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Because of the nonlocal interparticle forces inherent in peridynamics, surface, boundary, and end effects appear in 3D, 2D and 1D body problems, respectively. In certain situations, the effect is seen as a disturbance, and various efforts, mostly centering on 2D and 1D problems, have been made to reduce it. A simple method has been derived to remove the end effects in a 1D body by homogenizing the body. When a certain body type, common in practice, is homogenized, its linear elastic behavior, independent of the interparticle force range and with a finite number of material points, in the limit infinite, is identical to that of a corresponding classical continuum mechanics body.

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Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding spatial derivatives, which are not defined at discontinuities, such as crack surfaces. Rice's J-contour integral is a firmly established expression in classic continuum solid mechanics, used as a fracture characterizing parameter for both linear and nonlinear elastic materials. A corresponding nonlocal J-integral has previously been derived for peridynamic modelling, which is based on the calculation of a set of displacement derivatives and force interactions associated with the contour of the integral. In this paper, we present an alternative calculation of the classical linear elastic J-integral for use in peridynamics, by writing Rice's J-integral as a function entirely of displacement derivatives. The accuracy of the proposed J-integral on displacement formulation is investigated by applying it to the exact analytical displacement solution of an infinite specimen with a central crack and comparing the exact analytical expression of its J-integral K 2 I /E. Further comparison with a well-known peridynamic crack problem shows very good agreement. The suggested method is computationally efficient and further allows testing of the accuracy of a peridynamic model as such.

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