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Computational Techniques for Multiscale Analysis of Materials and Interfaces

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Modelling, Simulation and Software Concepts for Scientific-Technological Problems

Part of the book series: Lecture Notes in Applied and Computational Mechanics ((LNACM,volume 57))

Abstract

A series of four PhD projects worked out under the umbrella of the research training group GRK 615 are summarized in this contribution. The first is on the multiscale modeling of the mechanics of an atomic force microscope with special emphasis on the contact problem. At the relevant length scales atomic force interactions have been considered. The total device is modeled in a dimension adaptive manner using beam elements for the cantilever, solid elements for the tip and an atomic interaction approach for the contact problem. The second thesis is a straightforeward continuation of this research be setting up a powerful MD-FE coupling scheme especially for contact problems. Special emphasis has been led on the consistent coupling avoiding ghost forces by introducing dummy atoms and a boundary layer for the atomic domain. A second series is on the treatment of biomechanics of bones. For a better understanding of the biomechanical phenomena a computational multiscale environment has been implemented, where a cortical section with reinforcing osteons is modeled. The osteons itself are treated on a smaller length scale as laminar cross ply structures and the basic anisotropic properties of the layer are homogenized from the basic constituents, i.e. collagen matrix and hydroxyapatite crystals in dependency of the grade of mineralization. Based on a simple strain criterion detected at voids in between the layers of the osteons a closed control circuit has been realized to mimic the aging of bone. A micro-crack theory as basic origin for the cellular stimulation for bone remodeling has been realized in the last thesis. The strain driven evolution of interlaminar micro-cracks is simulated within an adaptively refined finite element framework. For studies on the released material integrity on the bone cells a sophisticated cell model in analogy to self-stabilizing tensegrity structures has been developed. By this model especially the amplification of stresses from the membrane into the nucleus is shown.

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  1. Institut für Baumechanik und Numerische Mechanik, Gottfried Wilhelm Leibniz Universität Hannover, Appelstraße 9A, 30167, Hannover, Germany

    Udo Nackenhorst, Dieter Kardas, Tobias Helmich, Christian Lenz & Wenzhe Shan

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  1. Gottfried Wilhelm Leibniz, Institut für Angewandte Mathematik, Universität Hannover, Welfengarten 1, 30167, Hannover, Deutschland, Germany

    Ernst Stephan

  2. Gottfried Wilhelm Leibniz, Institut für Kontinuumsmechanik, Universität Hannover, Appelstr. 11, 30167, Hannover, Germany

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Nackenhorst, U., Kardas, D., Helmich, T., Lenz, C., Shan, W. (2011). Computational Techniques for Multiscale Analysis of Materials and Interfaces. In: Stephan, E., Wriggers, P. (eds) Modelling, Simulation and Software Concepts for Scientific-Technological Problems. Lecture Notes in Applied and Computational Mechanics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20490-6_5

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