[Getfem-commits] r5314 - in /trunk/getfem: doc/sphinx/source/userdoc/model_plasticity_small_strain.rst src/getfem_plasticity.cc

[Yves . Renard]

Author: renard
Date: Sun May  1 15:34:42 2016
New Revision: 5314

URL: http://svn.gna.org/viewcvs/getfem?rev=5314&view=rev
Log:
minor fixes

Modified:
    trunk/getfem/doc/sphinx/source/userdoc/model_plasticity_small_strain.rst
    trunk/getfem/src/getfem_plasticity.cc

Modified: 
trunk/getfem/doc/sphinx/source/userdoc/model_plasticity_small_strain.rst
URL: 
http://svn.gna.org/viewcvs/getfem/trunk/getfem/doc/sphinx/source/userdoc/model_plasticity_small_strain.rst?rev=5314&r1=5313&r2=5314&view=diff
==============================================================================
--- trunk/getfem/doc/sphinx/source/userdoc/model_plasticity_small_strain.rst    
(original)
+++ trunk/getfem/doc/sphinx/source/userdoc/model_plasticity_small_strain.rst    
Sun May  1 15:34:42 2016
@@ -182,7 +182,7 @@
 Plane strain approximation
 ==========================
 
-A plane strain approximation is a 2D problem which corresponds to the 
deformation of a long cylindrical object where the strain in  the length 
direction (assumed to be along the :math:`z` axis) is considered small compared 
to the ones in the other directions and is neglected. It result in a plane 
strain tensor of the form
+A plane strain approximation is a 2D problem which corresponds to the 
deformation of a long cylindrical object where the strain in the length 
direction (assumed to be along the :math:`z` axis) is considered small compared 
to the ones in the other directions and is neglected. It result in a plane 
strain tensor of the form
 
 .. math:: \varepsilon(u) = \left(\hspace{-0.5em}\begin{array}{ccc} 
\varepsilon_{1,1} & \varepsilon_{1,2} & 0 \\ \varepsilon_{1,2} & 
\varepsilon_{2,2} & 0 \\ 0 & 0 & 0 \end{array}\hspace{-0.5em}\right).
 
@@ -190,21 +190,26 @@
 
 .. math:: \bar{\varepsilon}(u) =  \left(\hspace{-0.5em}\begin{array}{cc} 
\varepsilon_{1,1} & \varepsilon_{1,2} \\ \varepsilon_{1,2} & \varepsilon_{2,2} 
\end{array}\hspace{-0.5em}\right)
 
-the non neglected components of the strain tensor. The adaptation to the plane 
strain approximation to plastic model is most of the time an  easy task.
-
-An isotropic linearized elastic response reads
-
-.. math:: \bar{\sigma} = \lambda \mbox{tr}(\bar{\varepsilon}^e) I + 
2\mu\bar{\varepsilon}^e,
-
-Normally, one also has
-
-.. math:: \sigma_{3,3} = \lambda \mbox{tr}(\bar{\varepsilon}^e) = 
\Frac{\lambda}{2(\lambda+\mu)}.\mbox{tr}(\bar{\sigma})
-
-however, the fact that :math:`\dot{\varepsilon}_{3,3} = 0` and the normality 
law prescribes in general a relation of the type
-
-.. math :: \sigma_{3,3} = \Frac{\sigma_{1,1}+\sigma_{2,2}}{2}
-
-A compromize has to be made ...
+the non neglected components of the strain tensor.
+In the decomposition of plastic and elastic part of the strain tensor, we 
assume
+
+.. math:: \varepsilon^p_{1,3} = \varepsilon^p_{2,3} = \varepsilon^e_{1,3} = 
\varepsilon^e_{2,3} = 0
+
+and
+
+.. math:: \varepsilon^e_{3,3} + \varepsilon^p_{3,3} = \varepsilon_{3,3} = 0. 
+
+The adaptation to the plane strain approximation to plastic model is most of 
the time an  easy task. An isotropic linearized elastic response reads
+
+.. math:: \bar{\sigma} = \lambda (\mbox{tr}(\bar{\varepsilon}^e) + 
\varepsilon^e_{3,3}) I + 2\mu\bar{\varepsilon}^e,
+
+The nonzero :math:`\sigma_{3,3}` component of the stress tensor is given by
+
+.. math:: \sigma_{3,3} = \lambda (\mbox{tr}(\bar{\varepsilon}^e) + 
\varepsilon^e_{3,3}) + 2\mu\varepsilon^e_{3,3}.
+
+Note that in the common case where isochoric plastic strain is assumed, one has
+
+.. math:: \mbox{ tr}(\varepsilon^p) = 0 ~~~~ \Rightarrow  ~~~ 
\varepsilon^p_{3,3} = - (\varepsilon^p_{1,1} + \varepsilon^p_{2,2}).
 
 
 

Modified: trunk/getfem/src/getfem_plasticity.cc
URL: 
http://svn.gna.org/viewcvs/getfem/trunk/getfem/src/getfem_plasticity.cc?rev=5314&r1=5313&r2=5314&view=diff
==============================================================================
--- trunk/getfem/src/getfem_plasticity.cc       (original)
+++ trunk/getfem/src/getfem_plasticity.cc       Sun May  1 15:34:42 2016
@@ -566,9 +566,9 @@
     dict["Eptheta"] = Eptheta;
     Epnp1 = ga_substitute("(Eptheta - (1-(theta))*Epn)/(theta)", dict);
     dict["Epnp1"] = Epnp1;
-    sigma_np1 = ga_substitute("(lambda)*Trace((Enp1)-(Epnp1))*Id(meshdim)"
+    sigma_np1 = ga_substitute("(lambda)*Trace(Enp1)*Id(meshdim)"
                              " + 2*(mu)*((Enp1)-(Epnp1))", dict);
-    sigma_after = ga_substitute("(lambda)*Trace((Enp1)-(Epn))*Id(meshdim) "
+    sigma_after = ga_substitute("(lambda)*Trace(Enp1)*Id(meshdim) "
                                "+ 2*(mu)*((Enp1)-(Epn))", dict);
   }
 
@@ -629,12 +629,12 @@
     Epnp1 = ga_substitute("((Eptheta-(1-theta)*Epn)/theta)", dict);
     dict["Epnp1"] = Epnp1;
     sigma_np1 = ga_substitute
-      
("(lambda*Trace(Sym(Grad_u)-Epnp1)*Id(meshdim)+2*mu*(Sym(Grad_u)-Epnp1))",
+      ("(lambda*Trace(Sym(Grad_u))*Id(meshdim)+2*mu*(Sym(Grad_u)-Epnp1))",
        dict);
     fbound = ga_substitute
       
("(Norm(2*mu*Deviator(Etheta)-(2*mu)*Eptheta)-sqrt(2/3)*(sigma_y))",dict);
 
-    sigma_after = ga_substitute("(lambda)*Trace((Enp1)-(Epn))*Id(meshdim) "
+    sigma_after = ga_substitute("(lambda)*Trace(Enp1)*Id(meshdim) "
                                "+ 2*(mu)*((Enp1)-(Epn))", dict);
   }