Kalker's method applied to some improper integrals in fracture mechanics by J. Jäger, Blattwiesenstr. 7, D 76227 Karlsruhe, Germany Eng. Fracture Mech., 1996, Vol. 54, 229237 email: j_jaeger@tonline.de Abstract: This paper discusses some methods of contact mechanics, which can be applied to fracture problems. First, improper integrals with a singularity of the order r3 are treated, which some authors call hypersingular integrals. Compared with other publications, a simplified formulation is achieved by application of Kalker's analytical method for singularities of the order r1. The result is written in terms of hypergeometric functions, which are recursively reduced to standard elliptic integrals. Similar to the superposition of single forces in contact mechanics, a superposition of single displacements is used in fracture mechanics and the methods of contact mechanics are applied to fracture mechanics. In contrast to the modelling of the crack surface as a polynomial in x and y, a discrete displacement function with constant values on an equidistant rectangular mesh is more promising. The integration is performed as a matrix product and the cyclic structure of this matrix is used to reduce the required computer memory.
