From Polymer Coils to Continuum Flow: A Fully Lagrangian Heterogeneous Multiscale Framework for Viscoelastic Rheology
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Polymeric liquids and soft networks display rich mechanical responses, including strong elastic effects and long-lived memory, particularly when subjected to complex or time-dependent flows. Modeling these behaviors is difficult because they arise from highly nonlinear interactions between molecular-scale dynamics and bulk deformation. This is especially important for pressure-sensitive adhesives (PSAs), which achieve adhesion with minimal applied load but whose macroscopic performance is governed by molecular architecture, cross-link density, and network connectivity. We introduce a multiscale compu tational strategy based on the Lagrangian Heterogeneous Multiscale Method (LHMM) [1, 2] to model the flow and deformation of polymer solutions and melts. At the continuum level, the approach employs a thermodynamically consistent Smoothed Particle Hydrodynamics (SPH) formulation, while polymer-scale physics is resolved using particle-based mesoscale techniques such as Smoothed Dissipative Particle Dynamics (SDPD) and Dissipative Particle Dynamics (DPD). Information is exchanged between scales by linking SPH-computed deformation rates to polymer-level stress tensors through the Irving–Kirkwood procedure, allowing microscopic configurations to directly influence macroscopic stresses. Using this framework, we compute key rheological quantities, including viscosity, elastic relaxation times, and nonlinear viscoelastic response. The methodology is assessed using standard benchmark problems, such as reverse Poiseuille flow and transport through a periodic array of cylinders, for Weissenberg numbers between 0.5 and 30 at low Reynolds numbers. The model is further extended to PSAs by introducing a microscale network-formation algorithm [3] that captures cross-linking and gel formation. Experimental small-amplitude oscillatory shear and tensile measurements for four PSA formulations are used to tune the micro- and macroscale descriptions. The resulting simulations reproduce observed trends in storage and loss moduli and in stress–strain behavior, while elucidating how network density and topology govern adhesive mechanics. The LHMM platform integrates specialized solvers through custom C++ interfaces and uses the LAMMPS engine to achieve efficient micro–macro coupling on hybrid CPU–GPU systems, enabling large-scale simulations with hundreds of millions of particles.
