Axial Decay of Self-Equilibrating End Loads in Compressible Solids

Abstract

The axial diffusion rate of self-equilibrating surface loads is investigated for axially prestretched solids under plane-strain conditions. The perturbed field within the body, induced by an instantaneous end disturbance, is examined by using the eigenfunction spectral analysis. A general solution is given for a wide range of compressible materials. Particular examples are presented for a few hyperelastic solids. Very slow rate of decay, of the first antisymmetric eigencomponent, has been found near the stress-free configuration. Also, there is almost no decay of the first symmetric eigencomponent near the ultimate tension load. The diffusion length is greater for less compressible solids. Axial decay is exponential and depends quite strongly on material moduli and prestrain.