Thermal effects and initial stress on magneto‐thermo‐viscoelastic medium with two temperature under five theories

Abstract

The contribution of this study is to research how the initial stress and the application of a magnetic field affects the two-dimensional complication of a general, two temperature, and thermally activated viscoelastic material in five theories.In the physical domain, normal mode analysis is employed to obtain the analytical expressions for the physical quantities. A numerical pathway is chosen to calculate the analytical expressions and their explanation is done using various graphical methods. The results predicted by different theories (L-S, G-L, G-N II, and DPL) are also examined in both the scenarios, that is, existence and nonexistence of a magnetic field, viscosity, initial stress, and two temperatures. 1Nomenclature: 𝛼 0 , 𝛼 1 , 𝛼 2 , 𝛼 3 , 𝛼 4 , the viscoelastic parameters; 𝛼 𝑡 Coefficient of linear thermal expansion, 𝜌 density; 𝐾 Coefficient of thermal conductivity, 𝜏 0 , 𝜏 1 , 𝜐 0 relaxation times; 𝑒 𝑖𝑗 Components of strain tensor, 𝜙 the volume fraction field; 𝜎 𝑖𝑗 Components of stress tensor, 𝑟 the beam radius; 𝜃 Conductive temperature, 𝑎 two temperature parameter; 𝑢, 𝑤 Displacement components, 𝛿 𝑖𝑗 Kronecker's delta; 𝑇 0 Reference temperature |(𝑇 − 𝑇 0 )∕𝑇 0 | < 1, 𝑛 * , 𝑛 0 , 𝑛 1 parameters; 𝜇 0 the magnetic permeability, 𝑝 the initial stress; 𝜏 0 the thermal relaxation time, 𝜀 0 the electric permittivity; 𝑇 Thermodynamic temperature, 𝑐 𝑒 specific heat at constant strain; 𝑒 = 𝑒 𝑘𝑘 Cubic dilatation, 𝜆, 𝜇 Lame' constants