Instability and stress analysis for cavitation in soft graded elastic solids

For an infinitesimal initial cavity in homogeneous soft solids, a finite inflating pressure may cause an unbounded increase of cavity size. An asymptotic value of 2.5 times the initial shear modulus for incompressible homogeneous neo-Hookean solids is usually referred to as cavitation instability in soft solids. Recently, by detecting the drop of inflating pressure, the cavitation rheology technique has been developed to measure the local shear modulus of soft materials. In this article, we analytically extend our study on the cavitation problem to soft graded elastic solids. The mechanical property of the soft solid is assumed to vary according to power-law relations. We find that the relationship between inflating pressure and cavity size can be both a monotonic and nonmonotonic function when considering the size of initial cavity and the extent of inhomogeneity. The inflating pressure can reach a local maximum at intermediate cavity size and cause a decrease in the pressure even before fracture. The material inhomogeneity will also affect the stress distribution and the extent of stress concentration near the cavity surface. The results obtained in this article may be helpful for a better understanding of the cavitation phenomenon in complex soft solids.