Instability analysis of non-homogeneous materials under biaxial loading |
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| Institution: | 1. Centrale Lille, Cite Scientifique, 59651 Villeneuve d’Ascq, France;2. Laboratoire de Mecanique de Lille (LML), FRE CNRS 3723, Cite Scientifique, 59651 Villeneuve d’Ascq, France;3. PSA Peugeot Citroen, Direction de la Recherche et de l’Innovation Automobile, Route de Gisy, 78140 Velizy-Villacoublay Cedex, France;1. Young Investigator Group Computer Aided Material Modeling, Chair for Continuum Mechanics, Institute of Engineering Mechanics, Karlsruhe Institute of Technology (KIT), Kaiserstr. 10, D-76131 Karlsruhe, Germany;2. Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;1. University of Calgary, Calgary, AB, Canada T2N 1N4;2. Univ. Grenoble Alpes, 3SR, F-38000 Grenoble, France;3. CNRS, 3SR, F-38000 Grenoble, France;1. BMW Group, 80788 München, Germany;2. Lehrstuhl für Werkstoffkunde und Werkstoffmechanik, Technische Universität München, Boltzmannstr. 15, 85748 Garching, Germany |
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| Abstract: | In this paper, we formulate the instability problem of non-homogeneous materials under biaxial loading, in the sense that the mechanical parameters, and more specifically the strain hardening or softening and the strain-rate sensitivity, are spatially dependent functions. We first study the time behavior of the process and present the evolution of strain non-uniformities before the critical time, to show that it depends on the interplay between the spatial distribution of mechanical parameters and the initial non-uniformities. We next study the instability modes of a material exhibiting inhomogeneities along one direction by an effective instability analysis Dudzinski, D., Molinari, A., 1991. Perturbation analysis of thermoviscoplastic instabilities in biaxial loading. International Journal of Solids and Structures 27 (5), 601–628] adapted to the non-homogeneous case. This method is based on a suitable non-uniform reference solution and allows to select the localization modes activated at different deformation levels for different “deformation paths” of the material zones. |
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