Mapping Relationship for the Performance of Porous Structures Based on the Principle of Least Action

doi:10.3901/JME.2024.19.250

Abstract

Abstract: To expand the optimization design method of porous structures under existing topological configurations, a mapping relationship of mechanical characteristic for porous structures based on PLA is proposed inspired by PLA in physics.Combined with the extreme phenomenon of curvature for the BCC with different node optimized radius and most extreme phenomena in nature often revealed by PLA, a mapping relationship based on the mechanical properties of PLA porous structure is established through the mechanical model and influencing factors of porous structure.To verify the effectiveness and rationality of the mapping relationship, a series of BCC porous structures with different optimization radius are constructed, and the curvature evolution trend and mechanical properties of the structure are discussed by combining simulation analysis and experiment.The results indicate that the average curvature evolution characteristic of samples show an extreme value phenomenon, and the equivalent elastic modulus and yield strength corresponding to the extreme value phenomenon can be effectively increased by 26.29%, 9.53%; and the experiments of porous structure samples manufactured by SLM show that the equivalent elastic modulus and first peak strength of the porous structure are 18.81% and 20.14% higher than the unoptimized structure, respectively.Moreover, this study provides a new optimization idea for the design or multifunction application of porous structures and offers the theoretical basis for further innovative research of natural evolution optimization methods in porous structures.

Key words: porous structures, the principle of least action, mapping relationship, mean curvature, mechanical properties

CLC Number:

TH122

MA Xiangyu, ZHENG Xunjia, HE Zao. Mapping Relationship for the Performance of Porous Structures Based on the Principle of Least Action[J]. Journal of Mechanical Engineering, 2024, 60(19): 250-260.

References

[1] ATAEE A，LI Y，BRANDT M，et al. Ultrahigh-strength titanium gyroid scaffolds manufactured by selective laser melting (SLM) for bone implant applications[J]. Acta Materialia，2018，158：354-368.
[2] DU Y，LIANG H，XIE D，et al. Finite element analysis of mechanical behavior，permeability of irregular porous scaffolds and lattice-based porous scaffolds[J]. Materials Research Express，2019，6(10)：105407.
[3] XU Wei，TIAN Jingjing，LIU Zhuo，et al. Novel porous Ti35Zr28Nb scaffolds fabricated by powder metallurgy with excellent osteointegration ability for bone-tissue engineering applications[J]. Materials Science & Engineering C-materials for Biological Applications，2019，105：110015.
[4] BLAKEY-MILNER B，GRADL P，SNEDDEN G，et al. Metal additive manufacturing in aerospace：A review[J]. Materials & Design，2021，209：110008.
[5] KHALIL A，AHMED F E，HILAL N. The emerging role of 3D printing in water desalination[J]. Sci Total Environ，2021，790：148238.
[6] ATTARAN M. The rise of 3-D printing：The advantages of additive manufacturing over traditional manufacturing[J]. Business Horizons，2017，60(5)：677-688.
[7] ZHANG P，BILIGETU，QI D，et al. Mechanical design and energy absorption of 3D novel hybrid lattice metamaterials[J]. Science China Technological Sciences，2021，64(10)：2220-2228.
[8] NEJAT S A，CHANGIZI N，TOOTKABONI M，et al. Topology optimization of lightweight periodic lattices under stiffness and stability constraints[J]. International Journal of Mechanical Sciences，2021，209：106727.
[9] 廖中源，王英俊，王书亭. 基于拓扑优化的变密度点阵结构体优化设计方法[J]. 机械工程学报，2019，55(8)：65-72. LIAO Zhongyuan，WANG Yingjun，WANG Shuting. Graded-density lattice structure optimization design based on topology optimization[J]. Journal of Mechanical Engineering，2019，55(8)：65-72.
[10] DAS S，SUTRADHAR A. Multi-physics topology optimization of functionally graded controllable porous structures：Application to heat dissipating problems[J]. Materials & Design，2020，193：108775.
[11] HU J，LUO Y，LIU S. Three-scale concurrent topology optimization for the design of the hierarchical cellular structure[J]. Structural and Multidisciplinary Optimization，2022，65(5)：143.
[12] PAUL J. F. GANDY J K. Geometric quantization of curvature energy in equipotential surfaces of ionic crystals[J]. Journal of Chemical Physics，2002，116(21)：9431-9434.
[13] HIPPOLYTE LAZARD-HOLLY W H M I. Classification of doubly-periodic minimal surfaces of genus zero[J]. Inventions Mathematicae，2001，143(1)：1-27.
[14] YIN S，LI J，LIU B，et al. Honeytubes：Hollow lattice truss reinforced honeycombs for crushing protection[J]. Composite Structures，2017，160：1147-1154.
[15] CHEN F，MIAO Y，ZHANG L，et al. Triply periodic channels enable soft pneumatic linear actuator with single material and scalability[J]. IEEE Robotics and Automation Letters，2022，7(2)：2668-2675.
[16] PENG S，GUO Q，THIRUNAVUKKARASU N，et al. Tailoring of photocurable ionogel toward high resilience and low hysteresis 3D printed versatile porous flexible sensor[J]. Chemical Engineering Journal，2022，439：135593.
[17] ZHANG L，WANG B，SONG B，et al. 3D printed piomimetic metamaterials with graded porosity and tapering topology for improved cell seeding and bone regeneration[J]. Bioactive Materials，2023(7)：667-688.
[18] 王建强，郑讯佳，黄荷叶. 驾驶人驾驶决策机制遵循最小作用量原理[J]. 中国公路学报，2020，33(4)：155-168. WANG Jianqiang，ZHENG Xunjia，HUANG Heye. Decision-making mechanism of the drivers following the principle of least action[J]. China J. Highw. Transp，2020，33(4)：155-168.
[19] MA Xiangyu，ZHANG D，ZHENG Xunjia. Revealing the excellent properties of minimal surface lattice structures based on additive manufacturing through the principle of least action[J]. The International Journal of Advanced Manufacturing Technology，2022，121(3-4)：1575-1588.
[20] DE SAPIO V，KHATIB O，DELP S. Least action principles and their application to constrained and task-level problems in robotics and biomechanics[J]. Multibody System Dynamics，2007，19(3)：303-322.
[21] HUA Yuchao，GUO Zengyuan. The least action principle for heat conduction and its optimization application[J]. International Journal of Heat and Mass Transfer，2017，105：697-703.
[22] 韩玲，赵伟，曹越，等. 润滑机制下基于最小作用量原理的CVT传动安全裕度优化研究[J]. 机械工程学报，2022，58(10)：223-234. HAN Ling，ZHAO Wei，CAO Yue，et al. Research on safety margin optimization of CVT transmission based on principle of least action under lubrication mechanism[J] Journal of Mechanical Engineering，2022，58(10)：223-234.
[23] ZHENG X，HUANG H，WANG J，et al. Behavioral decision‐making model of the intelligent vehicle based on driving risk assessment[J]. Computer-Aided Civil and Infrastructure Engineering，2019，36：820-837.
[24] 付宝连. 有限位移理论线弹性动力学二类和三类混合变量的最小势作用量原理和驻值余作用量原理及其应用[J]. 应用数学和力学，2017，38(12)：1359-1376. FU Baolian. Principles of minimum potential action and stationary complementary action with dual and triple mixed variables for linear elastodynamics of finite displacement theory and the application[J]. Applied Mathematics and Mechanics，2017，38(12)：1359-1376.
[25] 魏淑强. 弹性力学最小势能原理[J]. 清远职业技术学院学报，2008，1(2)：116-117. WEI Shuqiang. Principle of minimum potential energy in theory of tlasticity[J]. Journal of Qingyuan Polytechnic，2008，1(2)：116-117.
[26] 吴枝根，李孝宝，孟增，等. 从受拉杆变形浅析弹性力学中的最小势能原理[J]. 力学与实践，2021，43(06)：964-966. WU Zhigen，LI Xiaobao，MENG Zeng，et al. On principle of minimum potential energy in elasticity from deformation of bars subjected to tension[J]. Mechanics in Engineering，2021，43(06)：964-966.
[27] MA Xiangyu，ZHANG D，ZHAO Miao，et al. Mechanical and energy absorption properties of functionally graded lattice structures based on minimal curved surfaces[J]. The International Journal of Advanced Manufacturing Technology，2021，118(3-4)：995-1008.
[28] 徐赣君，戴宁. 基于节点增强的功能点阵设计方法[J]. 中国机械工程，2022，33(13)：1537-1544. XU Ganjun，DAI Ning. Functional lattice structure design method based on strengthing nodes[J]. China Mechanical Engineering，33(13)：1537-1544.
[29] LIU Fei，ZHANG D，ZHANG Peng，et al. Mechanical properties of optimized diamond lattice structure for bone scaffolds fabricated via selective laser melting[J]. Materials (Basel)，2018，11(3)：374.
[30] BAI Long，XU Yue，CHEN Xiaohong，et al. Improved mechanical properties and energy absorption of Ti6Al4V laser powder bed fusion lattice structures using curving lattice struts[J]. Materials & Design，2021，211：110140.