Rate dependent finite strain constitutive modeling of polyurethane and polyurethane–clay nanocomposites

A finite strain nonlinear viscoplastic constitutive model for polyurethane (PU)–Montmorillonite clay (MTM) nanocomposites is developed with the goal of characterizing the mechanical response under different strain rates and strain amplitudes. In this model, both the elastic and viscous responses are considered to be nonlinear. It is shown that a simple mathematical extension of the model used to characterize the PU determines the nonlinear material constants for the PU–MTM. A finite deformation nonlinear viscoelastic model is used to represent the mechanical behavior of PU. The rate dependent viscous behavior and multiple relaxation times present in the PU response are determined using the frequency dependent tanδ measurements from Dynamic Mechanical Analysis (DMA). The model is capable of accurately capturing both the rate dependent behavior and frequency dependent damping of PU. The entire rate dependent hysteresis behavior (loading–unloading) is predicted accurately through the constitutive model for strains up to 10%. For the PU–MTM nanocomposite, the constitutive stress update is implemented in a finite element (ABAQUS/Explicit) framework and validated using a range of experimental results. The model predictions show excellent agreement with experimental results in capturing rate dependent loading/unloading responses for both PU and PU–MTM nanocomposites. The proposed model can easily be extended to characterize other polyurethane based nanocomposites.