## Titelangaben

Wehmann, Christoph ; Alber-Laukant, Bettina ; Rieg, Frank:

**Verification of Finite Element Analysis Results by 3-Dimensional Image Correlation.**

*In:*
NAFEMS
(Hrsg.):
NAFEMS World Congress 2013. -
Salzburg
,
2013
. - S. 251

ISBN 978-1-874376-91-0

## Abstract

Considering effects of large displacements, there are different ways to formulate finite elements for capturing these effects. In literature, the most popular methods are called Total Lagrangian formulation and Updated Lagrangian formulation. For guar-anteeing precise simulation results from Finite Element Analysis (FEA), especially at large displacements verifications by experimental investigations are necessary. In this contribution, the two mentioned formulations are compared when used for calcu-lating a given example. For verifying their results, experimental investigations are carried out.

To capture the geometrical nonlinearities or large displacement effects by FEA, spe-cial strain measurement quantities are required. Examples are the Lagrangian strain or the Eulerian strain, which are associated with the Total Lagrangian formulation or the Updated Lagrangian formulation. Furthermore, an iterative solution process as the Newton-Raphson-procedure is needed. This iterative procedure is aborted, when an adjustable tolerance is reached. Hence, experimental investigations have to verify that the tolerance limit is strict enough. In this context, measuring force displacement characteristics at special points can be used to get local verifications. For this pur-pose, measurement equipment consisting of a load cell and a dial gauge is applica-ble. The disadvantage of such an investigation is the limitation to a single point or a few points of measurement. In addition, no information concerning deformation gra-dients is available.

One possibility to improve the verification in this respect is to consider the defor-mation of whole surfaces. Modern systems of image correlation are able to capture the movement of marked surfaces during the deformation process. For comparing such experimental results with simulation results, it is necessary to do coordinate transformations. It has to be fulfilled, that compared results are described by the same coordinate system. Experimental investigations by 3-dimensional image corre-lation and the comparison with FEA results are the topics of this contribution. In this context, the deformation of disc springs is considered.

Disc springs are characterized by a nonlinear relation between force and displace-ment, which is resulting from large displacement effects. Here, these are captured by the two formulations mentioned before. In addition to their results, it is also reported about their implementation, which is done in the freeware FE-code Z88. Concerning the material behavior, the generalized Hooke’s law is applied. For both formulations, the same, constant material matrix connects stresses and strains. In the case of the

VERIFICATION OF FINITE ELEMENT ANALYSIS RESULTS

BY 3-DIMENSIONAL IMAGE CORRELATION

Updated Lagrangian formulation these are the Cauchy stresses and the Eulerian strains, whereas in the case of the Total Lagrangian formulation these are the se-cond Piola-Kirchhoff stresses and the Lagrangian strains. It follows from the constant material matrix, that the different formulations provide different displacement solu-tions. This point is reported in literature. Here, the scale of this effect, regarding disc springs, is investigated.

The results of this contribution include comparisons of simulation and experiment, the corresponding coordinate transformation calculations that are necessary and a de-tailed description of the applied finite element methods. In addition, sources of error appearing during the verification process are discussed. Furthermore, the experi-mental setup and the features of 3-dimensional image correlation measurements are reported. Finally, the experimental results of the image correlation are compared to experimental results of measurements by a dial gauge connected to the load cell.

## Weitere Angaben

Publikationsform: | Aufsatz in einem Buch |
---|---|

Begutachteter Beitrag: | Nein |

Keywords: | Bildkorrelationssystem; FEA |

Institutionen der Universität: | Fakultäten > Fakultät für Ingenieurwissenschaften > Lehrstuhl Konstruktionslehre/CAD Fakultäten > Fakultät für Ingenieurwissenschaften > Lehrstuhl Konstruktionslehre/CAD > Lehrstuhl Konstruktionslehre/CAD - Univ.-Prof. Dr.-Ing. Frank Rieg Fakultäten Fakultäten > Fakultät für Ingenieurwissenschaften |

Titel an der UBT entstanden: | Ja |

Themengebiete aus DDC: | 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften |

Eingestellt am: | 15 Mär 2016 10:00 |

Letzte Änderung: | 15 Mär 2016 10:00 |

URI: | https://eref.uni-bayreuth.de/id/eprint/31744 |