Thermal-stress concentration near inclusions in viscoelastic random composites

The determination of thermal-stress concentrations near inclusions in viscoelastic random composites is concerned with the prediction of the overall response of random nonlinear viscoelastic multi-component media. The continuum considered here is assumed to be subjected to a finite deformation. First Piola’s stress tensor and deformation gradient are used as conjugate field variables in a fixed reference state. A nonlinear problem is investigated in a second-order approximation theory when the gradient deformation terms higher than second order are neglected. A convex potential function in a thermo-elastic problem and time functionals in a viscoelastic one are used to construct overall constitutive relations. The technique of surface operators developed by R. Hill and others is used to determine stress concentrations near inclusions for nonlinear matrix creep.