Secant-based multiscale constitutive modeling toward coupled homogenized finite element method and molecular dynamics for polycarbonate

This study presents a secant-based multiscale constitutive modelling framework coupling homogenized finite element method (FEM) and molecular dynamics (MD) for the nonlinear and strain-dependent mechanical behavior of polymeric materials. Representative unit cells governed by MD simulations are assigned to each FEM integration point and deformed consistently with the macroscopic deformation gradient. In conventional atomistic-to-continuum approaches, constitutive responses are often derived from analytically evaluated tangent stiffness at the reference configuration, which is feasible only for simple interatomic potentials. For realistic polymeric systems, however, analytical evaluation of tangent stiffness is generally intractable, and the discrepancy in boundary condition treatment between FEM and MD further complicates direct constitutive coupling. To overcome these difficulties, the proposed framework employs a secant-based approach that enables the extraction of physically meaningful secant properties, such as the secant modulus and transverse contraction coefficient, from temporally averaged MD stress and strain data, which in turn serve as effective constitutive descriptors within the homogenization framework. The proposed method is demonstrated through three numerical examples: uniform tensile simulation on a single-element model, non-uniform tensile simulation on a single-element model, and tensile simulation on a multi-element model of a quarter perforated structure. The results show that the framework successfully reproduces key features of the nonlinear stress–strain behavior obtained from pure MD simulations, while preserving the continuum-scale consistency required for FEM. Overall, the proposed approach provides a robust pathway for incorporating atomistic dynamics into continuum constitutive modeling of polymeric materials.