Mathematical modeling approaches for vehicle crashworthiness: a comprehensive review


Aytimur E. E., Makaracı M.

TRANSPORTATION LETTERS, vol.1, no.1, pp.1-32, 2026 (Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 1 Issue: 1
  • Publication Date: 2026
  • Doi Number: 10.1080/19427867.2026.2650800
  • Journal Name: TRANSPORTATION LETTERS
  • Journal Indexes: Scopus, Compendex, INSPEC
  • Page Numbers: pp.1-32
  • Kocaeli University Affiliated: Yes

Abstract

Crashworthiness is a central consideration in the design of automotive and aerospace vehicles. Although regulatory crash tests remain essential, they are costly and time-consuming, prompting an increasing reliance on mathematical modeling during the early design stages. This review categorizes crashworthiness modeling approaches into three primary types: Lumped Mass Systems (LMS), Multi-Body Systems (MBS), and Finite Element Methods (FEM), alongside simplified techniques such as Response Surface Models (RSM), Crash Pulse Models, and Macro Element Models (MEM). The applications of these methods are examined at the vehicle, component, and biomechanical levels, reflecting the different scales of crash behavior and occupant safety analysis. This review highlights the dominance of the Finite Element Method, particularly through LS-DYNA, owing to its fidelity, versatility, and validation in front-end structural crash analyses. Finally, key research gaps and future opportunities are identified to support the continued advancement of efficient and reliable crashworthiness models.