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Nitsche Extended Finite Element Meth...

Coon, Ethan T.

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Nitsche Extended Finite Element Methods for Earthquake Simulation.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Nitsche Extended Finite Element Methods for Earthquake Simulation./
Author:	Coon, Ethan T.
Description:	122 p.
Notes:	Source: Dissertation Abstracts International, Volume: 72-05, Section: B, page: .
Contained By:	Dissertation Abstracts International72-05B.
Subject:	Applied Mechanics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3447856
ISBN:	9781124534152

Nitsche Extended Finite Element Methods for Earthquake Simulation.
Coon, Ethan T.

Nitsche Extended Finite Element Methods for Earthquake Simulation. - 122 p.

Source: Dissertation Abstracts International, Volume: 72-05, Section: B, page: .

Thesis (Ph.D.)--Columbia University, 2010.

Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities.

ISBN: 9781124534152Subjects--Topical Terms:

1018410
Applied Mechanics.

Nitsche Extended Finite Element Methods for Earthquake Simulation.
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020 $a 9781124534152
035 $a (UMI)AAI3447856
035 $a AAI3447856
040 $a UMI $c UMI
100 1 $a Coon, Ethan T. $3 1676601
245 1 0 $a Nitsche Extended Finite Element Methods for Earthquake Simulation.
300 $a 122 p.
500 $a Source: Dissertation Abstracts International, Volume: 72-05, Section: B, page: .
502 $a Thesis (Ph.D.)--Columbia University, 2010.
520 $a Modeling earthquakes and geologically short-time-scale events on fault networks is a difficult problem with important implications for human safety and design. These problems demonstrate a. rich physical behavior, in which distributed loading localizes both spatially and temporally into earthquakes on fault systems. This localization is governed by two aspects: friction and fault geometry. Computationally, these problems provide a stern challenge for modelers --- static and dynamic equations must be solved on domains with discontinuities on complex fault systems, and frictional boundary conditions must be applied on these discontinuities.
520 $a The most difficult aspect of modeling physics on complicated domains is the mesh. Most numerical methods involve meshing the geometry; nodes are placed on the discontinuities, and edges are chosen to coincide with faults. The resulting mesh is highly unstructured, making the derivation of finite difference discretizations difficult. Therefore, most models use the finite element method. Standard finite element methods place requirements on the mesh for the sake of stability, accuracy, and efficiency. The formation of a mesh which both conforms to fault geometry and satisfies these requirements is an open problem, especially for three dimensional, physically realistic fault. geometries. In addition, if the fault system evolves over the course of a dynamic simulation (i.e. in the case of growing cracks or breaking new faults), the geometry must he re-meshed at each time step. This can be expensive computationally. The fault-conforming approach is undesirable when complicated meshes are required, and impossible to implement when the geometry is evolving.
520 $a Therefore, meshless and hybrid finite element methods that handle discontinuities without placing them on element boundaries are a desirable and natural way to discretize these problems. Several such methods are being actively developed for use in engineering mechanics involving crack propagation and material failure. While some theory and application of these methods exist, implementations for the simulation of networks of many cracks have not yet been considered. For my thesis, I implement and extend one such method, the eXtended Finite Element Method (XFEM), for use in static and dynamic models of fault networks. Once this machinery is developed, it is applied to open questions regarding the behavior of networks of faults, including questions of distributed deformation in fault systems and ensembles of magnitude, location, and frequency in repeat ruptures. The theory of XFEM is augmented to allow for solution of problems with alternating regimes of static solves for elastic stress conditions and short, dynamic earthquakes on networks of faults. This is accomplished using Nitsche's approach for implementing boundary conditions. Finally, an optimization problem is developed to determine tractions along the fault, enabling the calculation of frictional constraints and the rupture front. This method is verified via a series of static, quasistatic, and dynamic problems.
520 $a Armed with this technique, we look at several problems regarding geometry within the earthquake cycle in which geometry is crucial. We first look at quasistatic simulations on a community fault model of Southern California, and model slip distribution across that system. We find the distribution of deformation across faults compares reasonably well with slip rates across the region, as constrained by geologic data. We find geometry can provide constraints for friction, and consider the minimization of shear strain across the zone as a function of friction and plate loading direction, and infer bounds on fault strength in the region. Then we consider the repeated rupture problem, modeling the full earthquake cycle over the course of many events on several fault geometries. In this work, we look at distributions of events, studying the effect of geometry on statistical metrics of event ensembles.
520 $a Finally, this thesis is a proof of concept for the XFEM on earthquake cycle models on fault systems. We identify strengths and weaknesses of the method, and identify places for future improvement. We discuss the feasibility of the method's use in three dimensions, and find the method to be a strong candidate for future crustal deformation simulations.
590 $a School code: 0054.
650 4 $a Applied Mechanics. $3 1018410
650 4 $a Geophysics. $3 535228
690 $a 0346
690 $a 0373
710 2 $a Columbia University. $3 571054
773 0 $t Dissertation Abstracts International $g 72-05B.
790 $a 0054
791 $a Ph.D.
792 $a 2010
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3447856