Generalized Thermoelasticity in Complex Media

Generalized thermoelasticity extends classical coupling of temperature and mechanical deformation by incorporating finite propagation speeds of thermal signals, memory-dependent heat conduction and multiscale interactions. In complex media such as functionally graded materials, nanostructures and viscoelastic composites, standard Fourier‐based heat flow proves inadequate to capture thermal relaxation, nonlocal stress fields and heterogeneous material properties. New frameworks introduce fractional derivatives, phase‐lag models and two‐temperature formulations to characterise thermal memory, microstructure effects and anisotropic responses. This enables prediction of coupled thermomechanical wave propagation, size‐dependent elasticity and dissipative phenomena across length scales. Such advances have direct applications in nano‐electromechanical systems, energy conversion devices, magnetic and semiconducting components, and bio‐inspired materials. The unified perspective of generalized thermoelasticity provides deeper insight into wave dispersion, attenuation and the influence of graded or multiphase architectures on stress and temperature distributions.

Research from Nature Portfolio

Recent studies have developed a fractional‐time thermoelastic model for functionally graded viscoelastic nanobeams that incorporates an Atangana–Baleanu fractional derivative with a non‐singular kernel. By introducing nonlocal constitutive relations alongside a fractional Kelvin–Voigt viscoelastic law, this approach captures size‐dependent thermal memory and mechanical heterogeneity across beam thickness. Numerical analyses reveal novel coupled thermomechanical wave characteristics under harmonic heating, demonstrating significant deviations from classical predictions in nanoscale devices.

Another contribution formulates a higher‐order phase‐lag heat conduction theory for non‐simple thermoelastic materials that integrates three time lags and two distinct temperatures—thermodynamic and conductive. This generalised model subsumes earlier two‐temperature and phase‐lag theories as special cases and is applied to sudden heating of isotropic solids under external loading. The work highlights the role of phase discrepancies and higher‐order time derivatives in modulating stress–temperature interactions and offers a versatile tool for probing rapid thermal–mechanical transients.

Generalized Thermoelasticity in Complex Media publication trend

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

Technical terms

Fractional derivative: A generalised differential operator of non‐integer order used to model memory effects in heat conduction and viscoelasticity.

Nonlocal constitutive relation: A stress–strain description in which material response at a point depends on field values over a finite neighbourhood, capturing size‐dependent effects.

Phase lag: A finite time delay between thermal flux and temperature gradient in non‐Fourier heat conduction models, accounting for wave‐type thermal propagation.

Thermal relaxation time: The characteristic time interval required for heat flux to adjust to changes in temperature gradient in generalized thermoelastic theories.

Moore–Gibson–Thompson equation: A hyperbolic heat conduction model incorporating thermal relaxation to resolve infinite‐speed paradoxes in classical Fourier theory.

References

1. Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative. Scientific Reports (2024).
2. A generalized heat conduction model of higher-order time derivatives and three-phase-lags for non-simple thermoelastic materials. Scientific Reports (2020).
3. Evaluation of the thermal and mechanical waves in anisotropic fiber-reinforced magnetic viscoelastic solid with temperature-dependent properties using the MGT thermoelastic model. Case Studies in Thermal Engineering (2022).
4. A Mathematical Study of a Semiconducting Thermoelastic Rotating Solid Cylinder with Modified Moore–Gibson–Thompson Heat Transfer under the Hall Effect. Mathematics (2022).