Mathematical Theories of Nanoporous Media
Elasticity and Thermoelasticity
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Beschreibung
This book presents a comprehensive framework for the linear theories of elasticity and thermoelasticity of nanoporous materials with quadruple voids, developing models based on pore volume fractions and extending them to rigid bodies with the same structure. Using the potential method and modern singular integral equation theory, it systematically analyzes a broad class of non-classical boundary value problems, including equilibrium, steady vibrations, pseudo-oscillations, quasi-static processes, and heat conduction. Combining original, previously unpublished results, the work significantly advances the mathematical foundations of nanoporous media and offers a unified continuum-mechanical approach with important applications in fields such as engineering, geomechanics, materials science, and biomechanics, particularly for modeling complex biological tissues.
Provides rigorous analysis of non-classical boundary value problems via potential methods Bridges theory with applications in engineering, geomechanics, materials science, and biomechanics Develops a unified framework for elasticity and thermoelasticity in nanoporous media with quadruple voids
Autor*in
Merab Svanadze
Themen in »Mathematical Theories of Nanoporous Media«
Elasticity Thermoelasticity Nanoporous materials Quadruple porosity Steady vibrations Equilibrium Quasi-statics Existence and uniqueness theorems Fundamental solution Potential method Fredholm integral equations Singular integral equations