Foam materials are used in many structural applications, especially where impact loads are expected. A common application is to absorb energy and reduce the forces that would otherwise be transferred to vehicle occupants in the event of a collision. A structure or material that does this effectively is said to have a high crashworthiness. Foam materials with high crashworthiness are essential for protecting infants and young children in child safety seats, also known as Child Restraint Systems (CRS). Physical testing is time-consuming and costly, and accurate modeling is required to evaluate safety performance.

High-fidelity models and advanced methods in computational dynamics to predict acceleration-time response are crucial for evaluating human safety. This thesis investigates the constitutive behavior of foams within LS-DYNA for advanced material modeling and uses a deductive methodology to explore this. More specifically, the work focuses on constitutive modeling, finite elements, and parameter- fitting using optimization. The work contributes to the field of computational dynamics and solid mechanics. The thesis aims to improve the modeling of foams by providing an accurate, efficient, and robust framework.

The results consist of best practices for how foams should generally be modeled for FEM applications. This includes the choice of constitutive material models, finite elements, mesh-free methods, optimization for parameter-fitting, contact formulations in contact robustness and stability, and the necessary experiments for defining material parameters for constitutive extrapolation of strain rates. Two constitutive relations, Jeong's and Nagy's, are proposed for modeling strain rate effects used in dynamic impact tests. Besides that, we propose two extrapolation schemes to artificially extend the densification range for numerical stability based on the proposal of Paul Du Bois. Python code is also presented for automatic input compatible with LS-DYNA when set accuracy is achieved.