# Peridynamic Functionally Graded and Porous Materials: Modeling Fracture and Damage

## Abstract

In this chapter, we present two peridynamic models for composite materials: a locally homogenized model (FH-PD model, based on results reported in Cheng et al. (Compos Struct 133: 529–546, 2015)) and an intermediately homogenized model (IH-PD model). We use these models to simulate fracture in functionally graded materials (FGMs) and in porous elastic materials. We analyze dynamic fracture, by eccentric impact, of a functionally graded plate with monotonically varying volume fraction of reinforcements. We study the influence of material gradients, elastic waves, and of contact time and magnitude of impact loading on the crack growth from a pre-notch in terms of crack path geometry and crack propagation speed. The results from FH-PD and IH-PD models show the same cracking behavior and final crack patterns. The simulations agree very well, through full failure, with experiments. We discuss advantages offered by the peridynamic models in dynamic fracture of FGMs compared with, for example, FEM-based models. The models lead to a better understanding of how cracks propagate in FGMs and of the factors that control crack path and its velocity in these materials. The IH-PD model has important advantages when compared with the FH-PD model when applied to composite materials with phases of disparate mechanical properties. An application to fracture of porous and elastic materials (following Chen et al. (Peridynamic model for damage and fracture in porous materials, 2017)) shows the major effect local heterogeneities have on fracture behavior and the importance of intermediate homogenization as a modeling approach of crack initiation and growth.

## Keywords

Peridynamics Functionally graded materials Composite materials Dynamic fracture Crack propagation Impact Brittle fracture Porous elastic materials## Notes

### Acknowledgments

This work was supported by a grant from ONR (program manager: William Nickerson) and by the AFOSR MURI Center for Material Failure Prediction through Peridynamics (program managers: Dr. David Stargel, Dr. Ali Sayir, Dr. Fariba Fahroo, and James Fillerup). This work was completed utilizing the Holland Computing Center of the University of Nebraska.

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