A molecular-informed multiscale framework for constitutive modeling of rubber materials: From coarse-grained molecular dynamics to finite element implementation

Rubber materials exhibit complex mechanical behavior characterized by superelasticity and viscoelasticity, making them critical for applications in soft robotics, sensors, and aerospace. However, a fundamental gap exists between molecular-level insights and macroscopic engineering models, limiting the predictive design of rubber materials. Traditional phenomenological models successfully fit experimental data but lack physical interpretability, while molecular statistical theory-based approaches are predominantly equilibrium-based and lack explicit mechanisms to track time-dependent network evolution, their critical parameters are typically treated as adjustable fitting parameters rather than being directly computed from molecular simulations. To address these challenges, we present a novel multiscale computational framework that establishes a direct and physically meaningful pathway from molecular simulations to macroscopic constitutive modeling. The key innovation lies in the explicit use of molecular parameters derived from coarse-grained molecular dynamics (CGMD) simulations to inform macroscopic constitutive models. Our framework tracks and quantifies specific molecular-level phenomena during the deformation process and systematically translates these microstructural insights into macroscopic model parameters through rigorously derived scale-bridging transfer functions. Furthermore, we incorporate a time-dependent viscoelastic formulation with relaxation terms directly derived from molecular network dynamics, capturing rate-dependent behavior often overlooked by traditional models. The complete implementation involves four stages: CGMD simulations for efficient molecular-level data generation, establishment of molecular-to-macroscale transfer functions, implementation through user-defined material subroutines (UMAT) integrated with finite element frameworks, and validation through uniaxial tensile and extended finite element method (XFEM)-based fracture simulations. This multiscale pipeline maintains physical interpretability at each stage while providing accurate predictions of both conventional mechanical responses and complex failure mechanisms, offering a powerful computational tool for rational design and optimization of rubber materials in advanced engineering applications.