New Lord–Shulman phase-lag models capture thermal shock response in viscoelastic annular disks

A new study presents a comprehensive analysis of generalized coupled thermoelastic responses in annular disks, formulated within the Lord–Shulman generalized theory of thermoelasticity. The work, authored by Maryam H. Aljadani, Ashraf M. Zenkour, Noha M. Seyam and Hamada F. El-Mekawy, establishes governing equations of coupled thermoelasticity in cylindrical coordinates and solves them in the Laplace domain, offering a mathematical framework for predicting how viscoelastic annular disks behave when subjected to thermal shock loading.

Technically, the researchers first derive the coupled thermoelastic equation system in cylindrical coordinates and solve it in the Laplace domain. A numerical inversion technique is then employed to transform these solutions back into the physical time domain, which makes it possible to analyze transient thermoelastic fields. From these solutions, the study produces time histories of displacement, temperature, dilatation and stress distributions within the disk, giving a detailed picture of the transient thermo-mechanical response as the thermal shock propagates through the material.

A central feature of the work is the comparison between outcomes anticipated by the simpler, classical version of the Lord–Shulman theory and those derived from the improved, novel phase-lag models. According to the authors, the improved formulations capture transient properties that the simpler theory does not fully represent, including finite propagation speeds of thermal disturbances, stress localization, and relaxation behaviour.

The established models are intended as predictive tools: the dynamic thermoelastic response of viscoelastic annular disks under thermal shock loading can be estimated with their help. The study is published as open access research in Discover Applied Sciences, with the article shared early under a citable permanent DOI ahead of the final Version of Record. As a theoretical and numerical modelling study, its findings concern the mathematical formulation and computed response of the disk problem rather than experimental measurements on physical specimens.

Subject of Research: Generalized Lord–Shulman thermoelastic modelling of thermal shock in viscoelastic annular disks

Article Title: A thermal shock problem for a viscoelastic annular disk using novel L–S phase-lag models

Article References: Aljadani, M. H., Zenkour, A. M., Seyam, N. M., & El-Mekawy, H. F. (2026). A thermal shock problem for a viscoelastic annular disk using novel L–S phase-lag models. Discover Applied Sciences. https://doi.org/10.1007/s42452-026-09767-8

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DOI: 10.1007/s42452-026-09767-8

Keywords: thermoelasticity, Lord–Shulman theory, phase-lag models, annular disk, thermal shock, viscoelasticity, Laplace transform, stress localization, finite propagation speed, transient response, thermal, shock