SIZE-DEPENDENT THERMOELASTICITY

Abstract

IN THIS PAPER A CONSISTENT THEORY IS DEVELOPED FOR SIZE-DEPENDENT THERMOELASTICITY IN HETEROGENEOUS ANISOTROPIC SOLIDS.  THIS THEORY SHOWS THAT THE TEMPERATURE CHANGE CAN CREATE NOT ONLY THERMAL STRAINS, BUT ALSO THERMAL MEAN CURVATURES IN THE SOLIDS.  THIS FORMULATION IS BASED ON THE CONSISTENT SIZE-DEPENDENT CONTINUUM MECHANICS IN WHICH THE COUPLE-STRESS TENSOR IS SKEW-SYMMETRIC.  HERE BY INCLUDING SCALE-DEPENDENT MEASURES IN THE ENERGY AND ENTROPY EQUATIONS, THE GENERAL EXPRESSIONS FOR FORCE- AND COUPLE-STRESSES, AS WELL AS ENTROPY DENSITY, ARE OBTAINED.  NEXT, FOR THE LINEAR MATERIAL THE CONSTITUTIVE RELATIONS AND GOVERNING COUPLED SIZE-DEPENDENT THERMOELASTICITY EQUATIONS ARE DEVELOPED.  FOR LINEAR MATERIAL, ONE CAN SEE THAT THE THERMAL PROPERTIES ARE CHARACTERIZED BY THE CLASSICAL SYMMETRIC THERMAL EXPANSION TENSOR AND THE NEW SIZE-DEPENDENT SKEW-SYMMETRIC THERMAL FLEXION TENSOR.  THUS, FOR THE MOST GENERAL ANISOTROPIC CASE, THERE ARE NINE INDEPENDENT THERMOELASTIC CONSTANTS.  INTERESTINGLY, FOR ISOTROPIC AND CUBIC MATERIALS THE THERMAL FLEXION TENSOR VANISHES, WHICH SHOWS THERE IS NO THERMAL MEAN CURVATURE.