### Peridynamic Analysis of Damage and Failure in Composites

Ebrahim Askari, Jifeng Xu, Stewart Silling
2006 44th AIAA Aerospace Sciences Meeting and Exhibit   unpublished
Nearly all finite element codes and similar methods for the analysis of deformation in structures attempt to solve the partial differential equations of the classical theory of continuum mechanics. Yet these equations, because they require the partial derivatives of displacement to be known throughout the region modeled, are in some ways unsuitable for the modeling of cracks and other discontinuities, in which these derivatives fail to exist. As a means of avoiding this limitation, the
more » ... ation, the peridynamic model of solid mechanics has been developed for applications involving discontinuities. The objective of this method is to treat crack and fracture as just another type of deformation, rather than as a pathology that requires special mathematical treatment. The peridynamic theory is based on integral equations, rather than differential equations, so there is no problem in applying the equations directly on a crack tip or crack surface. In the peridynamic model, displacements and internal forces are permitted to have discontinuities and other singularities. Particles interact with each other directly across finite distances through central forces known as "bonds". Damage is introduced into the peridynamic model by permitting these bonds to break irreversibly. Breakage occurs when a bond is stretched in tension (or possibly compression) beyond some prescribed critical amount. After a bond breaks, it sustains no force. A distinguishing feature of this approach is its ability to treat the spontaneous formation of cracks together with their mutual interaction and dynamic growth in a consistent framework. A three-dimensional code called EMU implements the peridynamic model on parallel computers. The peridynamic method has been applied successfully to the analysis of material and structural failure in aerospace composites, particularly in graphiteepoxy laminates. For example, the method has been applied to the prediction of failure mode and crack direction in large-notch composite panels under tension loads with different layups and stacking sequences. The results have reproduced the experimentally observed dependence of crack growth direction on the relative percentage of fibers in different directions. The authors also have analyzed the damage occurring in a composite panel due to low velocity impact. The method predicts in detail the delamination and matrix damage process. Although the numerical method in EMU lends itself to parallelization, threedimensional analysis of large problems is computationally intensive. The applications reported here were run on the Columbia supercomputer at NASA Advanced Supercomputing (NAS) division. The Columbia supercomputer is proving to be invaluable in high-resolution modeling of the failure of composite materials. Nomenclature ρ = material density x = spatial location t = time u = displacement vector σ = stress tensor