Thermoelastic wave propagation and reflection in biological tissue under nonlocal elasticity and Moore–Gibson–Thompson heat conduction: modeling and analysis

Abstract

The present work introduces a theoretical framework according to the Moore–Gibson–Thompson (MGT) heat conduction-based generalized thermoelasticity theory by using the Eringen’s nonlocal elasticity theory to analyze the reflection and propagation of plane waves in a homogeneous, isotropic biological tissue medium. The scalar and vector potential functions of displacement vector in the form of Helmholtz decomposition are adopted here. Three basic types of waves consisting of two dispersive attenuated coupled longitudinal waves and one uncoupled transverse shear wave are identified. Attempt is made to solve the dispersion relation equations to derive the expressions for propagation speeds and attenuation coefficients of plane waves analytically. Detailed analysis on wave characteristics is made by studying the problem under MGT theory along with three other generalized thermoelasticity theories, namely LS, GN-III, and TPL theories. Propagation speeds and attenuation coefficients of all three types of waves are shown to be affected by the working angular frequency under MGT, LS, GN-III, and TPL model of thermoelasticity with nonlocal elasticity theory. Furthermore, reflection of waves for incident longitudinal and incident transverse wave is investigated by finding the reflection coefficients. An analysis and visual investigation are conducted on the wave characteristics of the propagating plane waves with respect to the employed angular frequency, thermal boundaries, and characteristics of incident waves. An in-depth comparative analysis is also presented for various results under MGT, LS, GN-III, and TPL theories. © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2025.