Generalized Thermoelastic Problem of an Infinite Body with a Spherical Cavity under Dual-Phase-Lags
R. Karmakar, A. Sur, M. Kanoria
University of Calcutta, Kolkata, West Bengal, India
Keywords: обобщенная двухтемпературная теория термоупругости, модель с двумя фазами запаздывания, пространство состояний, векторно-матричное дифференциальное уравнение, two-temperature generalized thermoelasticity, dual-phase-lag model, state-space approach, vector-matrix differential equation
Abstract
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord-Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained for at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord-Shulman and dual-phase-lag models.
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