A two-network constitutive model for the rate-dependent compressive behavior of expanded polypropylene foams

Abstract

Expanded Polypropylene foams are used in energy-absorbing applications, yet their mechanical response exhibits complex rate-dependency, damage, and permanent set, making accurate constitutive modeling challenging. This work proposes and validates a two-network viscoplastic model to describe the large-deformation compressive behavior of Expanded Polypropylene foams. The framework combines a hyperelastic network to capture the instantaneous nonlinear elastic response with a parallel viscoplastic network governed by an overstress flow rule to account for rate-sensitive effects. Model parameters were calibrated using experimental data from uniaxial compression tests at low (4.5 mm/min) and high (450 mm/min) rates. The model’s predictive capability was then assessed against an independent dataset at an intermediate rate (45 mm/min), achieving a coefficient of determination exceeding 0.98. Furthermore, an analysis was performed to quantify uncertainty, showing that the 95% confidence intervals and 95% prediction intervals for the stress response successfully encompassed the experimental validation data. The framework also provided an accurate approximation of key energy absorption parameters, confirming its empirical adequacy.