Stress¶

Type:	2-Tensor, or section
Range:	[v_1, …, v_9]
Default:	-/-
Appearance:	optional

Specifies the mechanical stress $\TField{\sigma}$ within the physical domain or boundary. The unit of the stress are pascals, $\units{Pa}$ , which is equivalent newtons per square meter.

A constant stress can be defined by assigning a rank-2 tensor:

# define a constant stress
Stress = [..., ... , ...,
          ..., ... , ...,
          ..., ... , ...]

For more general cases, a stress field may be given as a section in order to deal with space, time, and parameter dependent definitions:

# define a force density as a section
Stress {
  Constant {...}
  Python {...}
  ...
}

Field definitions within this section are summed up. Consult the subsequent sections to see which types of field definitions are allowed.

Note

Within the context of linear continuum mechanics the stress is implicitly defined, when a displacement field $u$ is defined.

Then the stress is given by

$\begin{eqnarray*} \TField{\sigma}_{ij} = \TField{C}_{ij, kl} \left( \varepsilon_{kl} - \varepsilon_{\init, kl} \right), \end{eqnarray*}$

where $C$ is the stiffness tensor, $\varepsilon_{kl}={1}/{2}\left({\partial u_k}/{\partial x_l}+{\partial u_l}/{\partial x_k} \right)$ is the strain and $\varepsilon_{\init}$ it the initial strain.