Abstract
When a porous solid is subjected to both gas infiltration and heat transfer, thermal stresses are generated in such a solid. This paper presents fundamental theory for a porous solid under such a complex situation. The governing equations for gas and solid phases are used to identify the gas pressure in pores and the solid temperature. The constitutive equation for a porous solid is formulated in terms of the unit cell model in which a pore exists periodically in the matrix. Using the constitutive equation, equilibrium equation of stress tensor and strain tensor obtained by differentiating displacement vector, the partial differential equation of displacement components for obtaining the deformation and stresses occurred in a porous elastic solid is introduced consequentially. As a simple example, the thermal stress problem for an infinite porous solid with a spherical cavity into which coolant gas is injected is considered.
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