Modeling multiple crack propagation in the material point method by J-integral methods accounting for other cracks intersecting the J contour

Abstract

Numerical crack propagation modeling of multiple, explicit cracks requires methods that can resolve interacting, and potentially intersecting, cracks as well as methods to calculate crack-tip parameters with sufficient accuracy for predicting when and where cracks propagate. These problems were solved using the material point method (MPM). First, the MPM method for modeling a single explicit crack known as CRAMP method was extended to account for two interacting explicit cracks by tracking four instead of original two crack velocity fields needed to resolve one explicit crack. Second, crack propagation and propagation direction were found using crack-tip $J$ integral with partitioning into mode I and mode II stress intensity factors. $J$ calculations, however, must be augmented whenever other cracks intersect the $J$ contour for a propagating crack. If the intersecting crack’s tip is inside the $J$ contour, the contour must be adapted to avoid that tip. A robust $J$ calculation algorithm with intersecting-crack corrections is provided. Several examples show the new corrections are accurate. Selected crack propagation examples show the new methods have sufficient accuracy for interacting crack propagation calculations without any need to remesh or highly refine crack-tip regions.