[Getfem-users] eigenstrain

[fabien amiot]

Dear all,

I'm rather new to Getfem (Matlab-interface), and I'm trying to simulate 
a (linear elastic) bimorph :


%% DATA
% cantilever length
L=1;
% cantilever thickness
H=0.1;
% thickness ratio
r=0.1;
% Lame parameters
Young=60E9; nu=0.3;
lambda=Young.*nu./((1+nu).*(1-2.*nu));
mu=0.5.*Young./(1+nu);
lambda_layer=lambda;
mu_layer=mu;
%% Build the mesh
% cantilever
canti_m=gf_mesh('regular simplices',0:(L./10):L, (-H):(H./4):0);
% layer
layer_m=gf_mesh('regular simplices',0:(L./10):L, 0:(r.*H./4):(r.*H));
% retrieve the CVFIDs for the 2 regions
canti_cvfids = gf_mesh_get(canti_m, 'region',gf_mesh_get(canti_m, 
'regions'));
layer_cvfids = gf_mesh_get(layer_m, 'region',gf_mesh_get(layer_m, 
'regions'));
% merge the two meshes
gf_mesh_set(canti_m, 'merge', layer_m);
% set the region numbers
gf_mesh_set(canti_m, 'region', 1, canti_cvfids);
gf_mesh_set(canti_m, 'region', 2, layer_cvfids);
% integration method
mim=gf_mesh_im(canti_m);
gf_mesh_im_set(mim, 'integ',gf_integ('IM_TRIANGLE(6)'));
% fem object for displacement
mfu=gf_mesh_fem(canti_m,2);
gf_mesh_fem_set(mfu, 'fem',gf_fem('FEM_PK(2,2)'));
% fem object for pressure (used to impose the free strain as a 
incompressibility condition)
mfp=gf_mesh_fem(canti_m);
gf_mesh_fem_set(mfp, 'fem',gf_fem('FEM_PK(2,1)'));
%% build elastic model
md=gf_model('real');
gf_model_set(md, 'add fem variable', 'u', mfu);
gf_model_set(md, 'add initialized data', 'lambda', [lambda]);
gf_model_set(md, 'add initialized data', 'mu', [mu]);
gf_model_set(md, 'add initialized data', 'lambda_layer', [lambda_layer]);
gf_model_set(md, 'add initialized data', 'mu_layer', [mu_layer]);
% set the elastic parameters for the cantilever
gf_model_set(md, 'add isotropic linearized elasticity brick', ...
             mim, 'u', 'lambda', 'mu',1);
% set the elastic parameters for the layer
gf_model_set(md, 'add isotropic linearized elasticity brick', ...
             mim, 'u', 'lambda_layer', 'mu_layer',2);
% set the boundary condition (clamping)
P=gf_mesh_get(canti_m,'pts');
fleft =gf_mesh_get(canti_m,'faces from pid',find(abs(P(1,:))<1e-6));
gf_mesh_set(canti_m,'boundary',3,fleft);
gf_model_set(md, 'add Dirichlet condition with multipliers', ...
             mim, 'u', mfu, 3);



The idea is to describe the eigenstrain by exploiting the linear 
incompressibility brick :


% set the loading
gf_model_set(md, 'add fem variable', 'p', mfp);
gf_model_set(md, 'add initialized data', 'coef', 1.);
gf_model_set(md, 'add linear incompressibility brick', mim, 'u', 'p', 2, 
'coef');


But this produces a zero rhs (as seen from gf_model_get(md,'rhs') ). I 
guess I miss either an important thing or an efficient alternative way 
to achieve this...

Best regards,
Fabien

--
Fabien AMIOT
Chargé de recherche CNRS en colere / cross Research Associate
address@hidden
Tel : (+33) (0)3.81.66.60.14
Fax : (+33) (0)3.81.66.67.00
UMR6174 / FEMTO-ST, Dpt. Mécanique Appliquée
24, rue de l'Épitaphe
25000 Besancon
France