Nonlinear Finite Element Methods and Computational Contact...

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

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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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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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)

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[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

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[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

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© Andreas Maier @ TUM



LET’S GET STARTED!



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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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

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Sources of Nonlinearities

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Alexander Popp, Institute for Mathematics and Computer-Based Simulation (IMCS), UniBw M!11













Plasticity




Thermoplasticity




2.2 mm
















Agenda

ɠ MOTIVATION

ɡ METHODS 1

ɢ METHODS 2

ɣ ALGORITHMS

ɤ APPLICATION






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Prerequisites

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Nonlinear Motion of a Body

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Geometric Mapping

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Different Formulations

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Deformation Gradient

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(3.6)




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Polar Decomposition



Green–Lagrange Strains

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Euler–Almansi Strains

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Objectivity



Objectivity



Objectivity



Behavior for Large Strains

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Stress & Equilibrium

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Cauchy Stress

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Cauchy Stress

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Translatory Equilibrium

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Rotational Equilibrium

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Other Stress Measures

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St.Venant-Kirchhoff Material

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St.Venant-Kirchhoff Material



Strong Form in Statics

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Weak Form in Statics

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Agenda

ɠ MOTIVATION

ɡ METHODS 1

ɢ METHODS 2

ɣ ALGORITHMS

ɤ APPLICATION






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Nonlinear Equilibrium Path

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Incrementation & Iteration

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Nonlinear FEM

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Nonlinear FEM



Nonlinear FEM



Nonlinear FEM



Nonlinear FEM



Nonlinear FEM



Nonlinear FEM



Agenda

ɠ MOTIVATION

ɡ METHODS 1

ɢ METHODS 2

ɣ ALGORITHMS

ɤ APPLICATION






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Iterative Solution



Iterative Solution



Iterative Solution



Newton-Raphson Scheme

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Modified N-R Scheme



Agenda

ɠ MOTIVATION

ɡ METHODS 1

ɢ METHODS 2

ɣ ALGORITHMS

ɤ APPLICATION






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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 • (…)

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MATLAB Code

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Nonlinear Finite Element Methods and Computational Contact...

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