An efficient adaptive PD formulation for complex microstructures

  • The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood.The computational costs of newly developed numerical simulation play a critical role in their acceptance within both academic use and industrial employment. Normally, the refinement of a method in the area of interest reduces the computational cost. This is unfortunately not true for most nonlocal simulation, since refinement typically increases the size of the material point neighborhood. Reducing the discretization size while keep- ing the neighborhood size will often require extra consideration. Peridynamic (PD) is a newly developed numerical method with nonlocal nature. Its straightforward integral form equation of motion allows simulating dynamic problems without any extra consideration required. The formation of crack and its propagation is known as natural to peridynamic. This means that discontinuity is a result of the simulation and does not demand any post-processing. As with other nonlocal methods, PD is considered an expensive method. The refinement of the nodal spacing while keeping the neighborhood size (i.e., horizon radius) constant, emerges to several nonphysical phenomena. This research aims to reduce the peridynamic computational and imple- mentation costs. A novel refinement approach is introduced. The pro- posed approach takes advantage of the PD flexibility in choosing the shape of the horizon by introducing multiple domains (with no intersections) to the nodes of the refinement zone. It will be shown that no ghost forces will be created when changing the horizon sizes in both subdomains. The approach is applied to both bond-based and state-based peridynamic and verified for a simple wave propagation refinement problem illustrating the efficiency of the method. Further development of the method for higher dimensions proves to have a direct relationship with the mesh sensitivity of the PD. A method for solving the mesh sensitivity of the PD is intro- duced. The application of the method will be examined by solving a crack propagation problem similar to those reported in the literature. New software architecture is proposed considering both academic and in- dustrial use. The available simulation tools for employing PD will be collected, and their advantages and drawbacks will be addressed. The challenges of implementing any node base nonlocal methods while max- imizing the software flexibility to further development and modification will be discussed and addressed. A software named Relation-Based Sim- ulator (RBS) is developed for examining the proposed architecture. The exceptional capabilities of RBS will be explored by simulating three distinguished models. RBS is available publicly and open to further develop- ment. The industrial acceptance of the RBS will be tested by targeting its performance on one Mac and two Linux distributions.show moreshow less

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Metadaten
Document Type:Doctoral Thesis
Author: Ali Jenabidehkordi
DOI (Cite-Link):https://doi.org/10.25643/bauhaus-universitaet.4738Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20221116-47389Cite-Link
URL:https://e-pub.uni-weimar.de/opus4/frontdoor/index/index/docId/4742
Referee:Prof. Dr. Erdogan MadenciORCiDGND, Prof. Dr. Esteban Samaniego, Prof. Dr. rer. nat. Klaus HacklORCiDGND
Advisor:Prof. Dr.-Ing. Timon RabczukORCiDGND
Language:English
Date of Publication (online):2022/11/15
Date of first Publication:2022/11/15
Date of final exam:2022/10/06
Release Date:2022/11/16
Publishing Institution:Bauhaus-Universität Weimar
Granting Institution:Bauhaus-Universität Weimar, Fakultät Bauingenieurwesen
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Pagenumber:118
Tag:Numerical Simulation; Peridynamics
GND Keyword:Peridynamik
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik
BKL-Classification:31 Mathematik
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)