Tuning Elasticity of Open-Cell Solid Foams and Bone Scaffolds via Randomized Vertex Connectivity

Authors

  • Susan Nachtrab,

    1. Institut für Theoretische Physik Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7, 91058 Erlangen, (Germany)
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  • Sebastian C. Kapfer,

    1. Institut für Theoretische Physik Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7, 91058 Erlangen, (Germany)
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  • Dominik Rietzel,

    1. Lehrstuhl für Kunststofftechnik Friedrich-Alexander Universität Erlangen-Nürnberg Am Weichselgarten 9, 91058 Erlangen-Tennenlohe, (Germany)
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  • Dietmar Drummer,

    1. Lehrstuhl für Kunststofftechnik Friedrich-Alexander Universität Erlangen-Nürnberg Am Weichselgarten 9, 91058 Erlangen-Tennenlohe, (Germany)
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  • Mahyar Madadi,

    1. Applied Maths, Research School of Physical Sciences and Engineering The Australian National University 0200 ACT, Canberra, (Australia)
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  • Christoph H. Arns,

    1. Applied Maths, Research School of Physical Sciences and Engineering The Australian National University 0200 ACT, Canberra, (Australia)
    2. School of Petroleum Engineering The University of New South Wales NSW, (Australia)
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  • Andrew M. Kraynik,

    1. Department 1514 MS0836, Sandia National Laboratories Albuquerque, New Mexico 87185-0836, (USA)
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  • Gerd E. Schröder-Turk,

    Corresponding author
    1. Institut für Theoretische Physik Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7, 91058 Erlangen, (Germany)
    • Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7, 91058 Erlangen, (Germany)
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  • Klaus Mecke

    1. Institut für Theoretische Physik Friedrich-Alexander Universität Erlangen-Nürnberg Staudtstr. 7, 91058 Erlangen, (Germany)
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  • We are grateful to Carl Fruth (FIT GmbH, Parsberg) and Alexander Oster (NetFabb GmbH, Parsberg) for post-processing the sample data and producing multiple samples, free of charge. Many thanks to Jürgen Karsten for assistance with the mechanical testing. SN, GEST and KM acknowledge funding by the Deutsche Forschungsgemeinschaft (DFG) through the Cluster of Excellence “Engineering of Advanced Materials” in Erlangen. DD and DR acknowledge funding by the LGA Nordbayern (Leitprojekte Medizintechnik, BayMED). SN, GEST, CHA and MM acknowledge travel support by the German academic exchange service (DAAD) and the Australian Group of Eight universities through a joint program. Supporting Information is available from the Wiley Online Library or from the author.

Abstract

Tuning mechanical properties of and fluid flow through open-cell solid structures is a challenge for material science, in particular for the design of porous structures used as artificial bone scaffolds in tissue engineering. We present a method to tune the effective elastic properties of custom-designed open-cell solid foams and bone scaffold geometries by almost an order of magnitude while approximately preserving the pore space geometry and hence fluid transport properties. This strong response is achieved by a change of topology and node coordination of a network-like geometry underlying the scaffold design. Each node of a four-coordinated network is disconnected with probability p into two two-coordinated nodes, yielding network geometries that change continuously from foam- or network-like cellular structures to entangled fiber bundles. We demonstrate that increasing p leads to a strong, approximately exponential decay of mechanical stiffness while leaving the pore space geometry largely unchanged. This result is obtained by both voxel-based finite element methods and compression experiments on laser sintered models. The physical effects of randomizing network topology suggest a new design paradigm for solid foams, with adjustable mechanical properties.

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