# Axial Crushing of Multi-Cell Multi-Corner Tubes

An analytical formula for the prediction of mean crush force of multicorner multi-cell tubes is derived based on the super folding
element theory [1],[2],[3]. The analytical predictions for the mean crush force are found to be in good agreement with the FE solutions. Results also show a strong correlation between the cross-sectional geometry and the crash behavior with the method of connecting the inner to the outer walls having large influence on the energy absorption.

The present formulation considered four cross-sectional configurations as shown in below picture

## Theoretical Aspect

The theoretical aspect including the derivation of equations and the plastic approach can be found in links below:

```Multi-CRUSH 			*
|
|-- doc				* Documentation: license info, help files, and reports
|   |-- AIAA-2008-2014-577.pdf	* SDM Paper on the early developement of analytical model and finite element results for dynamic cases
|   |-- SDM-Tube_2008_6.ppt	* Presentation file for the above SDM paper
|   |-- Najafi_MS_thesis.pdf	* Master thesis contains detail description and derivation of analytical model
|   |-- TWS_UNDER REVIEW.pdf	* Journal paper that is under review in Thin Walled Structures
|   |-- UserLicence		* Help file to use mathematica codes
`-- src 			* Source files
|
|-- mathematica 			* Source files
|    |				* Mathematica source file
|    |-- C2CNEW_Revised1.nb	* implementation of the analytical model for corner to corner cross-sectional configuration
|    |-- C2WNEW_Revised1.nb	* implementation of the analytical model for corner to web cross-sectional configuration
|    |-- W2CNEW_Revised1.nb	* implementation of the analytical model for web to corner cross-sectional configuration
|    `-- W2WNEW_Revised1.nb	* implementation of the analytical model for web to web cross-sectional configuration
`-- lsdyna-validation 			* Source files
|				* Mathematica source file
|-- c2cp.k			* lsdyna input file for c2c configuration
|-- c2wp.k			* lsdyna input file for c2w configuration
|-- w2cp.k			* lsdyna input file for w2c configuration
`-- w2wp.k			* lsdyna input file for w2w configuration
```