Surface instability and splitting in compressed brittle elastic solids containing crack arrays

Surface instability in brittle solids may occur at relatively small values of the inplane compressive force if the solid contains shallow cracks parallel to its free surface. The instability may produce surface damage by spallation. Similarly, the buckling load of a longitudinally compressed strip that contains an array of central cracks is affected to a great extent by the size and the relative spacing of these cracks. The instability in this case may result in longitudinal splitting of the strip. To illustrate these phenomena, the compression of an elastic half space and a layer, each containing an array of coplanar equally spaced cracks, is studied for a special class of hypoelastic materials, and the corresponding weakening due to cracks is analytically estimated.