Hyperbolic Thermoelastic Analysis due to Pulsed Heat Input by Numerical Simulation

Abstract

Thermo-mechanical behavior in a rod subjected to a pulsed heat input was investigated by numerical simulation using the hyperbolic thermo-elasticity theory derived from the thermal dynamics in the present paper. Unlike the classical thermo-elastic theory with the parabolic energy equation and the hyperbolic motion equation, temperature response and thermal stress due to the temperature change exhibit significant wavy characteristics in the hyperbolic thermo-elasticity theory which is based on the non-Fourier heat conduction. The whole region of the rod is split into the heat disturbed region and the heat undisturbed region by the thermal wave front which is determined by the propagating velocity of the heat wave. The heat wave and elastic wave travel in the body at a finite velocity and reflect at the end of the rod. Thermal shock due to the discontinuous jump in thermal condition, and the reflection of thermal stress at the end terminate of the rod are significant during the heating process.

A comparison of the finite‐difference and finite‐volume methods for a numerical solution of a hyperbolic thermoelasticity problem utilizing the implicit and explicit schemes

“…For the numerical calculation the thermomechanical properties of copper are chosen: the Young's modulus = 127 GPa, the Poisson coefficient = 0.33, the density = 8960 kg/m 3 , the heat conductivity = 401 ∕( ⋅ ), the volume coefficient of the thermal expansion = 49.5 ⋅ 10 −6 1/K, the constant pressure heat capacity = 390 J/K, the radiation absorption constant = 11.7 −1 . In experimental [27][28][29] and theoretical [30][31][32][33][34] works various heat flux relaxation times for metals are presented, their range lies between 10 −8 and 10 −12 s. Basing on this information, is accepted to be 0.1 ns as the median value of the range. The radiation energy 0 is taken to be 0.15 J/m 2 .…”

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

“…However, numerical oscillations appeared and in [8], [9] developed a stabilization method. The Newmark-β algorithm, with optimized time steps and algorithm parameters, was used in [150], [152], [140].…”

Thermoelastic Waves in a Medium with Heat-Flux Relaxation

“…A number of experimental (Poletkin et al 2012) and theoretical papers (Wang et al 2011) are dedicated to the thermoelastic wave propagation processes in nanometer-sized films. Some numerical studies of the hyperbolic thermoelasticity problems were done in Yu et al (2006), Melnik (2001), and Youssef (2005). An extensive review on the hyperbolic thermoelasticity is given in Igna and Ostoja-Starzewski (2010) and Chandrasekharaiah (1998).…”