Mechanical & Materials Engineering, Department of


First Advisor

Florin Bobaru

Date of this Version

Winter 11-30-2021


J. Zhao, Novel Peridynamic Models for Material Degradation and Mass Transport, Doctoral Dissertation, University of Nebraska-Lincoln, 2021.


A DISSERTATION Presented to the Faculty of The Graduate College at the University of Nebraska In Partial Fulfillment of Requirements For the Degree of Doctor of Philosophy, Major: Mechanical Engineering and Applied Mechanics, Under the Supervision of Professor Florin Bobaru. Lincoln, Nebraska: December, 2021

Copyright © 2021 Jiangming Zhao


Fracture and corrosion are two major causes of structure failure. They can interact with each other, leading to faster material degradation. They are also under the influence of environmental conditions. The corrosion rate highly depends on the transportation rate of involving substances, while the fracture can be accelerated significantly due to fluid flow. These complex mechanisms involved in structure failure have troubled classical models for decades. The peridynamic (PD) theory introduced in 2000 has shown great potential in modeling such problems. In this work, we develop novel PD models for fracture, corrosion, mass transport, and viscous flow, which are building blocks to make comprehensive predictions on structure failure. We first introduce a partially-homogenized PD model for concrete fracture. The model links microscale information to macroscale fracture behavior, while costing the same as a fully homogenized model. This model successfully predicts corrosion-induced fracture in concretes with a single or multiple rebars. We then develop a new PD corrosion model which can update the distribution of corrosion rates along arbitrary metal surface, particularly useful for simulating galvanic corrosion. We couple the new PD corrosion model with the PD fracture model and solve a problem under combined electro-chemical attack and mechanical forces to demonstrate the capability of PD models. We also construct PD models for transient advection-diffusion and viscous flow from fundamental conservation principles. The constructive approach in deriving these models allows for future modeling of complex fluid-structure interaction problems in which solid degradation takes place, such as erosion-corrosion and hydraulic fracture. In PD models, boundary conditions (BCs) are naturally nonlocal, but usually only local BCs are available from measurements. The existing mirror-type fictitious nodes method (FNM) can convert local BCs to nonlocal ones, but its application is limited to domains with simple geometries. We introduce a new algorithm to make the mirror-type FNM work autonomously for domains with arbitrary geometries. The algorithm developed is general and should also work for any type of peridynamic model, including corrosion, fracture, and fluid-structure interactions.

Advisor: Florin Bobaru