PLANE-STRAIN DEFORMATIONS OF LOCKING MATERIALS NEAR A CRACK-TIP

Plane-strain deformations of an isotropic and homogeneous Hookean body containing a crack are studied and it is required that the dilatation everywhere in the body be greater than or equal to a constant. Following Prager, the region where the dilatation always equals the constant is identified as the locking region. For the case when the deformations of the body are symmetrical about the plane containing the crack, equations are derived that delimit the size of the locking region. It is shown that for a series type r,theta separable solution of the problem, the order of the singularity is essentially unchanged by the consideration of the higher-order terms in the constraint equation.