Nonlinear and Linear Transient Deformation Waves in Thermoelastic and Elastic Bodies,
FOREIGN TECHNOLOGY DIV WRIGHT-PATTERSON AFB OHIO
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Axiomatic thermomechanics of a continuum and the introduction of supplementary postulates are used to construct a nonlinear theory of thermoelasticity, one postulate of which is a nonlinear equation of thermal conductivity of comparatively general form. From this equation of thermal conductivity and as a result of appropriate simplifications, certain versions of the linear and nonlinear equations of thermal conductivity are derived. Based on this nonlinear theory of thermoelasticity concrete mathematical models are constructed closed systems of equations, which assume the first derivative of displacements in Lagrange coordinates and the relative temperature change to be small in comparison with unity. The theory of elasticity is considered as a particular case of the theory of thermoelasticity. It is shown that in the case of typical structural materials the geometric and physical nonlinearity cause nonlinear effects of identical order.