# Non-linear Structural Analysis

Three types of non-linear analysis are currently available: non-linear separating contact, geometric non-linear, and material non-linear.

## Types

- Separating Contact
- This analysis type provides a mechanism where parts may partially or completely separate from each other. When this happens, forces only transfer through the still connected portion of the connection. A friction coefficient is used to define the sticking/sliding threshold. Typical friction values are 0.1 to 0.2.
- Geometric
- To account for changes in geometry as the structure deforms, the
strain-displacement and equilibrium equations are iteratively solved.
Follower loads (loads that stay normal to the surface and the geometry
deforms/rotates) can be optionally defined. This is considered a large
displacement, small strain analysis. That is, while large deformations
can be predicted, the material properties remain linear and plastic
deformation is not considered. Typical uses for geometric non-linear
analysis are predicting deformations in slender structures in aerospace,
civil and mechanical engineering applications and stability (buckling)
analyses of all types.
The prescribed load can be applied as the full load or incrementally. Incremental loading provides a load history with results at the specified number of load increments. This can be used for non-linear buckling analysis to determine the load at which structural instabilities may occur.

- Material

Non-linear contains additional analysis operations where the solver must iterate to find the value of interest. Expect this to run slightly longer and as such, care should be taken to make sure the analysis defined makes sense physically.

## Notes

- Equivalent strain is calculated as:
(1) $$\text{Eq}\text{.}\text{\hspace{0.33em}}\text{strain}\text{\hspace{0.17em}}\text{=}\text{\hspace{0.17em}}\text{sqrt}\left(\text{2/9}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\left({\left(\text{Ex}\text{\hspace{0.17em}}\text{-}\text{\hspace{0.17em}}\text{Ey}\right)}^{\text{2}}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\left(\text{Ey}\text{\hspace{0.17em}}\text{-Ez}\right)}^{\text{2}}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\left(\text{Ez-Ex}\right)}^{\text{2}}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}\text{6}\text{\hspace{0.17em}}\text{*}\text{\hspace{0.17em}}\left({\text{Exy}}^{\text{2}}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\text{Eyz}}^{\text{2}}\text{\hspace{0.17em}}\text{+}\text{\hspace{0.17em}}{\text{Exz}}^{\text{2}}\right)\right)\right)$$