Jifeng Xu

Peridynamic analysis of damage and failure in composites.

*† ‡ 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 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.

Hail Impact Characteristics of a Hybrid Material by Advanced Analysis Techniques and Testing

The design of an aerospace structure using an off-the-shelf composite would involve increasing the gauge thickness until all the design requirements are met. This can lead to an inefficient design, because excess margins will exist for all properties except the one that determines the gauge. The design of a material can be made practical by creating a hybrid composite consisting of two or more types of fibers or resins, each embellishing a particular trait or function to the material. This paper investigates both high- and low-energy hail impact against a toughened-epoxy, intermediate-modulus, carbon-fiber composite using both experimental and analytical means. The effect of introducing ply-level hybridization by substituting up to 20% of the plies with glass-reinforced plies is considered. It is found that delamination can be reduced by this hybridization, but the benefits are dependent on the impact energy and the test conditions. A computational model based on the peridynamic theory of solid mechanics ...

Damage and Failure Analysis based on Peridynamics - Theory and Applications ∗

In this paper we give an overview over a recent non-local formulation of continuum mechanics called the Peridynamic theory in contrast to related non-local theories in the literature. The Peridynamic approach is fundamentally different as it avoids using any spatial derivatives which arise naturally when formulating balance laws in the classical, local theory. Motivated by molecular dynamics the differential operator in the equation of motion is replaced with an integral operator which can be applied to both continuous and discontinuous fields. By comparing the elastic energy density associated with homogeneous deformations in Peridynamics to the corresponding energy in classical elasticity we show how the connection to experimentally measurable material properties such as the Young’s modulus and the Poisson ratio can be established. This is done by expressing the elastic energy in Peridynamics as a function of the invariants of the strain tensor, a rigorously approach not previously published. The paper concludes with an example of a crack turning in a 3D isotropic material, illustrating the strength of the Peridynamic formulation in problems where the crack path is not known in advance.