Mechanical & Materials Engineering, Department of


First Advisor

Florin Bobaru

Date of this Version



S. Jafarzadeh, Novel and fast peridynamic models for material degradation and failure, 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: June, 2021

Copyright © 2021 Siavash Jafarzadeh


Fracture is one of the main mechanisms of structural failure. Corroded surfaces with chemically-induced damage are, notably, potential sites for crack initiation and propagation in metals, which can lead to catastrophic failure of structures. Despite some progress in simulating fracture and damage using classical models, realistic prediction of complex damage progression and failure has been out of reach for many decades. Peridynamics (PD), a nonlocal theory introduced in 2000, opened up new avenues in modeling material degradation and failure. Existing numerical methods used to discretize PD equations, however, are quite expensive as the PD nonlocal interactions make them unaffordable for large-scale 3D simulations.

In this work, we first introduce novel PD models for different types of corrosion damage. We modify and improve the original PD corrosion formulation introduced in 2015, based on the electro-chemo-mechanics of different corrosion regimes. We develop PD models for pitting, crevice, intergranular, and stress-dependent corrosion damage. Our 2D and 3D models can quantitatively predict, for the first time, the damage evolution observed experimentally, in great details. Our results show that the PD formulation for corrosion damage is a powerful, robust, and versatile tool for simulating its evolution under a variety of electro-chemo-mechanical conditions.

In the second part, we introduce a fast convolution-based method (FCBM) for efficient discretization of PD/nonlocal models. We express the PD integrals in convolutional forms and utilize the FFT and inverse FFT to compute those integrals at a low cost. We introduce two approaches to apply the desired boundary conditions in this framework. We derive the FCBM formulation for PD diffusion equation, equations of motion (with damage), and dissolution-transport equation (with application to corrosion damage). Our examples show that PD problems that would have required years of computations with existing discretization methods, can now be solved in a matter of days with FCBM. Memory allocation is also reduced by several orders of magnitude. Fast computation of fracture and damage with high accuracy are now possible with the method introduced in this work.

Advisor: Florin Bobaru