https://doi.org/10.1140/epjp/s13360-026-07635-3
Regular Article
Modeling reflection of plane waves in bio-thermoplastic diffusion with initial stress and temperature dependence via the MGT equation
1
Department of Mathematics, Osmania University, 500007, Hyderabad, India
2
Department of Mathematics, Kurukshetra University, 136119, Kurukshetra, India
a
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Received:
26
December
2025
Accepted:
31
March
2026
Published online:
15
April
2026
Abstract
This work explores how initial stresses, temperature-dependent material parameters, and impedance conditions affect the propagation and reflection of plane waves in a bio-thermoelastic diffusion half-space described by the Moore–Gibson–Thompson (MGT) heat conduction theory. The governing equations for a two-dimensional setting are nondimensionalized and reformulated using potential functions. By applying the reflection technique, it is shown that the medium supports four interacting longitudinal waves along with a single transverse mode, each traveling at different speeds. Expressions for the amplitude ratios of the reflected longitudinal (P), thermal (T), chemical potential (Pₒ), and shear vertical (SV) waves are obtained as functions of the incident angle under impedance boundary conditions. The effects of initial stress, thermal dependence of material properties, and impedance parameters on these amplitude ratios are illustrated through graphical results and interpreted in detail. Several limiting cases are also analyzed to verify the formulation. The findings contribute to a deeper understanding of wave behavior in bio-engineered materials, seismic environments, and broader thermoelastic wave propagation applications.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
