生物组织大变形柔性张紧机构的拓扑优化与3D打印
Topology Optimization and 3D printing of Large Deformation Compliant Mechanisms for Straining Biological Tissues
摘要：
本文提出了一种基于密度的拓扑优化设计方法来设计大变形柔性机构，以在生物组织中产生所需的应变。该建模是基于几何非线性与适当选择的超弹性材料模型，其中的机械平衡方程求解使用总拉格朗日有限元公式。一个目标的基础上最小二乘误差相对于目标菌株的制定和最小化与给定的一组约束条件和适当的周围环境的组织。为了避免拓扑优化过程中由于低刚度设计区域的大变形而产生的数值不稳定性，采用了基于应变能的插值方案。该方法使用扩展的稳健公式，即设计描述的侵蚀、中间和扩张投影以及组织刚度的变化。通过设计用于在生物组织构建体中提供不同靶菌株的各种顺应性机制来证明合成方法的功效。优化后的柔顺机构被3D打印出来，并在一个简化的实验中记录了它们的性能，并与商业软件获得的仿真结果进行了比较。
英文摘要：
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.
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