Parallel programming of a peridynamics code coupled with finite element method

Abstract

Using OpenMP (the Open MultiProcessing application programming interface), dynamic peridynamics code coupled with a finite element method is parallelized. The parallel implementation improves run-time efficiency and makes the realistic simulation of crack coalescence possible. To assess the accuracy and efficiency of the parallel code, we investigate its speedup and scalability. In addition, to validate the parallel code, experimental results for crack coalescence development sequences are compared. It is noted that this parallelized code markedly reduces computation time along with the coupling scheme. Moreover, the coupling approach used in this parallel code enables a more realistic and feasible numerical prediction of coalescing fractures. With the parallel implementation, two main types of crack coalescences between two flaws, formed by two short shear cracks and by a short central tensile segment and subsequent shear cracks are in detail discussed in terms of their development sequences. Consequently, this proposed coupled peridynamics code can be used to efficiently solve actual coalescence development sequences, thereby providing a numerical solution for fracture mechanics.

Morphological aspects of crack growth in rock materials with various flaws

“…To lessen the computational burden in a nonlocal peridynamics, we employ a coupling scheme where the dimensions of a peridynamic region are 70 mm (width) × 80 mm (height) × 30 mm (thickness), leading to a reduction in the total number of peridynamic nodes in Figure , thereby reducing the calculation time by half. Moreover, with a help of a multicore system based on a Dual Intel Xeron(R) CPU E5‐2687 v2 @ 3.40 GHz with 64‐GB RAM and 32 threads, the computational time for parallelized peridynamics is observed to be 15 times faster than that observed for sequential peridynamics in Lee et al Therefore, the numerical method used in this paper can feasibly reproduce realistic fracturing patterns in the complex geometries of flaws in rock specimens.…”

“…However, the TWCs appear to halt in their development, along with growing shear cracks from the left face of the bottom square and from the right face of the top square in Figure E‐H. Generally, the damage is severe at the CTCS‐induced coalescence and the two outer faces of squares, which is observed as an X‐shaped shear …”

“…However, the TWCs appear to halt in their development, along with growing shear cracks from the left face of the bottom square and from the right face of the top square in Figure 8E-H. Generally, the damage is severe at the CTCS-induced coalescence and the two outer faces of squares, which is observed as an X-shaped shear. 2,3,5,7,10,16,33 4 | CONCLUSIONS In this paper, we capture the crack development sequences in a rock specimen with flaws of various shapes through parallelized peridynamics coupled with a finite element. Demonstrating good fidelity to physical test results, the numerical results provide some insightful information on fracturing behaviors.…”

“…For typical patterns, the crack evolution progress is initiated by TWCs, while specimen failure is caused by shear cracks such as horsetail cracks and anti‐wing cracks. In a specimen with a flaw pair, as a complex problem, the interacting effects of the flaws on general fracturing patterns are obvious . Interestingly, the initiation position is subject to the interaction between flaws as well; when two flaws are aligned to partially or substantially overlap, the initiation position is affected more by the interaction than by the inclination angle, in a bridging region between two flaws .…”

“…In a specimen with a flaw pair, as a complex problem, the interacting effects of the flaws on general fracturing patterns are obvious. 6,[11][12][13][14][15][16] Interestingly, the initiation position is subject to the interaction between flaws as well; when two flaws are aligned to partially or substantially overlap, the initiation position is affected more by the interaction than by the inclination angle, in a bridging region between two flaws. 2,6,7,9,10,17 The internal TWC in the bridging region propagates toward and reaches its opposite flaw tip and then forms coalescence.…”