# Application of tensor product models for vehicle de-formational processes

Istvan Harmati, András Rövid, Péter Várlaki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

### Abstract

Modelling of vehicle deformational processes plays an important role in car body design and accident analysis. It is a difficult task and usually carried out applying a kind of finite element method. Determination of the absorbed energy by the deformation and the corresponding energy equivalent speed (EES) can be of great importance. Exact determination or measuring of these quantities is almost impossible, so one could estimate them. In this paper we introduce a modeling technique and a model for describing the deformation process. A short description of the main idea: let we have a 3-dimensional rectangular grid on the vehicle body (or on something else). The partition is determined by taking into consideration the energy absorbing properties of the parts of the vehicle, so each cell is approximately homogenous. The cells could be identified as the entries of a tensor of order 3. We concentrate on the energy absorbed by the cells, but not on the physical coordinates of the cells. Energy absorption property (rate of the input and the absorbed energy) of a certain cell could change during the deformational process, so the absorbed energy is calculated using a monotonous decreasing function. These functions can be defined for each possible orthogonal direction of the possible impact. Instead of the original impact we deal with its orthogonal components and the result will be the sum of the particular results. The rectangular grid allows us to compute from level to level. These computations can be realized applying tensor products, the model has low complexity which can be more decreased by complexity reducing methods known from linear algebra.

Original language English Proceedings of the 10th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2006 615-620 6 Published - Dec 1 2006 10th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2006 - Budapest, HungaryDuration: Nov 6 2006 → Nov 8 2006

### Publication series

Name Proceedings of the Mini Conference on Vehicle System Dynamics, Identification and Anomalies

### Other

Other 10th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2006 Hungary Budapest 11/6/06 → 11/8/06

### Keywords

• Car crash
• Tensor product model

### ASJC Scopus subject areas

• Mechanical Engineering

### Cite this

Harmati, I., Rövid, A., & Várlaki, P. (2006). Application of tensor product models for vehicle de-formational processes. In Proceedings of the 10th Mini Conference on Vehicle System Dynamics, Identification and Anomalies, VSDIA 2006 (pp. 615-620). (Proceedings of the Mini Conference on Vehicle System Dynamics, Identification and Anomalies).