Stress-field in a bone medium having a star-shaped crack

Abstract

The stress-field in a bone medium containing a star-shaped crack is analytically studied. The anisotropy of osseous tissues (as per previous experimental observations) has been taken into account. The star-crack is formed by the interaction of a number of Griffith cracks of equal lengths when the face of the crack is subjected to a prescribed pressure. By choosing a suitable Airy stress function, a fourth order differential equation is derived from the compatibility relations. By using the Mellin transform method, this equation is solved. The boundary conditions reduce the problem to that of solving a pair of dual integral equations. The dual equations are then reduced to a Fredholm integral equation of the second kind, which is solved by resorting to numerical techniques. Numerical computation is made for studying the variation of the stress-field in the bone medium in the vicinity of the crack. The effect of bone anisotropy on the intensified stress-field is also studied.