On Some Exact Results in Thermoplasticity of Composite Materials

The effect of uniform thermal changes and mechanical loads on the inelastic response is described for certain two-phase materials of arbitrary phase geometry, and for two-phase fibrous systems of any geometry in the transverse plane. Auxiliary uniform strain fields are derived by superposition of the actual thermal field with a field caused by specific uniform overall stresses or strains. For many actual composite systems, the uniform fields are shown to be isotropic and thus capable of causing only elastic strains in a plastically incompressible matrix. This property permits an exact replacement of the actual thermomechanical loading path with a modified mechanical path. The modified path is utilized in derivation of many closed-form expressions for evaluation of the translation vectors for centers of overall yield and relaxation surfaces, instantaneous inelastic moduli, and plastic strains during thermomechanical deformation of the composite materials.