Finite Thermoelasticity

Fractional Thermoelasticity

This new edition offers expanded coverage of fractional calculus, including Riemann–Liouville fractional integrals, Riemann–Liouville and Caputo fractional derivatives, Riesz fractional operators, and Mittag-Leffler and Wright functions. Additionally, it provides a comprehensive examination of fractional heat conduction and related theories of thermoelasticity. Readers will gain insights into the concepts of time and space nonlocality and their impact on the generalizations of Fourier's law in thermoelasticity. This edition presents a detailed formulation of the problem of heat conduction in different domains and the associated thermal stresses, covering topics such as the fundamental solution to the Dirichlet problem, constant boundary conditions for temperature, and the fundamental solution to the physical Neumann problem. New insights into time-harmonic heat impact on the boundary have also been added. Cracks in the framework of fractional thermoelasticity are also considered.

Dynamic Problems of Thermoelasticity

Internal Variables in Thermoelasticity

This book describes an effective method for modeling advanced materials like polymers, composite materials and biomaterials, which are, as a rule, inhomogeneous. The thermoelastic theory with internal variables presented here provides a general framework for predicting a material’s reaction to external loading. The basic physical principles provide the primary theoretical information, including the evolution equations of the internal variables. The cornerstones of this framework are the material representation of continuum mechanics, a weak nonlocality, a non-zero extra entropy flux, and a consecutive employment of the dissipation inequality. Examples of thermoelastic phenomena are provided, accompanied by detailed procedures demonstrating how to simulate them.