{"title":"A comprehensive study on numerical homogenization of re-entrant honeycomb lattice and analytical model assessment","authors":"Rajnandini Das, Gurunathan Saravana Kumar","doi":"10.1007/s10999-024-09732-6","DOIUrl":null,"url":null,"abstract":"<div><p>Re-entrant honeycomb lattice structures offer significant advantages, such as a high strength-to-weight ratio, superior energy absorption capabilities, and efficient material usage. However, for design optimization, the computational challenges posed by simulating extensive structures featuring lattice cells demand an exponential increase in degrees of freedom, inevitably prolonging computational time. The present work addresses some of the challenges in simulating these structures by employing numerical homogenization and investigating the effective elastic properties, aiming to reduce computational costs while maintaining accuracy. The homogenization approach is validated using experiments on lattice structures made in polymer. The study also evaluates the applicability of existing analytical models by comparing their predictions with numerical homogenization results. A comprehensive analysis considering the structural parameters, namely re-entrant angle (<span>\\(\\theta\\)</span>) and relative density (<span>\\(\\rho _{\\text {rel}}\\)</span>), is presented to understand the prediction accuracy of different analytical models. Both uncertainty and sensitivity analyses were conducted to quantify the influence of these structural parameters on the effective properties and to assess the variability due to probable geometric uncertainties introduced in manufacturing. Additionally, the influence of cell density on the homogenization model’s accuracy is also examined. The findings reveal good agreement between the lattice simulation, the homogenized model, and the experimental result within the linear elastic limit. The study infers that amongst the analytical models, Malek’s model is highly accurate for predicting <span>\\(E_{11}\\)</span>, <span>\\(E_{33}\\)</span>, and Poisson’s ratio <span>\\(\\mu _{12}\\)</span> for higher <span>\\(\\theta\\)</span> and up to 30% <span>\\(\\rho _{\\text {rel}}\\)</span> but shows significant deviations for <span>\\(G_{12}\\)</span>, <span>\\(G_{23}\\)</span>, and <span>\\(\\mu _{23}\\)</span>, necessitating numerical homogenization for higher accuracy beyond these ranges. The uncertainty analysis indicates that elastic moduli such as <span>\\(E_{11}/E_{s}\\)</span> and <span>\\(E_{33}/E_{s}\\)</span> exhibit the highest sensitivity to variations in strut thickness and angle, highlighting the need for precise manufacturing control to mitigate variability in effective elastic properties. The sensitivity analysis revealed that strut thickness (<i>t</i>) significantly influences the elastic and shear moduli, while the interaction of <span>\\(\\theta\\)</span> and <i>t</i> plays a crucial role in determining Poisson’s ratios for the auxetic honeycomb lattice. Additionally, numerical homogenization effectively predicts the elastic properties of re-entrant honeycomb structures with higher accuracy and lower computational costs. This comprehensive analysis enhances the understanding and practical application of both analytical and numerical methods in lattice structure design.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"21 1","pages":"181 - 207"},"PeriodicalIF":2.7000,"publicationDate":"2024-11-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s10999-024-09732-6","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
引用次数: 0
Abstract
Re-entrant honeycomb lattice structures offer significant advantages, such as a high strength-to-weight ratio, superior energy absorption capabilities, and efficient material usage. However, for design optimization, the computational challenges posed by simulating extensive structures featuring lattice cells demand an exponential increase in degrees of freedom, inevitably prolonging computational time. The present work addresses some of the challenges in simulating these structures by employing numerical homogenization and investigating the effective elastic properties, aiming to reduce computational costs while maintaining accuracy. The homogenization approach is validated using experiments on lattice structures made in polymer. The study also evaluates the applicability of existing analytical models by comparing their predictions with numerical homogenization results. A comprehensive analysis considering the structural parameters, namely re-entrant angle (\(\theta\)) and relative density (\(\rho _{\text {rel}}\)), is presented to understand the prediction accuracy of different analytical models. Both uncertainty and sensitivity analyses were conducted to quantify the influence of these structural parameters on the effective properties and to assess the variability due to probable geometric uncertainties introduced in manufacturing. Additionally, the influence of cell density on the homogenization model’s accuracy is also examined. The findings reveal good agreement between the lattice simulation, the homogenized model, and the experimental result within the linear elastic limit. The study infers that amongst the analytical models, Malek’s model is highly accurate for predicting \(E_{11}\), \(E_{33}\), and Poisson’s ratio \(\mu _{12}\) for higher \(\theta\) and up to 30% \(\rho _{\text {rel}}\) but shows significant deviations for \(G_{12}\), \(G_{23}\), and \(\mu _{23}\), necessitating numerical homogenization for higher accuracy beyond these ranges. The uncertainty analysis indicates that elastic moduli such as \(E_{11}/E_{s}\) and \(E_{33}/E_{s}\) exhibit the highest sensitivity to variations in strut thickness and angle, highlighting the need for precise manufacturing control to mitigate variability in effective elastic properties. The sensitivity analysis revealed that strut thickness (t) significantly influences the elastic and shear moduli, while the interaction of \(\theta\) and t plays a crucial role in determining Poisson’s ratios for the auxetic honeycomb lattice. Additionally, numerical homogenization effectively predicts the elastic properties of re-entrant honeycomb structures with higher accuracy and lower computational costs. This comprehensive analysis enhances the understanding and practical application of both analytical and numerical methods in lattice structure design.
可重新进入的蜂窝晶格结构具有显著的优势,例如高强度重量比,优越的能量吸收能力和高效的材料使用。然而,对于设计优化而言,模拟具有晶格单元的广泛结构所带来的计算挑战要求自由度呈指数级增长,不可避免地延长了计算时间。目前的工作通过采用数值均匀化和研究有效弹性特性来解决模拟这些结构的一些挑战,旨在降低计算成本,同时保持准确性。通过对聚合物晶格结构的实验验证了均匀化方法。通过将现有分析模型的预测结果与数值均匀化结果进行比较,评估了现有分析模型的适用性。综合考虑结构参数,即重入角(\(\theta\))和相对密度(\(\rho _{\text {rel}}\)),了解不同分析模型的预测精度。进行了不确定性和敏感性分析,以量化这些结构参数对有效性能的影响,并评估由于制造中可能引入的几何不确定性而引起的可变性。此外,还研究了细胞密度对均质模型精度的影响。结果表明,在线弹性极限内,晶格模拟、均匀化模型与实验结果吻合较好。该研究推断,在分析模型中,Malek的模型在预测\(E_{11}\)、\(E_{33}\)和泊松比\(\mu _{12}\)(更高\(\theta\)和最高30)方面具有很高的准确性% \(\rho _{\text {rel}}\) but shows significant deviations for \(G_{12}\), \(G_{23}\), and \(\mu _{23}\), necessitating numerical homogenization for higher accuracy beyond these ranges. The uncertainty analysis indicates that elastic moduli such as \(E_{11}/E_{s}\) and \(E_{33}/E_{s}\) exhibit the highest sensitivity to variations in strut thickness and angle, highlighting the need for precise manufacturing control to mitigate variability in effective elastic properties. The sensitivity analysis revealed that strut thickness (t) significantly influences the elastic and shear moduli, while the interaction of \(\theta\) and t plays a crucial role in determining Poisson’s ratios for the auxetic honeycomb lattice. Additionally, numerical homogenization effectively predicts the elastic properties of re-entrant honeycomb structures with higher accuracy and lower computational costs. This comprehensive analysis enhances the understanding and practical application of both analytical and numerical methods in lattice structure design.
期刊介绍:
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.