Author ORCID Identifier


Defense Date


Document Type


Degree Name

Doctor of Philosophy


Mechanical and Nuclear Engineering

First Advisor

Ibrahim Guven

Second Advisor

Stewart Silling

Third Advisor

Hooman Tafreshi

Fourth Advisor

Karla Mossi

Fifth Advisor

Erdogan Madenci


Peridynamics, presented by Silling in 2000 [1], is a reformulation of the elastic theory from differential equations to integral equations, which are more equipped to handle discontinuities, such as crack initiation and propagation. Because of this, peridynamics is an effective tool to address many of the problems relevant to the aerospace and defense industries. For example, airborne sand particles and raindrops cause local damage to aircraft in flight. This damage manifests itself as radial and subsurface lateral cracking, as well as increased surface roughness. All of these damage morphologies may result in undesired degradation of mechanical and optical properties.

This dissertation aims to address the question of how peridynamics (PD) can be used as a tool to help understand impact problems and resultant damage. Three main types of problems will be discussed: (1) modeling of quasi-static nano- and micro-indentation in PD; (2) solid impact experiments and simulations involving glass micro-spheres impacting coated and uncoated advanced ceramics, and sand particles impacting optical glasses; and (3) the implementation of a new, fully three-dimensional hyperelastic material model in state-based PD to simulate nylon bead impact and capture the damage patterns relevant to raindrop impact.

In the first portion, a new method for modeling indentation in PD is presented using the principle of viscous damping and automatic convergence checking. In these simulations, depth-controlled indentation is performed by splitting up the total indentation depth into multiple stages, and applying damping at each stage to ensure the system reaches equilibrium before allowing for failure. PD results show good agreement to experimental data, in terms of crack lengths and force-displacement curves.

In a chapter about solid particle impact, two studies are presented. In the first, glass spheres with diameters ranging from 200 to 700 um impact multi-spectral zinc sulfide (MS-ZnS) with various coating systems. It was found that samples containing the REP coating had better resistance to damage than those without. This resistance was evident in all three damage metrics used: impact pit diameter, radial crack length, and lateral crack size. Simulations were carried out in bond-based PD, with good agreement to experiments regarding damage metrics and rebound velocity.

The second solid particle impact study involved sand particles impacting four different types of optical glasses: BK7, alumino-boro-silicate, fused silica, and Pyrex. First, data from experiments was analyzed, and a multi-variable power law regression was performed to show that sand particle shape plays a significant role in resultant damage. This was confirmed via bond-based PD simulations, with damage quantities agreeing well with experimental values.

Finally, the problem of how to model raindrop impact using nylon beads was examined. Due to the large amounts of elastic strain experienced by the nylon beads during impact experiments, it was determined that a hyperelastic material model could be a good fit. Based on elastic theory and classical continuum mechanics, a new, fully three-dimensional Neo-Hookean material model was implemented in nonordinary state-based peridynamics. This model was verified against results and finite element analysis, with very good agreement. Preliminary simulations including damage show good results, consistent with experiments.


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