nonlinear finite element methods and computational contact...
TRANSCRIPT
![Page 1: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/1.jpg)
Alexander Popp
ECCOMAS Advanced Course 2018- Computational Structural Dynamics - Prague, Czech Republic, June 4-8, 2018
Nonlinear Finite Element Methods and Computational
Contact Mechanics
Institute for Mathematics and Computer-Based Simulation (IMCS)University of the Bundeswehr Munich (UniBw M), Germany
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
University of the Bundeswehr Munich(Web: www.unibw.de)
• 2800 students (young military officersof the German Federal Armed Forces)
- of which 300 are women- and 50 exchange students- and 100 civil students
• 1260 employees
- of which 750 are scientific staff- in total 180 professors
• student per professor ratio of 15:1 • excellent infrastructure, labs and facilities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Institute for Mathematics and Computer-Based Simulation (IMCS)
(Web: www.unibw.de/imcs)
• founded in 2018 • Prof. Thomas Apel (Mathematics) & Prof. Alexander Popp (Simulation) • currently 3 postdocs and 4 PhD students • HPC cluster (480 cores Intel Scalable CPUs) to be installed in late 2018 • research at the crossroads of mathematics and computational mechanics
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
AcknowledgementsPhD students • Christoph Meier, Philipp Farah,
Alexander Seitz, Michael Hiermeier,Ivo Steinbrecher, Nora Hagmeyer,…
Collaborators (since 2013) • Wolfgang A. Wall, Barbara Wohlmuth, Michael W. Gee, Tobias Wiesner,
Andreas Ehrl, Volker Gravemeier, Anh-Tu Vuong, Georg Hammerl,Markus Gitterle, Marie Oshima, Sota Yamamoto, Katsuyuki Hoshina,…
Research funding (since 2013)
!4
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
[FUNDED BY GERMAN FEDERAL MINISTRY FOR ECONOMIC AFFAIRS 2015-2018]
© Rolls-Royce plc.
Current research snapshots• turbine blade-to-disc joints (firtrees)
in aircraft engines operate at extreme thermomechanical load conditions
• accurate modeling of contact and the related interface effects is crucial for a reliable lifetime prediction
• blade-to-disc interaction is affected by several complex interface phenomena such as thermal dissipation, fretting wear and fretting fatigue
!5
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
[IN COLLABORATION WITH M. OSHIMA AND UNIV. TOKYO HOSPITAL – 2015-2018]
• stent grafts for endovascular repair of aneurysms (AAA) strengthen the arterial wall and exclude AAA from blood flow
• advanced stent placement simulation helps vascular surgeons to assess or avoid stent migration or endoleakage
• typical stenting risks are highly sensitive to the stent / arterial wall contact and the interplay between FSI effects and contact during stent lifetime
Current research snapshots
!6
© Andreas Maier @ TUM
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
LET’S GET STARTED!
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Unit 16 - FINITE ELEMENT METHOD 10 (Thursday, 09:00-10:00)
• source of nonlinearities • nonlinear continuum mechanics • FEM for nonlinear problems • incremental-iterative approach • nonlinear solvers: Newton-Raphson
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Agenda
ɠ MOTIVATION
ɡ METHODS 1
ɢ METHODS 2
ɣ ALGORITHMS
ɤ APPLICATION
Source of Nonlinearities in Continuum Mechanics
Aspects of Nonlinear Continuum Mechanics
Nonlinear Finite Element Methods (FEM)
Iterative Solution / Newton-Raphson Scheme
A Simple Nonlinear FEM Code in MATLAB
!9
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Sources of Nonlinearities
!10
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!11
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!12
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!13
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!14
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!15
Plasticity
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!16
Thermoplasticity
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!17
2.2 mm
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!18
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!19
Sources of Nonlinearities
![Page 20: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/20.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!20
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!21
Sources of Nonlinearities
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Agenda
ɠ MOTIVATION
ɡ METHODS 1
ɢ METHODS 2
ɣ ALGORITHMS
ɤ APPLICATION
Source of Nonlinearities in Continuum Mechanics
Aspects of Nonlinear Continuum Mechanics
Nonlinear Finite Element Methods (FEM)
Iterative Solution / Newton-Raphson Scheme
A Simple Nonlinear FEM Code in MATLAB
!22
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Prerequisites
!23
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Nonlinear Motion of a Body
!24
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Geometric Mapping
!25
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Different Formulations
!26
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Deformation Gradient
!27
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Deformation Gradient
!28
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Deformation Gradient
!29
(3.6)
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Deformation Gradient
!30
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!31
Polar Decomposition
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Green–Lagrange Strains
!32
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Euler–Almansi Strains
!33
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!34
Objectivity
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!35
Objectivity
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!36
Objectivity
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Behavior for Large Strains
!37
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Stress & Equilibrium
!38
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Cauchy Stress
!39
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Cauchy Stress
!40
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Translatory Equilibrium
!41
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Rotational Equilibrium
!42
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Other Stress Measures
!43
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Other Stress Measures
!44
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Other Stress Measures
!45
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
St.Venant-Kirchhoff Material
!46
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!47
St.Venant-Kirchhoff Material
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Strong Form in Statics
!48
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Weak Form in Statics
!49
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Agenda
ɠ MOTIVATION
ɡ METHODS 1
ɢ METHODS 2
ɣ ALGORITHMS
ɤ APPLICATION
Source of Nonlinearities in Continuum Mechanics
Aspects of Nonlinear Continuum Mechanics
Nonlinear Finite Element Methods (FEM)
Iterative Solution / Newton-Raphson Scheme
A Simple Nonlinear FEM Code in MATLAB
!50
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Nonlinear Equilibrium Path
!51
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!52
Nonlinear Equilibrium Path
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!53
Nonlinear Equilibrium Path
![Page 54: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/54.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Incrementation & Iteration
!54
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!55
Incrementation & Iteration
![Page 56: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/56.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!56
Incrementation & Iteration
![Page 57: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/57.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!57
Incrementation & Iteration
![Page 58: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/58.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Nonlinear FEM
!58
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!59
Nonlinear FEM
![Page 60: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/60.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!60
Nonlinear FEM
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!61
Nonlinear FEM
![Page 62: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/62.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!62
Nonlinear FEM
![Page 63: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/63.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!63
Nonlinear FEM
![Page 64: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/64.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!64
Nonlinear FEM
![Page 65: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/65.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Agenda
ɠ MOTIVATION
ɡ METHODS 1
ɢ METHODS 2
ɣ ALGORITHMS
ɤ APPLICATION
Source of Nonlinearities in Continuum Mechanics
Aspects of Nonlinear Continuum Mechanics
Nonlinear Finite Element Methods (FEM)
Iterative Solution / Newton-Raphson Scheme
A Simple Nonlinear FEM Code in MATLAB
!65
![Page 66: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/66.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!66
Iterative Solution
![Page 67: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/67.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!67
Iterative Solution
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!68
Iterative Solution
![Page 69: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/69.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Newton-Raphson Scheme
!69
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!70
Newton-Raphson Scheme
![Page 71: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/71.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!71
Newton-Raphson Scheme
![Page 72: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/72.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!72
Modified N-R Scheme
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
Agenda
ɠ MOTIVATION
ɡ METHODS 1
ɢ METHODS 2
ɣ ALGORITHMS
ɤ APPLICATION
Source of Nonlinearities in Continuum Mechanics
Aspects of Nonlinear Continuum Mechanics
Nonlinear Finite Element Methods (FEM)
Iterative Solution / Newton-Raphson Scheme
A Simple Nonlinear FEM Code in MATLAB
!73
![Page 74: Nonlinear Finite Element Methods and Computational Contact …shortcourse2018.it.cas.cz/im/data/my/2018_Lecture_16.pdf · 2018-06-04 · Alexander Popp ECCOMAS Advanced Course 2018](https://reader035.vdocuments.net/reader035/viewer/2022070705/5e9364e59e0b8a04522b9a9e/html5/thumbnails/74.jpg)
Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
MATLAB Code• can be downloaded from the course website:
popp_matlab.zip • based on the (linear) FEM toolkit CALFEM
Getting started: • (1) extract ZIP file • (2) set the parent folder /matlab and all sub-folders as working path • (3) run some examples from the /nonlinear folder
Some interesting code parts: • (1) /elements2d/cont2d.nl.m —> a nonlinear quad4 element • (2) /elements3d/cont3dnl.m —> a nonlinear hex8 element • (…)
!74
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Technische Universität München
Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M
MATLAB Code
!75