Generalized Thermoelasticity with Fractional Order Dynamics

Generalized thermoelasticity with fractional order dynamics extends classical thermoelastic theory by incorporating non-integer derivatives into the heat conduction and mechanical governing equations. This approach captures memory and hereditary effects in materials, predicts finite speeds of thermal wave propagation and overcomes paradoxes inherent to Fourier’s law. Fractional operators introduce power-law kernels that model long-range temporal correlations, enabling more accurate simulation of transient thermal shocks, guided wave attenuation and coupled thermo-mechanical responses in complex media. Applications range from high-temperature pipelines and nano-scale resonators to porous and functionally graded structures under magnetic or moving heat sources. Analytical and semi-analytical methods—such as Laplace transform with numerical inversion, Legendre polynomial expansions and normal mode analysis—are routinely employed to solve the resulting integro-differential systems. Recent advances have deepened understanding of phase lag effects, two-temperature interactions and nonlocal elasticity, highlighting the global relevance of fractional models for improving design, diagnostics and control of thermal-mechanical devices.

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Generalized Thermoelasticity with Fractional Order Dynamics publication trend

The graph below shows the total number of articles in generalized thermoelasticity with fractional order dynamics across all publications each year (not limited to Nature Index journals).

Technical terms

Thermoelasticity: The coupled interaction between temperature variations and elastic deformation in a solid material.

Fractional Derivative: A generalization of the integer-order derivative defined via integral operators with power-law kernels, capturing memory effects.

Memory-Dependent Derivative: A variant of fractional derivative incorporating time-delay kernels to model hereditary behaviour in thermal and mechanical fields.

Generalized Thermoelasticity: An extension of classical theory that includes finite thermal wave speed, phase lags or nonlocal interactions in heat conduction.

Green–Naghdi Model: A class of hyperbolic heat conduction theories that allow thermal waves without energy dissipation, classified into type-I, II and III.

Nonlocal Elasticity: A theory in which stress at a point depends on strain over an extended region, accounting for long-range spatial interactions.

References

1. Generalized thermoelastic wave response in a hollow cylinder with temperature-dependent properties based on the memory-dependent derivative of the heat conduction model. Case Studies in Thermal Engineering (2024).
2. Influence of the fractional-order strain on an infinite material with a spherical cavity under Green-Naghdi hyperbolic two-temperature thermoelasticity theory. Journal of Engineering and Thermal Sciences (2023).
3. Functionally graded nonlocal thermoelastic nanobeam with memory-dependent derivatives. Discover Applied Sciences (2022).
4. Effect of Variable Properties and Moving Heat Source on Magnetothermoelastic Problem under Fractional Order Thermoelasticity. Advances in Materials Science and Engineering (2016).
5. Influence of a magnetic field on a nonlocal thermoelastic porous solid with memory-dependent derivative. Indian Journal of Physics (2023).