Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization
Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization
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DOI：
10.1016/j.ijsolstr.2020.08.013
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发表时间：
2020-12-01
影响因子：
3.6
通讯作者：
Kochmann, Dennis M.
中科院分区：
文献类型：
--
作者：
Glaesener, Raphael N.;Traff, Erik A.;Kochmann, Dennis M.
由于尺度桥接制造技术，基于桁架的超材料获得了普及和复杂性，最终导致结构网络，其基于经典离散数值计算的描述变得难以处理。在这里，我们提出了一个框架进行非线性变形（占线性弹性梁进行有限旋转）的大型周期性三维（3D）桁架网络的有效和准确的模拟。虽然重点是弹性梁，该方法是足够的一般性，以扩展到非弹性材料的行为。我们的方法是基于连续表示的桁架（及其通过有限元数值实现），其本构行为是从在飞周期性均匀化在微观结构单胞水平。我们追求一个半解析策略（以前只在两个维度上报道），它允许收敛隐式解方案的一致切线的分析计算;扩展到3D -通过添加扭转变形模式和处理3D旋转-结果在一个强大的工具，用于预测大型结构网络的复杂机械响应。我们通过与解析解的比较来验证小应变响应，然后通过有限应变基准将模拟结果与完全解析的离散计算结果进行比较。梁单元的均匀化导致具有内在长度尺度的正则化宏观尺度模型，这在建模分叉或局部化时尤其明显。最后，我们将我们的方法应用到宏观边界值问题，涉及复杂形状的桁架超材料（桁架单元附近的身体的边界映射到一个共形表面），这只揭示了一个微不足道的影响边界层的整体机械响应，再次支持我们的均匀化方法的适用性。(C)2020作者（S）爱思唯尔有限公司出版
Thanks to scale-bridging fabrication techniques, truss-based metamaterials have gained both popularity and complexity, ultimately resulting in structural networks whose description based on classical discrete numerical calculations becomes intractable. We here present a framework for the efficient and accurate simulation of large periodic three-dimensional (3D) truss networks undergoing nonlinear deformation (accounting for linear elastic beams undergoing finite rotations). Although the focus is on elastic beams, the method is sufficiently general to extend to inelastic material behavior. Our approach is based on a continuum representation of the truss (and its numerical implementation via finite elements) whose constitutive behavior is obtained from on-the-fly periodic homogenization at the microstructural unit cell level. We pursue a semi-analytical strategy (previously reported only in two dimensions) which admits the analytical calculation of consistent tangents for convergent implicit solution schemes; the extension to 3D - through the addition of torsional deformation modes and the handling of 3D rotations - results in a powerful tool for the prediction of the complex mechanical response of large structural networks. We validate the small-strain response by comparison to analytical solutions, followed by finite-strain benchmarks that compare simulation results to those of fully-resolved discrete calculations. The homogenization of beam unit cells results in a regularized macroscale model with an intrinsic length scale, which manifests especially when modeling bifurcations or localization. We finally apply our approach to macroscopic boundary value problems involving complex-shaped truss metamaterials (with truss unit cells near the body's boundary mapped onto a conformal surface), which reveal only an insignificant effect of boundary layers on the overall mechanical response, again supporting the applicability of our homogenization approach. (C) 2020 The Author(s). Published by Elsevier Ltd.