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On a Thermodynamic Theory of Porous Cosserat Elastic Shells

This paper presents a theory for porous thermoelastic shells using the model of Cosserat surfaces and the Nunziato–Cowin theory for materials with voids. To describe the porosity of the thin body, we introduce two scalar fields: one field accounts for the changes in volume fraction along the middle surface of the shell, and the other field characterizes the porosity variations along the shell's thickness. First, we postulate the principles of thermodynamics for these two-dimensional continua and we obtain the equations of the nonlinear theory. Then, we consider the linearized theory and prove the uniqueness of solution to the boundary initial value problem with no definiteness assumption on the constitutive coefficients. Finally, we consider the deformation of isotropic and homogeneous shells and determine the constitutive coefficients for Cosserat surfaces, by comparison with the results obtained from the three-dimensional approach to shell theory.