# A New Method for the Dynamics Analysis of Super-Elastic-Plastic Foams under Inhomogeneous Loading and Unloading Conditions

## TL;DR

This paper introduces a new computational method to analyze the mechanical behavior of super-elastic-plastic foams under uneven compression and unloading.

## Contribution

The novelty lies in combining hyper-elastic and elastoplastic layers to model foam behavior under inhomogeneous loading.

## Key findings

- Four-layer foam configurations showed converged performance curves, indicating sufficient accuracy.
- The method effectively captured residual deformation and mechanical behavior of foam materials.
- Simulation results matched experimental data, validating the model's reliability.

## Abstract

In this research, a new computational method was proposed for describing the mechanical behavior of super-elastic-plastic foams under inhomogeneous compressive impacts. The method regarded the foam material as composed of two typical mechanical properties superimposed multiple times: one was the hyper-elastic layer, and the other was the elastoplastic layer. The hyper-elastic layer and the elastoplastic layer were interwoven and overlapped, divided into double-layer, four-layer, and six-layer configurations to characterize the foam material. After the equivalent layering of the foam, by comparing the results of the four-layer and six-layer divisions, it was found that when the layering reached four layers, the foam performance curve had already converged. The study utilized the HYPERFOAM model and Mullins effect in the ABAQUS software to establish the constitutive relationship of the hyper-elastic layer. It adopted the Crushable foam model to develop the constitutive relationship of the elastoplastic layer. Under uniaxial compression conditions, quasi-static and intermediate strain rate compression tests were performed on polyethylene (PE) foam materials with three different densities. Based on the experimental results, the parameter values of the hyper-elastic-plastic foam model in the ABAQUS code were determined. By comparing the computational results and the experimental results, the established finite element (FE) model was validated using the mechanical behavior of indentation and compression tests. The results showed that this method could effectively describe the complex mechanical behavior and residual deformation of hyper-elastic-plastic foam packaging materials under non-uniform compression, and the experimental and simulation results agreed well, proving the reliability of this method.