Term Overview¶
Term Syntax¶
In general, the syntax of a term call is:
<term name>.<i>.<r>( <arg1>, <arg2>, ... )
,
where <i>
denotes an integral name (i.e. a name of numerical quadrature
to use) and <r>
marks a region (domain of the integral).
The following notation is used:
symbol 
meaning 

volume (sub)domain 

surface (sub)domain 

volume or surface (sub)domain 

dimension of space 

time 

any function 

any vector function 

unit outward normal 

, 
scalar test function 
, 
scalar unknown or parameter function 
scalar parameter function 

vector test function 

, 
vector unknown or parameter function 
vector parameter function 

Cauchy strain tensor () 

deformation gradient 

right CauchyGreen deformation tensor 

Green strain tensor 

second PiolaKirchhoff stress tensor 

vector volume forces 

scalar volume force (source) 

density 

kinematic viscosity 

any constant 

Kronecker delta, identity matrix 

trace of a second order tensor () 

deviator of a second order tensor () 

th element of triangulation (= mesh) of domain 

is assigned values from in ascending order 
The suffix “” denotes a quantity related to a previous time step.
Term names are (usually) prefixed according to the following conventions:
prefix 
meaning 
evaluation modes 
meaning 

dw 
discrete weak 
‘weak’ 
terms having a virtual (test) argument and zero or more unknown arguments, used for FE assembling 
ev 
evaluate 
‘eval’, ‘el_eval’, ‘el_avg’, ‘qp’ 
terms having all arguments known, modes ‘el_avg’, ‘qp’ are not supported by all ev_ terms 
de 
discrete einsum 
any (work in progress) 
multilinear terms defined using an enriched einsum notation 
Term Table¶
Below we list all the terms available in automatically generated tables. The first column lists the name, the second column the argument lists and the third column the mathematical definition of each term. The terms are devided into the following tables:
Table of large deformation terms (total/updated Lagrangian formulation)
The notation <virtual>
corresponds to a test function,
<state>
to a unknown function and <parameter>
to a known function. By
<material>
we denote material (constitutive) parameters, or, in general, any
given function of space and time that parameterizes a term, for example
a given traction force vector.