UDC 519.633: 536.212 Numerical Simulation of Thermoelastic Waves Arising in Materials Under the Action of Different Physical Factors I. V. Amirkhanov∗, I. Sarhadov∗, A. F. Ghaleb†, N. H. Sweilam† ∗ Laboratory of Information Technologies Joint Institute for Nuclear Research Joliot-Curie, 6, 141980 Dubna, Moscow Region, Russia † Department of Mathematics, Faculty of Science Cairo University at Giza, Egypt, 12613 In this work, a system of equations of one-dimensional thermoelasticity is presented, which takes into account the nonlinear dependence between stresses and deformation. <...> Different problems are considered, which correspond to different external actions on the sample. <...> The numerical simulation of thermoelastic waves arising in a metallic sample under a variable external pressure on the sample’s boundary is considered, when the maximum of the absolute value of pressure changes in the interval of observation or violation of the linear Hooke’s Law. <...> The numerical investigation of the dynamics of these waves in two-layered structures is also performed. <...> It is shown that the nonlinear dependence of stresses on deformation strongly affects the form dynamics of the thermoelastic wave. <...> Key words and phrases: thermoelasticity, thermoelastic waves, numerical simulation, nonlinearity, Hooks law, deformation, stress. 1. <...> Introduction electron beams and powerful pulsed ion beams has provided a unique opportunity for the study of the irradiation effect of concentrated energy streams on materials (c.f. [1] and the references therein). <...> This is one of the most promising trends of the beam technology from the viewpoint of modification of material properties [1–6] (microsolidity, wear resistance, corrosion resistance, heat resistance, etc.), as the modification provides a way for changing purposely the element composition and the structural-phase state of pre-surface layers by means of a pulsed thermal treatment. <...> The interaction of the charged particle beams with the surface of metals and alloys can cause elastic stresses in the whole irradiated area. <...> When the charged particles affect the surface of the solid, there are different causes leading to the formation of elastic stresses [3]. <...> The material temperature changes not only because of heat supplied from external sources, but also because of the deformation processes. <...> Elastic and thermal waves are produced by deformation. <...> In previous papers we studied thermoelastic waves arising in materials <...>