Hyperelastic Multi-Scale Modeling of a Thermoplastic Polyurethane Elastomer Using Molecular Mechanics

In an effort to explore a structure-property relationship of an elastomer, we develop a multi-scale model of a thermoplastic polyurethane (PU) elastomer. A hyperelastic nonlinear constitutive equation of PU is constructed from a molecular simulation and is implemented for obtaining macroscopic mechanical properties. A full-atomic model of the PU, whose polymeric chains consist of hard and soft segments, is built using a commercial molecular modeling code — Materials Studio. The long hard segments are decomposed again into two beads for a better coarse grained (CG) model. The probability distribution functions for bond lengths, angles, and pairs are found among the beads to derive the effective potential functions using Inverse Boltzmann Method (IBM). Using the effective potential functions, a CG Molecular Mechanics (MM) model of the PU is built and run in LAMMPS. Initial IBM-derived effective potentials are iterated through CGMD simulations along with pressure correction to keep the distribution functions, density, and thermodynamic states the same for both models at two different scales. The final model is run with iterated force-fields using isobaric-isochoric ensemble (constant pressure, constant temperature) and validated with six full-atomic radial distribution functions (RDFs) and density from experiment. After building a validated CG model, hyperelastic strain energy functions are constructed from the CGMM simulation results of the PU under volumetric and isochoric deformation at the molecular level in order to develop an equivalent continuum model. Considering energy equivalence between the molecular and continuum models, the material constants for a hyperelastic strain energy function of the PU are determined. The derived parameters are used to predict macroscopic properties; bulk, shear, and Young’s moduli, and Poisson’s ratio from volumetric and three-dimensional shear loadings using the multi-scale approach. A coupon test of the PU at a macroscopic level is followed for comparison with the CGMM simulation. By the end of the study, we may answer the following research question: how sensitive are the iterative processes and pressure correction while building the effective CG potentials through inverse Boltzmann method.