Modeling of elasto-viscoplastic behavior for polyurethane foam under various strain rates and temperatures

The polyurethane foam (PUF) is one of the most widely used composite materials in industrial and biomedical fields. It is frequently adopted in a wide range of environmental conditions, i.e., from static to dynamic compressive loads, and from cryogenic to high temperatures. Under these various environments, the PUF shows an elasto-viscoplastic behavior including three stages of material characteristics, namely, linear elasticity, a plateau with stress drop, and densification. Hence, the establishment of material model as well as the identification of material characteristics is the key of design and fabrication for PUF-based structures. In the present study, the strain rate- and the temperature-dependent elasto-viscoplastic behavior of polyurethane foam (PUF) which is extensively used in various fields and environments was computationally estimated under static/dynamic compression and the low/high temperature. To depict the three stages of material characteristics such as linear elasticity, a plateau with stress drop, and densification under uniaxial compression numerically, a Frank-Brockman type plastic multiplier and a Zairi type hardening-softening internal stress state variable were introduced. Then, the constitutive model was transformed as an implicit form using algorithmic tangential stiffness (ATS) method and was programmed as a user-defined material subroutine of commercial finite element analysis (FEA) code, namely, ABAQUS UMAT. Through the developed material subroutine, the strain rate- and the temperature-dependent static and dynamic stress-strain behaviors were numerically assessed. In addition, the change of material constants such as elastic modulus, yield stress, and hardening and softening control parameters was investigated quantitatively, and the polynomial multiple regression models were suggested. Consequently, the calculated results considerably correspond to experimental results, and through some supplements, accuracy can be improved. On using the proposed numerical method with some revision, it might be possible to anticipate the nonlinear behavior of the unknown material in various strain rate and temperature environment.