sentences:  Since partial derivatives do not exist on crack surfaces and other singularities, the classical equations of continuum mechanics cannot be applied directly when such features are present in a deformation.The integral equations of the peridynamic theory can be applied directly, because they do not require partial derivatives.The ability to apply the same equations directly at all points in a mathematical model of a deforming structure helps the peridynamic approach avoid the need for the special techniques of fracture mechanics.