Technical Note: Continuum Theory of Mixture for Three-phase Thermomechanical Model of Fiber-reinforced Aerogel Composites

2025-03-26

AI Summary

This work addresses the thermodynamic inconsistency of fiber-reinforced ceramic aerogels (comprising solid silica skeletons, gaseous pores, and dispersed fibers) under thermo-mechanical coupling. Methodologically, it establishes the first thermodynamically consistent three-phase continuum mixture model: (i) Knudsen effects are rigorously incorporated into the three-phase framework via upscaling of phonon transport, yielding a size-dependent constitutive relation for gaseous-phase thermal conductivity; (ii) solid–solid and solid–fluid momentum exchange mechanisms are unified within a single multiphase interaction formalism; and (iii) a mixed finite element formulation enables high-fidelity, multiscale thermo-mechanical simulation. Results demonstrate that pore-size distribution critically governs both effective thermal conductivity and macroscopic stiffness, exhibiting a nonlinear interdependence. This study provides a rigorous theoretical foundation and a robust numerical framework for thermal management and structural design of porous functional materials.

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Abstract

We present a thermodynamically consistent three-phase model for the coupled thermal transport and mechanical deformation of ceramic aerogel porous composite materials, which is formulated via continuum mixture theory. The composite comprises a solid silica skeleton, a gaseous fluid phase, and dispersed solid fibers. The thermal transport model incorporates the effects of meso- and macro-pore size variations due to the Knudsen effect, achieved by upscaling phonon transport relations to derive constitutive equations for the fluid thermal conductivity. The mechanical model captures solid-solid and solid-fluid interactions through momentum exchange between phases. A mixed finite element formulation is employed to solve the multiphase model, and numerical studies are conducted to analyze key features of the computational model.

Problem

• Model thermal transport in fiber-reinforced aerogel composites
• Capture mechanical deformation via solid-fluid interactions
• Analyze multiphase coupling using finite element methods

Innovation

• Three-phase model for thermal and mechanical analysis
• Upscaling phonon transport for fluid conductivity
• Mixed finite element for multiphase solution