A Theoretical Analysis of Stress Concentrations in Gels Containing Spherical Fillers

Abstract

Stress conditions in a model biocomposite system undergoing uniaxial compression have been theoretically analyzed. The composite structure considered was that of an incompressible isotropic gel system containing a dilute dispersion of spherical filler particles. The analysis was based on the theory of elasticity and the assumption that particle-particle interactions were negligible. The stress concentration in the vicinity of the filler was calculated for adhesive and nonadhesive interfaces between the filler and the medium. The analysis indicates that localized stress concentrations are induced in the medium within two radii from the filler particle. The level of stress concentration depends upon the condition of the interface and the ratio of the shear moduli of the two materials. The stress concentration factor may be as high as 3 at the interface in the case where rigid filler particles are loosely embedded in a soft gel. The minimum stress concentration occurs at a bonded interface when the two materials have similar elastic moduli.