Date of Award

12-2024

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Aerospace, Physics, and Space Sciences

First Advisor

Mirmilad Mirsayar

Second Advisor

David C. Fleming

Third Advisor

Reza Jahanbakhshi

Fourth Advisor

Sayed Ehsan Saghaian

Abstract

The main objective of this work is the development and application of a novel Timoshenko-based multipolar peridynamic (MPPD) model to advance the field of dynamic fracture mechanics. The traditional two-dimensional bond-based peridynamic (BBPD) framework, which considers only pairwise normal forces between material points, is enhanced by incorporating shear deformation effects. By modeling each bond as a short Timoshenko beam, the approach introduces a length-dependent shear influence factor and a strain-based shear deformation failure criterion, effectively transforming BBPD into a more comprehensive MPPD model. This extension allows for the accommodation of materials with Poisson's ratios up to 1/3, surpassing the limitations of the original BBPD.

The proposed MPPD model is rigorously validated against benchmark experimental tests, including standard pure mode I edge cracks and Kalthoff-Winkler configurations under in-plane dynamic loading and plane stress conditions. The results demonstrate that the proposed MPPD model predicts crack paths with greater accuracy compared to equivalent existing methods. Additionally, the model exhibits sensitivity to variations in Poisson's ratio and loading rates, influencing crack branching and propagation paths.

Building upon this foundation, the MPPD model is extended to investigate dynamic crack propagation in functionally graded materials (FGMs). Validation is conducted using experimental three-point bending tests with different material gradients, loading rates, and durations. Further analyses involve various boundary conditions and material distributions to predict crack initiation and propagation in these complex mediums. The effects of material anisotropy induced by functional gradation on crack paths are thoroughly examined. The extended model retains computational efficiency while achieving results comparable to more complex peridynamic methods such as state-based.

The research progresses to explore mixed-mode dynamic fracture in anisotropic, functionally varying microcellular structures. A novel homogenization technique is developed, capable of accounting for material and geometry-induced anisotropy, resulting in a continuous medium with equivalently distributed mechanical properties. The MPPD model is applied to this homogenized domain, accurately capturing deformation and rupture in materials with complex and directionally dependent displacement fields. Numerical simulations of compact-tension (CT) and Kalthoff-Winkler specimens with various void sizes, shapes, and distribution patterns are performed. The studies reveal how material orthotropy and void patterns affect crack initiation angles and paths. Notably, strategic void distribution near the crack tip is shown to control crack progression, preventing propagation into critical structural areas. The phenomenon known as the "wall effect" is also observed, where stress waves reflect off higher-density regions, reducing their impact elsewhere.

This work significantly enhances the peridynamic modeling framework by incorporating shear deformation effects and extending its application to materials with complex behaviors and structures. The developed Timoshenko-based MPPD model offers a computationally efficient and accurate tool for predicting crack initiation and propagation across a range of materials. The findings provide valuable insights for the design and analysis of engineering structures, contributing to the advancement of dynamic fracture mechanics.

Comments

Copyright is held by Victor Manuel Bautista Katsalukha

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