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Abstract
In this work, the governing equations of generalized magneto-thermo-viscoelasticity (MTVE) with one relaxation time and variable electrical and thermal conductivity for a one-dimensional problem are formulated into a matrix form using the state space and Laplace transform techniques. The resulting formulation is applied to a half-space medium subjected to ramp-type heating and zero-traction. The inversion of Laplace is carried out using a numerical approach. Numerical results for the dimensionless temperature, the stress, and the displacement distribution are given and illustrated graphically. According to the numerical results, some comparisons have been shown in figures to estimate the effect of some parameters on all variable fields, and discussion has been established.
Nomenclature
| λ, μ | = | Lame's constants |
| ρ | = | density |
| t | = | time |
| cE | = | specific heat at constant strain |
| k | = | thermal conductivity |
| κ | = | thermal diffusivity |
| θ | = | absolute temperature |
| T○ | = | reference temperature so that |θ/To| ≪ 1 |
| τ0 | = | relaxation time |
| αt | = | coefficient of linear thermal expansion |
| γ | = | (3λ + 2μ)αt |
| R(t) | = | relaxation function |
| K | = |
|
| α*, β | = | nondimensional empirical constants |
| Γ(•) | = | gamma function |
| t0 | = | ramping parameter |
| ui | = | components of displacement vector |
| eij | = | components of strain deviator tensor |
| τij | = | components of stress tensor |
| μ0 | = | magnetic permeability |
| ϵ0 | = | electric permittivity |
| Bi | = | components of magnetic field strength |
| Ei | = | components of electric field vector |
| Ji | = | components electric density vector |
| Hi | = | magnetic field intensity |
| M | = | magnetic field parameter |