Constitutive modeling, computational implementation and material parameter identification for polymeric foams considering density and foaming direction

Abstract Polyurethane foam (PUF) is a porous material and significantly affected by compressive loads. Under a uniaxial compressive load, the PUF exhibits various types of material nonlinear behavior under varying conditions, such as density, foaming direction, and strain rate. This study investigates the nonlinear behavior of a PUF through phenomenological approach. A Frank–Brockman–Zairi elasto-viscoplastic constitutive model was adopted to investigate the behavior of PUFs with different densities, directions, and strain rates when subjected to compressive loads. The proposed model was discretized using the implicit time integration algorithm and implemented into a user-defined subroutine of ABAQUS. In this study, parameter determination method was also implemented to identify material parameters containing the constitutive equations. Furthermore, the detailed process of determining the material parameters containing the shape of the work-hardening rate–stress curve dependent on the type of material behavior was presented. Consequently, the macroscopic material response of the PUF, such as the stress–strain curve, can be predicted based on the proposed constitutive model. In future studies, the mechanical behavior of porous materials can be analyzed more successfully by supplementing the constitutive model. This can allow the model to simulate the complex plastic flow of porous materials after yielding that is presently difficult to implement.