Thermoelastic buckling. An unstable . . .


The instability of thermodynamic equilibrium of a system in a state of minimum entropy is analyzed by treating the particular example of thermoelastic buckling of a thin elastic plate in an initial state of compression in its own plane. There are two critical buckling loads, one for slow isothermal deformation, the other for fast adiabatic deformation. For an intermediate load the buckling occurs at a finite rate controlled by the thermal conductivity of the elastic material. Thus a purely thermoelastic creep buckling is obtained. The general analysis is based on Lagrangian thermodynamics in the vicinity of an equilibrium state with initial stress. The general theory is compared with the solution derived from classical differential equations of thermoelasticity. The instability is non-oscillatory in accordance with a general theorem. Due to the phenomenological nature of the general theory, results are applicable to porous solids or materials which exhibit mechanical relaxation associated with internal diffusion, phase change, and mass transport

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