Automotive crash and impact simulations require a large amount of computational resources, which is a challenge for optimization and robustness assessments. Thus, this work presents data-driven model order reduction and hyper-reduction techniques for faster evaluation of such problems. Efficient subspace approximation and element sampling methods are proposed. The numerical stability of the reduced models under explicit time integration is analyzed mathematically and experimentally. Finally, the achievable online stage accuracy and speed-ups are studied for different test cases.