[SY-E11] Symposium E-11

[SY-E11] Graph theory analysis of rich fiber-scale data yields very fast simulations of damage evolution in composites

jerry quek², ^○brian n cox¹ (1.arachne consulting, United States of America, 2.IHPC, Singapore)

Simple mechanistic arguments suggest that the loci of cracks that initiate and propagate among fine-scale, stochastic, heterogeneous material domains might be predictable by fast graph theoretic methods, without executing explicit fracture mechanics simulations. Here we explore the usefulness of graph theoretic methods for analyzing the microcracking that develops in continuous fiber composites loaded transversely to the fiber direction. We use graph theoretic methods to analyze rich data published elsewhere for two types of fiber composite. The data describe the irregularity of the spatial distribution of the fiber population, and meandering of fibers within the population, which is seen when the fibers are tracked along the nominal fiber direction. Graph analysis yields very fast predictions of the likely sites of crack initiation in the fiber composite, as well as plausible indications of the likely direction in which an initiated crack will grow, the developing shape of the crack, and the frequency of instances of fibers that will bridge the crack obliquely, thereby raising the composite fracture resistance. From the results of the graph analysis, we infer a stochastic population of effective defects in the composite, whose location and effective strength are related to the Euclidean and topological characteristics of the fiber population in the vicinity of the defect. We propose that, if the predicted distribution of defects is entered as an initial material condition in an homogenized finite element simulation of the composite, then the important effects of the stochastic fiber distribution, in regard to crack initiation, preferred directions of growth, and toughening due to fiber-bridging, can be captured in a simulation of tractable size. This strategy carries the pertinent spatial information content of any measured random distribution of fibers into a simulation in which the fibers are not represented explicitly.