Large-deformation constitutive modeling of viscoelastic foams: Application to a closed-cell foam material

Abstract

Elastomeric foams display a nonlinear viscoelastic mechanical response, which is relevant to impact protection applications. In this paper, we present a methodology for the experimental characterization and constitutive modeling of the rate-dependent, large-deformation mechanical behavior of isotropic, viscoelastic foam materials under quasi-static and moderate loading rates. We conduct large-deformation, homogeneous simple compression/tension experiments under quasi-static and moderate strain rates for a closed-cell elastomeric foam to inform a phenomenological, isotropic constitutive model. The model is based on a multi-mechanism strategy, consisting of a rate-independent, hyperelastic contribution and several rate-dependent, viscoelastic contributions. This structure is motivated by the rheological concept of a hyperelastic spring in parallel with several nonlinear Maxwell elements. The hyperelastic modeling utilizes the invariants of the logarithmic strain and accounts for high compressibility and strong volumetric–distortional coupling. For the rate-dependent mechanisms, we employ the framework of the multiplicative decomposition of the deformation gradient into non-equilibrium elastic and viscous parts. Validation experiments that involve inhomogeneous deformation and deformation-rate fields are conducted, which include spherical indentation, simple-shear-like deformation both without and with a fixed pre-compression, and tension of a specimen with circular holes at different deformation rates. The responses from the validation experiments are compared against model predictions obtained from finite-element-based numerical simulations, demonstrating that the experimental results are accurately captured by the proposed model.