7.13  Defining fields trough tables, expressions, ...

Finite element fields are used in four main formats

• def field at DOFs
• InfoAtNode field at nodes of an element group can be built from a pro.MAP field which can be an VectFromDir structure, a structure with fields .bas and .EltId with EltId=0 to define material orientations.
  info,EltOrient is an alternative to specify the orientation of all elements rather than associate values for each property entry. The format is a structure with field .EltId giving the identifiers and .bas giving an orientation for each element in the basis format. To interpolate constitutive properties as a function of temperature, ... see section 7.3.
• gstate field at integration points of an element group (can be built from a pro.gstate field).
• a field definition structure to be transformed to the other formats using a elem0('VectFromDir') command as illustrated below.

The VectFromDir structure has fields

data.dir	a cell array specifying the value of various fields. Each cell of data.dir can give a constant value, a position dependent value defined by a string FcnName that is evaluated using
	fv(:,jDir)=eval(FcnName) or fv(:,jDir)=feval(FcnName,node) if the first fails. Note that node corresponds to nodes of the model in the global coordinate system and you can use the coordinates x,y,z for your evaluation.
data.lab	cell array giving label for each field of an InfoAtNode or gstate structure.
data.DOF	a vector defining the DOF associated with each .dir entry. The transformation to a vector defined at model.DOF is done using vect=elem0('VectFromDirAtDof',model,data,model.DOF).

For example

 % Analytical expression for a displacement field
 model=femesh('testubeam');
 data=struct('dir',{{'ones(size(x))','y','1*x.^3'}}, ...
    'DOF',[.01;.02;.03]);
 model.DOF=feutil('GetDOF',model);
 def=elem0('VectFromDirAtDof',model,data,model.DOF)
% Orientation field at nodes
data=struct('dir',{{'x./sqrt(x.^2+y.^2)','y./sqrt(x.^2+y.^2)',0}}, ...
'lab',{{'v1x','v1y','v1z'}});
pro=struct('il',1,'type','p_solid','MAP',data);
model=stack_set(model,'pro','WithMap',pro);
C1=fe_mknl('init',model);InfoAtNode=C1.GroupInfo{7}
feplot(model);fecom('showMap','WithMap') % display map
% Material field at node
sdtweb('_eval','d_mesh.m#RVEConstitInterp')