**deformation_gradient#

Description#

This boundary condition imposes the displacement vector \(\vect u\) of a node by the following formula:

\[\vect u = \ten F \vect r\]

where \(\ten F\) is the deformation gradient tensor, and \(\vect r\) the position vector of the node considered. The origin of \(\vect r\) may be a fixed point or a node of the mesh.

For the case where the origin is a fixed point the node set considered must be given, as well as the position of the origin point in the form of a vector, and the components of the tensor \(\ten F\). The tensor components are named F11, F22, F12, F21, F33 (2D and 3D), and F23, F31, F32, F13 (for 3D only). If a component is not defined its value is set to zero. The values may be set by using a table for all of the components, or a table for each individual component (only for non-zero components). The given values of F11, F22, and F33 are adjusted by adding 1 (see examples below).

Syntax#

**deformation_gradient [ dof dof ] [ node ] \(~\,~\,\) nset_name (position | num_node) \(~\,~\,\) [ free:dof_to_free … ] \(~\,~\,\) compos_name value [ table ] … compos_name value [ table ]

dof dof

to impose only one displacement component. dof can be U1, U2 or U3.

node

is an optional keyword indicating that the origin of \(\vect r\) is a node of the mesh.

nset_name

Character name of the nset group upon which the displacement will be imposed.

position

Position of the origin point in the form of a vector. This is in the case where the center is not a node of the mesh. Recall the vector form is 2 or three real values enclosed in parenthesis such as ( 1. 0. 0. ).

num_mode

Integer number of a node in the case where the node keyword was given.

free:dof_to_free

The displacement component to free ( dof_to_free can be U1, U2 or U3).

compos_name value

Character string giving the name of a component of the \(\ten F\) tensor as defined above, followed by a real giving the components value. Any number of these components may be given in any order thereby specifying the deformation_gradient tensor.

table

character name of the table(s) used to describe the field amplitude. See the command ***table.

Examples#

The following examples can be found at

  1. To apply a simple glide: \(F_{ij}=1~ \text{if}~ i=j\), \(F_{12}=\gamma\), \(F_{ij}=0\) otherwise. For \(\gamma = 1.\):

    ***bc
 **deformation_gradient
   ALL_NODE  (0. 0. 0.) F12 1. time

  2. To apply a simple extension \(F_{11}=1+\lambda\), \(F_{22}=F_{33}=1\), \(F_{ij}=0 ~\text{for}~ i\neq j\). For \(\lambda = 1.\):

    ***bc
 **deformation_gradient
   ALL_NODE  (0. 0. 0.) F11 1. tab

  3. To apply a simple tension \(F_{11}=1+\lambda\), \(F_{22}=?, F_{33}= ?\), \(F_{ij}=0~ \text{for}~ i\neq j\). For \(\lambda = 1.\):

    ***bc
 **impose_nodal_dof
   y0 U2 0.
   z0 U3 0.
 **deformation_gradient
   ALL_NODE  (0. 0. 0.) free:U2 free:U3 F11 1. tab