Topology optimization and 3D printing of large deformation compliant mechanisms for straining biological tissues
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RESEARCH PAPER
Topology optimization and 3D printing of large deformation compliant mechanisms for straining biological tissues P. Kumar1
· C. Schmidleithner2 · N. B. Larsen2 · O. Sigmund1
Received: 31 March 2020 / Revised: 19 August 2020 / Accepted: 8 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper presents a synthesis approach in a density-based topology optimization setting to design large deformation compliant mechanisms for inducing desired strains in biological tissues. The modelling is based on geometrical nonlinearity together with a suitably chosen hypereleastic material model, wherein the mechanical equilibrium equations are solved using the total Lagrangian finite element formulation. An objective based on least-square error with respect to target strains is formulated and minimized with the given set of constraints and the appropriate surroundings of the tissues. To circumvent numerical instabilities arising due to large deformation in low stiffness design regions during topology optimization, a strain-energy-based interpolation scheme is employed. The approach uses an extended robust formulation, i.e., the eroded, intermediate, and dilated projections for the design description as well as variation in tissue stiffness. Efficacy of the synthesis approach is demonstrated by designing various compliant mechanisms for providing different target strains in biological tissue constructs. Optimized compliant mechanisms are 3D printed and their performances are recorded in a simplified experiment and compared with simulation results obtained by a commercial software. Keywords Topology optimization · Biological tissue · Compliant mechanisms · 3D printing · Stereolithography · Flexible poles method
1 Introduction Development of new drugs is challenged by the limited predictive accuracy of current simple cell models on safety and efficacy in the human body (Mordwinkin et al. 2013). Functional mini-organ models with higher predictive value are increasingly used in the pharmaceutical industry to meet this challenge (Ikeda et al. 2017). These mini-organ models can be derived from a healthy/diseased person’s tissues, adult stem cells (which can be differentiated into the particular type of tissues in vitro relatively faster and in few
Responsible Editor: Seonho Cho P. Kumar
[email protected] 1
Department of Mechanical Engineering, Solid Mechanics, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark
2
Department of Health Technology, Technical University of Denmark, 2800, Kgs. Lyngby, Denmark
steps), human embryonic stem cells (hESCs)1 , or by inducing pluripotency in human adult cells (hiPSCs) (Duelen and Sampaolesi 2017). To facilitate maturation of differentiated tissue cells, local static- and dynamic-mechanical forces are essential to induce the required strains (Vining and Mooney 2017). In general, uni-axial stretching up to 15– 20% in mini-organs (e.g., skeletal- and cardio-myocytes) is needed (Vandenburgh et al. 1995) for achieving alig
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