A new mixed finite element based on different approximations of the minors of deformation tensors |
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| Authors: | Jörg Schröder Peter Wriggers Daniel Balzani |
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| Affiliation: | 1. Institut für Mechanik, Fakultät für Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universität Duisburg-Essen, Universitätsstr. 15, 45117 Essen, Germany;2. Institut für Kontinuumsmechanik, Fakultät für Maschinenbau, Leibniz Universität Hannover, Appelstr. 11, 30167 Hannover, Germany;1. Fatigue and Fracture Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, Department of Mechanical Engineering, Iran University of Science and Technology, Narmak 16846, Tehran, Iran;2. NTNU Department of Engineering Design and Materials, Richard Birkelands vei 2b, 7491 Trondheim, Norway;1. Dipartimento di Ingegneria Strutturale e Geotecnica, Via Eudossiana, 18, 00198 Roma, Italy;2. Chair of Applied Mechanics, University of Erlangen–Nuremberg, Egerlandstr. 5, 91058 Erlangen, Germany;1. Institute of Mechanics, University of Duisburg–Essen, Universitätsstr. 15, 45141 Essen, Germany;2. Institute of Applied Mechanics (CE), Chair I, University of Stuttgart, Pfaffenwaldring 7, 70569 Stuttgart, Germany |
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| Abstract: | ![]()
Finite element formulations for arbitrary hyperelastic strain energy functions that are characterized by a locking-free behavior for incompressible materials, a good bending performance and accurate solutions for coarse meshes need still attention. Therefore, the main goal of this contribution is to provide an improved mixed finite element for quasi-incompressible finite elasticity. Based on the knowledge that the minors of the deformation gradient play a major role for the transformation of infinitesimal line-, area- and volume elements, as well as in the formulation of polyconvex strain energy functions a mixed finite element with different interpolation orders of the terms related to the minors is developed. Due to the formulation it is possible to condensate the mixed element formulation at element level to a pure displacement form. Examples show the performance and robustness of the element. |
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