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

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.

Figures (4)

• Figure 1: Domains for (left) mechanical and (right) thermal transport models.
• Figure 2: Contour plots of fluid pressure(top row), aerogel skeleton displacement (middle row) and fiber displacement (bottom row) at $t=$33 s, 66 s and 100 s from left to right.
• Figure 3: Contour plots of the fluid temperature (top row), fiber temperature (middle row) and solid aerogel skeleton temperature (bottom row) at $t=$5s, 30s and 80s respectively from left to right.
• Figure 4: Temperature of all three phases along the thickness of domain through middle ($x = 0.5L$) across different times for $t=$ 5, 20, 40 and 80 s through numerical experiments for the heat transfer model