The J-contour integral in peridynamics via displacements

Abstract

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.

Review of Peridynamics: Theory, Applications, and Future Perspectives

“…The peridynamic non-local J-integral has also been thoroughly analysed in [72] and [24]. The displacement-based J-integral formulation, developed in [73], can be obtained with bond-based or state-based peridynamic models. In the article of Panchadhara and Gordon [74], a new peridynamic stress intensity factor (SIF) was introduced.…”

An Ordinary State-Based Peridynamic Model for Fatigue Cracking of Ferrite and Pearlite Wheel Material

“…In the state-based peridynamic theory, there is no concept of this driving force. To better characterize the propagating crack-tip fields, an equivalent stress intensity factor J equ can be expressed as follows [54]:…”

Fracture parameter analysis of flat shells under out-of-plane loading using ordinary state-based peridynamics

“…Le and Bobaru [25] investigated the effectiveness of surface effect corrections in the PD J-integral evaluation. Stenström and Eriksson [26] presented the alternative J-integral approach via displacements obtained from BBPD. These studies mentioned above were investigated under pure mode-I fracture conditions.…”