Universität zu Köln

Klawonn, Axel ORCID: 0000-0003-4765-7387, Lanser, Martin, Rheinbach, Oliver ORCID: 0000-0002-9310-8533 and Uran, Matthias (2021). Fully-coupled micro-macro finite element simulations of the Nakajima test using parallel computational homogenization. Comput. Mech., 68 (5). S. 1153 - 1179. NEW YORK: SPRINGER. ISSN 1432-0924

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Abstract

The Nakajima test is a well-known material test from the steel and metal industry to determine the forming limit of sheet metal. It is demonstrated how FE2TI, our highly parallel scalable implementation of the computational homogenization method FE2, can be used for the simulation of the Nakajima test. In this test, a sample sheet geometry is clamped between a blank holder and a die. Then, a hemispherical punch is driven into the specimen until material failure occurs. For the simulation of the Nakajima test, our software package FE2TI has been enhanced with a frictionless contact formulation on the macroscopic level using the penalty method. The appropriate choice of suitable boundary conditions as well as the influence of symmetry assumptions regarding the symmetric test setup are discussed. In order to be able to solve larger macroscopic problems more efficiently, the balancing domain decomposition by constraints (BDDC) approach has been implemented on the macroscopic level as an alternative to a sparse direct solver. To improve the computational efficiency of FE2TI even further, additionally, an adaptive load step approach has been implemented and different extrapolation strategies are compared. Both strategies yield a significant reduction of the overall computing time. Furthermore, a strategy to dynamically increase the penalty parameter is presented which allows to resolve the contact conditions more accurately without increasing the overall computing time too much. Numerically computed forming limit diagrams based on virtual Nakajima tests are presented.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Klawonn, Axel UNSPECIFIED orcid.org/0000-0003-4765-7387 UNSPECIFIED Lanser, Martin UNSPECIFIED UNSPECIFIED UNSPECIFIED Rheinbach, Oliver UNSPECIFIED orcid.org/0000-0002-9310-8533 UNSPECIFIED Uran, Matthias UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-573491
DOI:	10.1007/s00466-021-02063-9
Journal or Publication Title:	Comput. Mech.
Volume:	68
Number:	5
Page Range:	S. 1153 - 1179
Date:	2021
Publisher:	SPRINGER
Place of Publication:	NEW YORK
ISSN:	1432-0924
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language PRIMAL FETI METHODS; DOMAIN DECOMPOSITION; DP; BDDC; SOLVER Multiple languages Mathematics, Interdisciplinary Applications; Mechanics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57349