INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2007; 71:454–472 Published online 8 January 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/nme.1954 A new finite element based on the theory of a Cosserat point—Extension to initially distorted elements for 2D plane strain E. F. I. Boerner 1, ∗, † , S. Loehnert 2 and P. Wriggers 1 1 Institute of Mechanics and Computational Mechanics, Leibniz University of Hannover, Appelstrasse 9A, Hannover 30167, Germany 2 Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, U.S.A. SUMMARY This paper describes an improvement of the Cosserat point element formulation for initially distorted, non-rectangular shaped elements in 2D. The original finite element formulation for 3D large deformations shows excellent behaviour for sensitive geometries, large deformations, coarse meshes, bending dominated and stability problems without showing undesired effects such as locking or hourglassing, as long as the initial element shape resembles that of a rectangular parallelepiped. In the following, an extension of this element formulation for 2D plane strain is presented which has the same good properties also for the case of non-rectangular initial element shapes. Results of numerical tests are presented, that clearly show the advantages of the improved Cosserat point element compared to the standard displacement elements and the original version of the Cosserat point element. Copyright 2007 John Wiley & Sons, Ltd. Received 24 August 2006; Revised 25 October 2006; Accepted 30 October 2006 KEY WORDS: finite element technology; Cosserat point theory; finite elasticity; locking; hourglassing 1. INTRODUCTION Many state-of-the-art finite element formulations still face problems such as locking or hourglass- ing, e.g. in the case of large deformations in bending, pressure or for incompressible materials. Additional requirements for finite element formulations are robustness, computational efficiency as well as good coarse mesh accuracy. Standard displacement elements perform well in most cases, but ∗ Correspondence to: E. F. I. Boerner, Institute of Mechanics and Computational Mechanics, University of Hannover, Appelstrasse 9A, Hannover 30167, Germany. † E-mail: boerner@ibnm.uni-hannover.de Contract/grant sponsor: German Science Foundation; contract/grant number: WR 19/29-1 Copyright 2007 John Wiley & Sons, Ltd.