STM Article Repository

Biot [97] formulated the equations of the classical coupled theory of thermoelasticity (CCTE) based on
Fourier’s law, which are dealing with the interaction of thermal field and elastic deformation such that
these two fields are linked together. Biot gave this investigation to eliminate the paradox inherent in
the classical uncoupled theory that elastic changes have no effects on the temperature. The heat
equations in the coupled theory of thermo-elasticity of the diffusion type, which predicting infinite
speeds of propagation for heat waves that contradicts to physical observations since any changes of
the temperature leads to the presence of strain, in the elastic body and vice versa. In most cases, the
solutions which are obtained by the classical dynamical uncoupled theory differ little from that
obtained by using the theory of coupled thermo-elasticity. The coupling between thermal and strain
fields gives rise to the coupled theory of thermo-elasticity when this coupling vanishes, the two fields
become independent of each other and the problem is termed as static, while the coupling effects
between thermal and strain fields were taken into consideration in the work of Lesson [98] and Weiner
[99]. One of the most important contributions in the subject of coupled thermo-elasticity is the work of
Nowacki who solved a problem for a half-space with heat sources [100]. Ignaczak [101] solved a one
dimensional problem for a spherical cavity. A one dimensional thermal shock problem solved by
Hetnarski [102] and obtained the fundamental solution of the coupled problem [103]. Bahar and
Hetnarski [104] have used the method of the matrix exponential, which constitutes the basis of the
state space approach of the modern control theory and applied to the non-dimensional equations of
the coupled theory of thermo-elasticity.