu)+(H))*(meshdim*(lambda)+2*(mu)+(H)))';
+B_inv = sprintf('((2*(mu)/(2*(mu)+(H)))*(%s) + (%s)*(%s))', Is, coeff_long, 
IxI);
+B = sprintf('((1+(H)/(2*(mu)))*(%s) - 
(((lambda)*(H))/(2*(mu)*(meshdim*(lambda)+2*(mu))))*(%s))', Is, IxI);
+ApH = sprintf('((2*(mu)+(H))*(%s) + (lambda)*(%s))', Is, IxI);
+Enp1 = '((Grad_u+Grad_u'')/2)';
+En = '((Grad_Previous_u+Grad_Previous_u'')/2)';
+ %expression de sigma for Implicit Euler method
+  expr_sigma = strcat('(', B_inv, '*(Von_Mises_projection((-(H)*', Enp1, 
')+(', ApH, '*(',Enp1,'-',En,')) + (', B, '*sigma), von_mises_threshold) + H*', 
Enp1, '))');
+  
+ 
+if(alpha_method)
+ %expression de sigma for generalized alpha algorithms
+  expr_sigma = strcat('(', B_inv, 
'*(Von_Mises_projection((',B,'*(1-alpha)*sigma)+(-(H)*(((1-alpha)*',En,')+(alpha*',
 Enp1, ')))+(alpha*', ApH, '*(',Enp1,'-',En,')) + (alpha*', ...
+    B, '*sigma), von_mises_threshold) + (H)*(((1-alpha)*',En,')+(alpha*', 
Enp1, '))))');
+end
+
+
+gf_model_set(md, 'add nonlinear generic assembly brick', mim, 
strcat(expr_sigma, ':Grad_Test_u'));
+% gf_model_set(md, 'add finite strain elasticity brick', mim, 'u', 
'SaintVenant Kirchhoff', '[lambda; mu]');
+
+
+
+  gf_model_set(md, 'add initialized data', 'dirichletdata', [0; 
dirichlet_val]);
+  gf_model_set(md, 'add Dirichlet condition with multipliers', mim, 'u', mf_u, 
GAMMAD, 'dirichletdata');
+
+%  gf_model_set(md, 'add initialized data', 'dirichletdata', [0; 
dirichlet_val]);
+% % Add homogeneous Dirichlet condition to u on the left hand side of the 
domain
+% set(md, 'add Dirichlet condition with multipliers', mim, 'u', mf_u, GAMMAD);
+
+% Add a source term to the system
+set(md,'add initialized fem data', 'VolumicData', mf_data, get(mf_data, 
'eval',{f(1,1)*sin(0);f(2,1)*sin(0)}));
+set(md, 'add source term brick', mim, 'u', 'VolumicData', 2);
+
+
+
+% Contact brick 
+
+
+% ldof = gf_mesh_fem_get(mflambda, 'dof on region', GAMMAC);
+% mflambda_partial = gf_mesh_fem('partial', mflambda, ldof);
+% gf_model_set(md, 'add fem variable', 'lambda_n', mflambda_partial);
+% gf_model_set(md, 'add initialized data', 'r', [r]);
+% OBS = gf_mesh_fem_get(mflambda, 'eval', { obstacle });
+% gf_model_set(md, 'add initialized fem data', 'obstacle',mflambda , OBS);
+% gf_model_set(md, 'add integral contact with rigid obstacle brick', ...
+%       mim, 'u', 'lambda_n', 'obstacle', 'r', GAMMAC, 1);
+
+  
+pause
+
+% interpolate the initial data
+%U0 = get(md, 'variable', 'u');
+U0 = (gf_mesh_fem_get(mf_u, 'eval', {0, sprintf('%g +0.0+0.00*y', 
dirichlet_val)}));
+V0 = 0*U0;
+
+if(alpha_method)
+gf_model_set(md, 'add explicit matrix', 'u', 'u',rho* M/(dt*dt*alpha));
+ind_rhs = gf_model_set(md, 'add explicit rhs', 'u', zeros(nbdofu,1));
+MV0=M*V0';
+else
+    
+    
+% Initial data.
+gf_model_set(md, 'variable', 'Previous_u',  U0);
+gf_model_set(md, 'variable', 'Previous_Dot_u',  V0);
+
+
+% Initialisation of the acceleration 'Previous_Dot2_u'
+gf_model_set(md, 'perform init time derivative', dt/20.);
+gf_model_get(md, 'solve');
+
+end
+
+
+
+
+
+
+
+VM=zeros(1,get(mf_vm, 'nbdof'));
+ step=1;
+% Iterations
+for t = 0:dt:T
+  
+  % coeff = sin(16*t);
+  coeff=- 1;
+  
+   disp(sprintf('step %d, coeff = %g', step , coeff)); 
+   set(md, 'variable', 'VolumicData', get(mf_data, 
'eval',{f(1,1)*coeff;f(2,1)*coeff}));  
+  
+if(alpha_method)
+    
+   MU0=M*U0';
+     
+   LL = rho*(( 1/(dt*dt*alpha))*MU0+( 1/(dt*alpha))*MV0);
+ 
+   gf_model_set(md, 'set private rhs', ind_rhs, LL);
+   get(md, 'solve', 'noisy', 'lsearch', 'simplest',  'alpha min', 0.8, 
'max_iter', 100, 'max_res', 1e-6);
+   U = gf_model_get(md, 'variable', 'u');
+   MV = ((M*U' - MU0)/dt -(1-alpha)*MV0)/alpha;
+
+  
+else
+   
+   get(md, 'solve', 'noisy', 'lsearch', 'simplest',  'alpha min', 0.8, 
'max_iter', 100, 'max_res', 1e-6);
+   U = gf_model_get(md, 'variable', 'u');
+   V = gf_model_get(md, 'variable', 'Dot_u'); 
+  
+end
+
+      
+  if (test_tangent_matrix)
+      gf_model_get(md, 'test tangent matrix', 1E-8, 10, 0.000001);
+  end;
+    
+ if (alpha_method)
+      sigma_0 = gf_model_get(md, 'variable', 'sigma');
+      sigma = gf_model_get(md, 'interpolation', expr_sigma, mim_data);
+      U_0 = gf_model_get(md, 'variable', 'Previous_u');
+      U_nalpha = alpha*U + (1-alpha)*U_0;
+       
+       
+       
+      M_vm = gf_asm('mass matrix', mim, mf_vm);
+      L = gf_asm('generic', mim, 1, 'sqrt(3/2)*Norm(Deviator(sigma))*Test_vm', 
-1, 'sigma', 0, mim_data, sigma, 'vm', 1, mf_vm, zeros(gf_mesh_fem_get(mf_vm, 
'nbdof'),1));
+      VM = (M_vm \ L)';
+      coeff1='-lambda/(2*mu*(meshdim*lambda+2*mu))';
+      coeff2='1/(2*mu)';
+      Ainv=sprintf('(%s)*(%s) + (%s)*(%s)', coeff1, IxI, coeff2, Is);
+      Ep = sprintf('(Grad_u+Grad_u'')/2 - (%s)*sigma', Ainv);
+      L = gf_asm('generic', mim, 1, sprintf('Norm(%s)*Test_vm', Ep), -1, 
'sigma', 0, mim_data, sigma, 'u', 0, mf_u, U, 'vm', 1, mf_vm, 
zeros(gf_mesh_fem_get(mf_vm, 'nbdof'),1), 'mu', 0, mf_data, mu, 'lambda', 0, 
mf_data, lambda);
+      plast = (M_vm \ L)';
+      
+      gf_model_set(md, 'variable', 'u', U_nalpha);
+      Epsilon_u = gf_model_get(md, 'interpolation', '((Grad_u+Grad_u'')/2)', 
mim_data);
+ 
+      nb_gauss_pt_per_element = size(sigma, 2) / (N*N*gf_mesh_get(m, 'nbcvs'));
+      % ind_gauss_pt = 22500;
+      ind_gauss_pt = nb_gauss_pt_per_element * 1100 - 1;
+      ind_elt = floor(ind_gauss_pt / nb_gauss_pt_per_element);
+       P = gf_mesh_get(m, 'pts from cvid', ind_elt);
+      disp(sprintf('Point for the strain/stress graph (approximately): 
(%f,%f)', P(1,1), P(2,1)));
+
+    if (size(sigma, 2) <= N*(ind_gauss_pt + 1))
+      ind_gauss_pt = floor(3*size(sigma, 2) / (4*N*N));
+    end
+      sigma_fig(1,step)=sigma(N*N*ind_gauss_pt + 1);
+      Epsilon_u_fig(1,step)=Epsilon_u(N*N*ind_gauss_pt + 1);
+      sigma = (sigma - (1-alpha)*sigma_0)/alpha;
+      gf_model_set(md, 'variable', 'sigma', sigma);
+      gf_model_set(md, 'variable', 'Previous_u', U);
+  else
+   
+    
+    sigma = gf_model_get(md, 'interpolation', expr_sigma, mim_data);
+    gf_model_set(md, 'variable', 'sigma', sigma);
+    gf_model_set(md, 'variable', 'Previous_u', U);
+    
+
+      
+    M_VM = gf_asm('mass matrix', mim, mf_vm);
+    L = gf_asm('generic', mim, 1, 'sqrt(3/2)*Norm(Deviator(sigma))*Test_vm', 
-1, 'sigma', 0, mim_data, sigma, 'vm', 1, mf_vm, zeros(gf_mesh_fem_get(mf_vm, 
'nbdof'),1));
+    VM = (M_VM \ L)';
+    coeff1='-lambda/(2*mu*(meshdim*lambda+2*mu))';
+    coeff2='1/(2*mu)';
+    Ainv=sprintf('(%s)*(%s) + (%s)*(%s)', coeff1, IxI, coeff2, Is);
+    Ep = sprintf('(Grad_u+Grad_u'')/2 - (%s)*sigma', Ainv);
+    L = gf_asm('generic', mim, 1, sprintf('Norm(%s)*Test_vm', Ep), -1, 
'sigma', 0, mim_data, sigma, 'u', 0, mf_u, U, 'vm', 1, mf_vm, 
zeros(gf_mesh_fem_get(mf_vm, 'nbdof'),1), 'mu', 0, mf_data, mu, 'lambda', 0, 
mf_data, lambda);
+    plast = (M_VM \ L)';
+      
+    Epsilon_u = gf_model_get(md, 'interpolation', '((Grad_u+Grad_u'')/2)', 
mim_data);
+    nb_gauss_pt_per_element = size(sigma, 2) / (N*N*gf_mesh_get(m, 'nbcvs'));
+    % ind_gauss_pt = 22500;
+    ind_gauss_pt = nb_gauss_pt_per_element * 1100 - 1;
+    ind_elt = floor(ind_gauss_pt / nb_gauss_pt_per_element);
+    P = gf_mesh_get(m, 'pts from cvid', ind_elt);
+    disp(sprintf('Point for the strain/stress graph (approximately): (%f,%f)', 
P(1,1), P(2,1)));
+
+    if (size(sigma, 2) <= N*(ind_gauss_pt + 1))
+      ind_gauss_pt = floor(3*size(sigma, 2) / (4*N*N));
+    end
+    sigma_fig(1,step)=sigma(N*N*ind_gauss_pt + 1);
+    Epsilon_u_fig(1,step)=Epsilon_u(N*N*ind_gauss_pt + 1);
+    
+    
+ end  
+    
+    
+       
+    if (do_plot)
+      figure(2)
+      subplot(2,2,1);
+      gf_plot(mf_vm,VM, 'deformation',U,'deformation_mf',mf_u,'refine', 4, 
'deformation_scale',1, 'disp_options', 0); % 'deformed_mesh', 'on')
+      colorbar;
+      axis([-10 30 -5 120]);
+      % caxis([0 10000]);
+      n = t;
+       title(['Von Mises criterion for t = ', num2str(t)]);
+      subplot(2,2,2);
+      gf_plot(mf_vm,plast, 'deformation',U,'deformation_mf',mf_u,'refine', 4, 
'deformation_scale',1, 'disp_options', 0);  % 'deformed_mesh', 'on')
+      colorbar;
+      axis([-10 30 -5 120]);
+      % caxis([0 10000]);
+      n = t;
+      title(['Plastification for t = ', num2str(t)]);
+    
+      
+      subplot(2,2,[3 4]);
+      plot(Epsilon_u_fig, sigma_fig,'r','LineWidth',2)
+      xlabel('Strain');
+      ylabel('Stress')
+      axis([-0.3 0.3 -16500 16500 ]);
+      title(sprintf('step %d / %d, coeff = %g', step,size([0:dt:T],2) , 
coeff));
+      
+      pause(0.1);
+    end
+    
+     step= step+ 1;
+     
+     if(alpha_method)
+         
+  U0 = U;
+  MV0 = MV;
+ 
+     else
+         
+        
+    gf_model_set(md, 'shift variables for time integration');
+    
+     end
+end;
+
+
+
+
+
+
+
+
+
+
+