Multiscale modelling of thermally stressed superelastic polyimide

TL;DR

This work presents a sequential multiscale MD–SPH framework to model thermo-mechanical coupling in the thermally stressed, superelastic polyimide used as insulation. By extracting elastic, volumetric, thermal, and transport properties from atomistic MD simulations (via ReaxFF, NPT/NVT ensembles, and rNEMD) and feeding them into a corrected SPH formulation, the authors simulate heat transfer, thermal stresses, and deformation, validating against 1D/2D benchmarks. They demonstrate a substantial insulating benefit of the polyimide in an aluminium plate, reducing thermal stress and temperature field development. The approach provides a predictive, mesh-free pathway to capture thermo-mechanical interactions across scales, with potential extensions to fracture and defect engineering and experimental validation.

Abstract

Many thermo-mechanical processes, such as thermal expansion and stress relaxation, originate at the atomistic scale. We develop a sequential multiscale approach to study thermally stressed superelastic polyimide to explore these effects. The continuum-scale smoothed particle hydrodynamics (SPH) model is coupled with atomistic molecular dynamics (MD) through constitutive modelling, where thermo-mechanical properties and equations of state are derived from MD simulations. The results are verified through benchmark problems of heat transfer. Finally, we analyse the insulating capabilities of superelastic polyimide by simulating the thermal response of an aluminium plate. The result shows a considerable reduction in the thermal stress, strain and temperature field development in the aluminium plate when superelastic polyimide is used as an insulator. The present work demonstrates the effectiveness of the multi-scale method in capturing thermo-mechanical interactions in superelastic polyimide.

Figures (17)

• Figure 1: (a) Ball and stick figure of the molecular structure of Pristine Kapton, (b) the central crosslinker necessary for the structure of superelastic polyimide and (c) molecular structure of superelastic polyimide.
• Figure 2: Equilibration of superelastic polyimide chain. (a) Density convergence plot. (b) Converged structure visualised in OVITO.
• Figure 3: Instantaneous variation of normal stress, $\sigma^{xx}_v$, with normal strain, $\epsilon^{xx}$ across the 8 simulations along with its average, linear and quadratic fit. The variation of $\sigma^{xx}_v$ with $\epsilon^{xx}$ is best explained by a quadratic equation.
• Figure 4: (Left) Hydrostatic pressure fluctuations during bulk modulus calculations, obtained from eight repeated simulations with identical setups. (Right) The averaged pressure is fitted with a linear curve, showing that, except for the endpoints, the hydrostatic pressure difference exhibits a linear trend with the volumetric strain ($\frac{\Delta V}{V}$). This validates the assumption of linear behaviour in the equation of state for SPH calculations.
• Figure 5: Plot illustrating the variation of the simulation box length (L) with temperature (T), along with linear and quadratic fits. The quadratic fit shows better alignment with the data and simplifies the determination of the coefficient of thermal expansion, an essential thermal field parameter in the SPH study. Without this empirical fit, an MD simulation would need to be conducted for every combination of $T_0$ and $T$, which is computationally expensive.