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Peridynamic models in multi-physics applications on bounded and unbounded domains
Citation Link: https://doi.org/10.15480/882.13738
Publikationstyp
Doctoral Thesis
Date Issued
2024
Sprache
English
Author(s)
Advisor
Referee
Title Granting Institution
Technische Universität Hamburg
Place of Title Granting Institution
Hamburg
Examination Date
2024-11-22
Institute
TORE-DOI
Citation
Technische Universität Hamburg (2024)
The following dissertation concerns with elevating the role of nonlocal peridynamic continuum models in real-world engineering and material applications by establishing efficient and robust numerical techniques and providing comprehensive model descriptions that aim to accurately represent the underlying physical properties. A number of versatile numerical discretization schemes are thoroughly evaluated for both bond-based peridynamic models in brittle fracture modeling as well as nonlocal diffusion-type models for up to three-dimensional problems. These schemes can adaptively refine the computational grid around areas of interest, are asymptotically compatible, computationally efficient, and easy to implement. Efficient solution schemes are further provided for unbounded domain problems, based on residual-free exponential basis functions, which may be used in a collocation scheme to obtain Dirichlet-type boundary conditions to approximate the far-field domain solution over a truncating boundary. The feasibility and improved capability of the proposed numerical schemes are demonstrated on the complex multi-physics simulation of the biodegradation of magnesium-based bone implant screws under physiological conditions on (nearly) unbounded three-dimensional domains, utilizing the standard bi-material peridynamic corrosion model with an efficient constitutive model of the corrosion kinetics that directly links to the experimentally easy-to-measure macroscopic volume loss. In order to augment the capabilities of standard peridynamic models towards the description of multi-ionic mass transport of electromigration, a generalized peridynamic framework of nonlocal Nernst-Planck-Poisson equations is proposed, which effectively models the diffusion-electromigration-reaction and moving boundary problems of corrosion models with arbitrary constitutive corrosion kinetics.
Subjects
Peridynamics | Nonlocal Diffusion | Meshfree Methods | Absorbing Boundary Conditions | Corrosion | Biodegradble Implants
DDC Class
620.1: Engineering Mechanics and Materials Science
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Hermann_Alexander_Peridynamic-Models-in-Multi-Physics-Applications-on-Bounded-and-Unbounded Domains.pdf
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