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:

Notation.

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 Cauchy-Green deformation tensor  Green strain tensor  second Piola-Kirchhoff 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:

Term name prefixes.

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)

multi-linear 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:

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.