金属增材制造若干关键力学问题研究进展

廉艳平; 王潘丁; 高杰; 刘继凯; 李取浩; 刘长猛; 贺小帆; 高亮; 李好; 雷红帅; 李会民; 肖登宝; 郭旭; 方岱宁

doi:10.6052/1000-0992-21-037

金属增材制造若干关键力学问题研究进展

doi: 10.6052/1000-0992-21-037

1.
北京理工大学先进结构技术研究院, 北京 100081
2.
华中科技大学航空航天学院, 武汉 430074
3.
山东大学机械工程学院, 济南 250100
4.
北京理工大学机械与车辆工程学院, 北京 100081
5.
北京航空航天大学航空科学与工程学院, 北京 100191
6.
华中科技大学机械科学与工程学院, 武汉 430074
7.
大连理工大学运载工程与力学学部, 辽宁 116023

基金项目: 国家自然科学基金(11972086, 12002031, 12027901, 12072029, 52075195)、科技部重点研发计划(2017YFB1104003)、装备发展部预先研究项目(41423010102)、国防基础科研计划(JCKY2016110C012)资助.

详细信息

作者简介:
廉艳平, 男, 1985年出生, 北京理工大学先进结构技术研究院教授、博导. 现任固体力学专业委员会委员, 数据驱动的计算力学方法专业组成员, 《力学学报》《计算力学学报》《Materials》期刊编委等. 2007年获哈尔滨工程大学工程力学学士学位, 2012年获清华大学力学博士学位, 2012—2014年在清华大学航天航空学院、2014—2018年在美国西北大学机械工程系开展博士后研究. 主要从事于计算固体力学, 具体包括冲击侵彻计算力学、增材制造多场多尺度耦合、数据驱动计算方法等问题的研究. 目前主持基础加强重点项目、中组部海外高层次人才项目、国家自然科学基金面上项目，参与国家自然科学基金重大仪器等项目. 曾获国际增材制造数值模拟挑战赛第1名(AM-Bench 2018)、中国大学出版社优秀学术著作奖、清华大学优秀博士学位论文及美国西北大学博士后Travel Award等荣誉

通讯作者:
yanping.lian@bit.edu.cn

中图分类号: O341
计量
- 文章访问数: 7571
- HTML全文浏览量: 2015
- PDF下载量: 1438
- 被引次数: 0
出版历程
- 收稿日期: 2021-06-29
- 录用日期: 2021-08-02
- 网络出版日期: 2021-08-25
- 刊出日期: 2021-09-25

Fundamental mechanics problems in metal additive manufacturing: A state-of-art review

1.
Institute of Advanced Structure Technology, Institute of Beijing Technology, Beijing 100081, China
2.
School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhang 430074, China
3.
School of Mechanical Engineering, Shandong University, Jinan 250100, Shandong, China
4.
School of Mechanical Engineering, Institute of Beijing Technology, Beijing 100190, China
5.
School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
6.
School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhang 430074, China
7.
Department of Engineering Mechanics, Dalian University of Technology, Dalian 116023, Liaoning, China

More Information

Corresponding author: yangping.lian@bit.edu.cn

摘要

摘要: 金属增材制造是一种兼顾复杂结构和高性能构件成形需求的颠覆性制造技术, 在航空、航天、交通、核电等领域具有广阔的应用前景和发展空间. 该技术大规模推广应用所面临的制造效率和控形保性挑战是一个涉及力学、光学、材料、机械、控制等多学科交叉的难题. 本文针对其中涉及的若干关键力学问题, 阐述了近年来国内外在面向金属增材制造的结构拓扑优化设计、制造过程数值模拟、成形材料与结构的缺陷表征和性能评价方面的研究进展, 并对金属增材制造的结构设计−制造模拟−性能评价的发展趋势进行了展望.
- 增材制造 /
- 拓扑优化 /
- 数值模拟 /
- 缺陷分析 /
- 力学性能
Abstract: Metal additive manufacturing (AM) is a kind of disruptive manufacturing technology that considers the needs of complex geometry fabrication and high-performance part fabrication. Hence, it has broad applications and extensive development space in aviation, aerospace, transportation, nuclear power, to name a few. However, its large-scale applications suffer from the challenge, including improving manufacturing efficiency and achieving the geometry and mechanical property as desired, which is a cross-cutting problem involving multi-discipline such as mechanics, optics, material science, mechanical engineering, control science. In the viewpoint of mechanics associated with the challenge, this paper critically reviews the recent research progress of AM-oriented structure topology optimization design, numerical simulation of the metal AM process, as-built defects characterization, and mechanical performance evaluation of the fabricated metal materials and components, which are referred to as structure design-process modelling-performance evaluation for metal AM. Finally, research topics that are required to address the fundamental mechanical problems in terms of structure design-process modelling-performance evaluation in AM of metallic components are provided.
- additive manufacturing /
- topology optimization /
- numerical simulation /
- defect analysis /
- mechanical property

HTML全文

图 1 金属增材制造技术原理示意图. (a)激光选区熔融技术(PBF_LB), (b)激光立体成形技术/激光近净成形技术(DED_LB), (c)电子束选区熔融技术(PBF_EB), (d)电子束送丝增材制造技术(DED_EB), (e)电弧送丝增材制造技术(DED_ARC)

下载: 全尺寸图片幻灯片

图 2 金属增材制造的三个关键力学问题: 面向增材制造的拓扑优化设计、数值模拟、缺陷表征与性能评价

下载: 全尺寸图片幻灯片

图 3 (a) 最小特征尺寸约束, 结果来源于Zhu等(2021), (b) 悬角约束, 结果来源于Gaynor等(2016), (c) 连通性约束, 结果来源于Xiong等(2020)

下载: 全尺寸图片幻灯片

图 4 混合型路径与结构拓扑的协同优化设计结果 (Dapogny et al. 2019). (a)悬臂梁, (b) L形梁

下载: 全尺寸图片幻灯片

图 5 (a) 金属增材制造构件的开裂现象 (Cheng et al. 2019), (b) 基于固有应变法的残余应力与变形计算结果(Chen et al. 2019), (c) 金属增材制造的变形约束拓扑优化支撑结构(Zhang et al. 2020)

下载: 全尺寸图片幻灯片

图 6 卫星支架三类设计及其制造原型(Zhu et al. 2021): (a)传统拓扑优化设计; (b)点阵结构填充式设计; (c)实体−点阵填充式设计

下载: 全尺寸图片幻灯片

图 7 仅具备单一类型微结构的多尺度填充式设计案例. (a) 二维多孔材料周期性设计(Li et al. 2016), (b) 三维周期性点阵材料设计(He et al. 2017)

下载: 全尺寸图片幻灯片

图 8 材料/结构多尺度优化设计结果. (a)(b)多类微结构多尺度设计模型及其增材制造样例 (Xiao et al. 2021), (c)考虑宏观结构拓扑、多类微结构拓扑与多类微结构在宏观结构内分布的多尺度设计 (Gao et al. 2019a)

下载: 全尺寸图片幻灯片

图 9 不同周期性约束的桥梁结构设计. (a) 骨骼类结构尺度相关多尺度设计(Wu et al. 2018), (b) 座椅类结构尺度相关多尺度设计 (Wu J et al. 2021)

下载: 全尺寸图片幻灯片

图 10 增材制造数值模拟研究方向经同行评议发表的论文数量(该数据基于Web of Science 数据库统计, 采用的关键词搜索组合为“additive manufacturing”或者“3D printing”和“numerical simulation”)

下载: 全尺寸图片幻灯片

图 11 基于高保真“热−流”耦合模型的数值模拟. (a) PBF_LB 316L不锈钢粉末的温度和速度场计算结果, 其中红色射线表示激光光束 (Khairallah et al. 2020); (b) DED_LB IN625合金粉末落入熔池过程的计算结果 (Aggarwal et al. 2021); (c) DED_EB Ti-6Al-4V丝材熔化过程计算结果(Hu et al. 2018)

下载: 全尺寸图片幻灯片

图 12 基于等效连续体假设“热−流”耦合模型的数值模拟. (a)DED_LB增材制造IN718粉末熔融成形过程的计算结果 (Lian et al. 2019), (b) DED_ARC增材制造H13工具钢丝材熔融成形过程的计算结果 (Ou et al. 2018)

下载: 全尺寸图片幻灯片

图 13 基于“热−固”耦合模型的数值模拟. (a) PBF_LB 增材制造IN718材料成形立方体的残余应力分布及变形模式计算结果 (Denliner et al. 2017), (b) DED_ARC增材制造ER70S-6材料成形4层薄壁件的应力分布计算结果 (Huang et al. 2020)

下载: 全尺寸图片幻灯片

图 14 基于“热−流−固”强耦合模型的数值模拟. (a) PBF_LB 增材制造IN718合金粉末成形过程计算结果 (Dao et al. 2021), (b) DED_LB增材制造 S390不锈钢粉末成形过程计算结果 (Wang H et al. 2020)

下载: 全尺寸图片幻灯片

图 15 基于相场模型的微观组织数值模拟. (a)DED_LB增材制造Ti-Nb合金凝固二维枝晶形貌计算结果 (Gong et al. 2015), (b) PBF_EB增材制造Ti-6Al-4V合金凝固二维枝晶形貌计算结果(Chu et al. 2020), (c) PBF_L增材制造 AlSi10Mg合金凝固三维枝晶形貌计算结果 (Park et al. 2020)

下载: 全尺寸图片幻灯片

图 16 基于晶粒尺度CA方法的微观组织数值模拟. (a) DED_LB增材制造IN718合金凝固微观组织计算结果 (Lian et al. 2019), (b) PBF_EB增材制造Ti-6Al-4V合金凝固初始相计算结果 (Xiong et al. 2021)

下载: 全尺寸图片幻灯片

图 17 基于顺序耦合的金属增材制造“过程−组织−性能”多尺度多物理场耦合模拟方法

下载: 全尺寸图片幻灯片

图 18 增材制造构件典型缺陷特征(Suard et al. 2015, Liu L et al. 2017, Amani et al. 2018)

下载: 全尺寸图片幻灯片

图 19 100 kN力学在位加载CT成像装置及增材制造样件在位表征结果

下载: 全尺寸图片幻灯片

图 20 点阵结构的有限元建模. (a) 实体单元模型 (Babamiri et al. 2020), (b)实体单元与梁单元模型的仿真结果对比(Guo et al. 2020), (c)对称边界的梁单元模型(Ruiz et al. 2020), (d)周期性边界的实体单元模型(Jia et al. 2020), (e)图像有限元模型(Amani et al. 2018)

下载: 全尺寸图片幻灯片

图 21 典型断面 (Sterling et al. 2016). (a)锻造Ti–6Al–4V合金材料及其, (b)裂纹萌生位置, (c) DED_LB 增材制造Ti–6Al–4V合金材料及其, (d)裂纹萌生位置, (e)退火DED_LB 增材制造Ti–6Al–4V合金材料及其, (f)裂纹萌生位置

下载: 全尺寸图片幻灯片

图 22 原始和修正后的K-T图 (Hu et al. 2020)

下载: 全尺寸图片幻灯片

图 23 缺陷等效法则(Murakami et al. 2019). (a)不规则内部缺陷, (b)不规则表面缺陷, (c)不规则亚表面缺陷, (d)两相邻缺陷, (e)倾斜表面缺陷

下载: 全尺寸图片幻灯片

图 24 增材制造金属材料冲击试验常用试样制备示意图. (a) OZ试样, (b)OX试样

下载: 全尺寸图片幻灯片

图 25 PBF_LB增材制造AlSi10Mg_200C合金材料不同应变率加载下的应力应变曲线(Asgari et al. 2018). (a) OX试样, (b) OZ试样

下载: 全尺寸图片幻灯片

图 26 PBF_LB增材制造GP1不锈钢材料动态力学性能(史同亚等2019). (a)不同应变率下单轴拉伸试样的真实应力−应变曲线, (b)不同初始速度下平板撞击试样的层裂剖面, (c)初始层裂的微观金相显示微孔洞形核于冶金界面结合处

下载: 全尺寸图片幻灯片

图 27 PBF_LB增材制造AlSi10Mg合金材料在激光冲击加载下的实验结果(Laurencon et al. 2019). (a)冲击加载方向示意图; (b)试样的雨贡纽弹性极限(Hugoniot elastic limit)值对比; (c) 层裂面上的不同断裂模式, 黄色圆圈为“池间”断裂模式, 红色圆圈为“池内”断裂模式

下载: 全尺寸图片幻灯片

map

参考文献(205)

[1]	陈嘉伟, 熊飞宇, 黄辰阳, 廉艳平. 2020. 金属增材制造数值模拟. 中国科学: 物理学力学天文学, 50: 090007 (Chen J W, Xiong F Y, Huang C Y, Lian Y P. 2020. Numerical simulation on metallic additive manufacturing. Scientia Sinica Physica, Mechanics & Astronomica, 50: 090007).
[2]	耿汝伟, 杜军, 魏正英, 魏培. 2018. 金属增材制造中微观组织相场法模拟研究进展. 材料导报, 32: 1145-1150 (Geng R W, Du J, Wei Z Y, Wei P. 2018. Current research status of phase field simulation for microstructures of additive manufactured metals. Materials Review A, 32: 1145-1150). doi: 10.11896/j.issn.1005-023X.2018.07.015
[3]	耿汝伟, 杜军, 魏正英. 2020. 电弧增材制造成形规律、组织演变及残余应力的研究现状. 机械工程材料, 44: 11-17 (Geng R W, Du J, Wei Z Y. 2020. Research process of formation law, microstructure evolution and residual stress in wire and arc additive manufacturing. Materials for Mechanical Engineering, 44: 11-17). doi: 10.11973/jxgccl202012002
[4]	贾文鹏, 林鑫, 陈静, 杨海鸥, 钟诚文, 黄卫东. 2007. 空心叶片激光快速成形过程的温度/应力场数值模拟. 中国激光, 34: 1308-1312 (Jia W P, Lin X, Chen J, Yang H O, Zhong C W, Huang W D. 2007. Temperature/stress field numerical simulation of hollow blade produced by laser rapid forming. Chinese Journal of Lasers, 34: 1308-1312). doi: 10.3321/j.issn:0258-7025.2007.09.031
[5]	李涤尘, 苏秦, 卢秉恒. 2015. 增材制造——创新与创业的利器. 航空制造技术, 10: 40-43 (Li D C, Su Q, Lu B H. 2015. Additive manufacturing - Tool for innovation and entrepreneurship. Aeronautical Manufacturing Technology, 10: 40-43).
[6]	刘洋, 徐怀忠, 汪小锋, 李治国, 胡建波, 王永刚. 2021. 冲击载荷下增材制造金属材料的动态响应及微观结构演化研究进展. 高压物理学报, 35: 040102 (Liu Y, Xu H Z, Wang X F, Li Z G, Hu J B, Wang Y G. 2021. Progress in dynamic responses and microstructure evolution of the additive manufactured alloys under impact load. Chinese Journal of High Pressure Physics, 35: 040102).
[7]	倪辰旖, 张长东, 刘婷婷, 廖文和. 2018. 基于固有应变法的激光选区熔化成形变形趋势预测. 中国激光, 45: 0702004 (Ni C Y, Zhang C D, Liu T T, Liao W H. 2018. Deformation prediction of metal selective laser melting based on inherent strain method. Chinese Journal of Lasers, 45: 0702004). doi: 10.3788/CJL201845.0702004
[8]	史同亚, 刘东升, 陈伟, 谢普初, 汪小锋, 王永刚. 2019. 激光选区熔化增材制造 GP1 不锈钢动态拉伸力学响应与层裂破坏. 爆炸与冲击, 39: 073101 (Shi T Y, Liu D S, Chen W, Xie P C, Wang X F, Wang Y G. 2019. Dynamic tensile behavior and spall fracture of GP1 stainless steel processed by selective laser melting. Explosion and Shock Waves, 39: 073101).
[9]	田小永, 李涤尘, 卢秉恒. 2016. 空间3D打印技术现状与前景. 载人航天, 22: 471-476 (Tian X Y, Li D C, Lu B H. 2016. Status and prospect of 3D printing technology in space. Manned Spaceflight, 22: 471-476).
[10]	王超, 徐斌, 段尊义, 荣见华. 2021. 面向增材制造的应力最小化连通性拓扑优化. 力学学报, 53: 1070-1080 (Wang C, Xu B, Duan Z Y, Rong J H. 2021. Additive manufacturing-oriented stress minimization topology optimization with connectivity. Chinese Journal of Theoretical and Applied Mechanics, 53: 1070-1080). doi: 10.6052/0459-1879-20-389
[11]	王华明. 2014. 高性能大型金属构件激光增材制造: 若干材料基础问题. 航空学报, 35: 2690-2698 (Wang H M. 2014. Materials’ fundamental issues of laser additive manufacturing for high-performance large metallic components. Acta Aeronautica et Astronautica Sinica, 35: 2690-2698).
[12]	魏雷, 林鑫, 王猛, 等. 2017. 金属激光增材制造过程数值模拟. 航空制造技术, 13: 15-25 (Wei L, Lin X, Wang M, et al. 2017. Numerical simulation on laser additive manufacturing process for metal components. Aeronautical Manufacturing Technology, 13: 15-25).
[13]	魏青松, 史玉升. 2016. 增材制造技术原理与应用. 北京: 科学出版社 Wei Q S, Shi Y S. 2016. Additive Manufacturing Technology Principles and Applications. Beijing: Science Press
[14]	吴正凯, 吴圣川, 张杰, 宋哲, 胡雅楠, 康国政, 张海鸥. 2019. 基于同步辐射X射线成像的选区激光熔化Ti-6Al-4V合金缺陷致疲劳行为. 金属学报, 55: 811-820 (Wu Z K, Wu S C, Zhang J, Song Z, Hu Y N, Kang G Z, Zhang H O. 2019. Defect induced fatigue behaviors of selective laser melted Ti-6Al-4V via synchrotron radiation X-ray tomography. Acta Metallurgica Sinica, 55: 811-820). doi: 10.11900/0412.1961.2018.00408
[15]	庄茁, 柳占立, 成健. 2020. 连续体和结构的非线性有限元. 北京: 清华大学出版社 Zhuang Z, Liu Z L, Cheng J. 2020. Nonlinear Finite Elements for Continua and Structures. Beijing: Tsinghua University Press
[16]	Aggarwal A, Patel S, Vinod A R, Kumar A. 2021. An integrated Eulerian-Lagrangian-Eulerian investigation of coaxial gas-powder flow and intensified particle-melt interaction in directed energy deposition process. International Journal of Thermal Sciences, 166: 106963. doi: 10.1016/j.ijthermalsci.2021.106963
[17]	Ahmadi A, Mirzaeifar R, Moghaddam N S, et al. 2016. Effect of manufacturing parameters on mechanical properties of 316L stainless steel parts fabricated by selective laser melting: A computational framework. Materials and Design, 112: 328-338. doi: 10.1016/j.matdes.2016.09.043
[18]	Åkerfeldt P, Colliander M H, Pederson R, et al. 2018. Electron backscatter diffraction characterization of fatigue crack growth in laser metal wire deposited Ti-6Al-4V. Materials Characterization, 135: 245-256. doi: 10.1016/j.matchar.2017.11.041
[19]	Akgun E, Zhang X, Biswal R, et al. 2021. Fatigue of wire+arc additive manufactured Ti-6Al-4V in presence of process-induced porosity defects. International Journal of Fatigue, 150: 106315. doi: 10.1016/j.ijfatigue.2021.106315
[20]	Alaghmandfard R, Dharmendra C, Odeshi A G, Mohammadi M. 2020. Dynamic mechanical properties and failure characteristics of electron beam melted Ti-6Al-4V under high strain rate impact loadings. Materials Science and Engineering A, 793: 139794. doi: 10.1016/j.msea.2020.139794
[21]	Alexandersen J, Lazarov B S. 2015. Topology optimisation of manufacturable microstructural details without length scale separation using a spectral coarse basis preconditioner. Computer Methods in Applied Mechanics and Engineering, 290: 156-182. doi: 10.1016/j.cma.2015.02.028
[22]	Amani Y, Dancette S, Delroisse P, et al. 2018. Compression behavior of lattice structures produced by selective laser melting: X-ray tomography based experimental and finite element approaches. Acta Materialia, 159: 395-407. doi: 10.1016/j.actamat.2018.08.030
[23]	Ammer R, Markl M, Ljungblad U, Korner C, Rude U. 2014. Simulating fast electron melting with a parallel thermal free surface lattice Boltzmann method. Computers & Mathematics with Applications, 67: 318-330.
[24]	Asgari H, Odeshi A, Hosseinkhani K, Mohammadi M. 2018. On dynamic mechanical behavior of additively manufactured AlSi10Mg. Materials Letters, 211: 187-190. doi: 10.1016/j.matlet.2017.10.001
[25]	Babamiri B B, Askari H, Askari H, Hazeli K. 2020. Deformation mechanisms and post-yielding behavior of additively manufactured lattice structures. Materials & Design, 188: 108443.
[26]	Bagheri Z S, Melancon D, Liu L, et al. 2017. Compensation strategy to reduce geometry and mechanics mismatches in porous biomaterials built with Selective Laser Melting. Journal of the Mechanical Behavior of Biomedical Materials, 70: 17-27. doi: 10.1016/j.jmbbm.2016.04.041
[27]	Bao H, Wu S, Wu Z, Kang G, Peng X, Withers P J. 2021. A machine-learning fatigue life prediction approach of additively manufactured metals. Engineering Fracture Mechanics, 242: 107508. doi: 10.1016/j.engfracmech.2020.107508
[28]	Beghini L L, Stender M, Moser D, Trembacki B L, Veilleux M G, Ford K R. 2021. A coupled fluid-mechanical workflow to simulate the directed energy deposition additive manufacturing process. Computational Mechanics, 67: 1041-1057. doi: 10.1007/s00466-020-01960-9
[29]	Bendsøe M P, Kikuchi N. 1988. Generating optimal topologies in structural design using a homogenization method. Computer Methods in Applied Mechanics and Engineering, 71: 197-224. doi: 10.1016/0045-7825(88)90086-2
[30]	Beretta S, Gargourimotlagh M, Foletti S, et al. 2020. Fatigue strength assessment of “as built” AlSi10Mg manufactured by SLM with different build orientations. International Journal of Fatigue, 139: 105737. doi: 10.1016/j.ijfatigue.2020.105737
[31]	Biswal R, Zhang X, Shamir M, et al. 2019. Interrupted fatigue testing with periodic tomography to monitor porosity defects in wire + arc additive manufactured Ti-6Al-4V. Additive Manufacturing, 28: 517-527. doi: 10.1016/j.addma.2019.04.026
[32]	Biswas N, Ding J L, Balla V K, et al. 2012. Deformation and fracture behavior of laser processed dense and porous Ti6Al4V alloy under static and dynamic loading. Materials Science and Engineering A, 549: 213-221. doi: 10.1016/j.msea.2012.04.036
[33]	Chen Q, Liang X, Hayduke D, Liu J, Cheng L, Oskin J, Whitmore R, To A C. 2019. An inherent strain based multiscale modeling framework for simulating part-scale residual deformation for direct metal laser sintering. Additive Manufacturing, 28: 406-418. doi: 10.1016/j.addma.2019.05.021
[34]	Chen J, Wei H, Bao K, et al. 2021. Dynamic mechanical properties of 316L stainless steel fabricated by an additive manufacturing process. Journal of Materials Research and Technology, 11: 170-179. doi: 10.1016/j.jmrt.2020.12.097
[35]	Chen S, Duan Q. 2020. An adaptive second-order element-free Galerkin method for additive manufacturing process. Computational Materials Science, 183: 109911. doi: 10.1016/j.commatsci.2020.109911
[36]	Chen S, Wang M Y, Liu A Q. 2008. Shape feature control in structural topology optimization. Computer-Aided Design, 40: 951-962. doi: 10.1016/j.cad.2008.07.004
[37]	Chen X, Li C, Bai Y. 2021. Topology optimization of sandwich structures with solid-porous hybrid infill under geometric constraints. Computer Methods in Applied Mechanics and Engineering, 382: 113856. doi: 10.1016/j.cma.2021.113856
[38]	Chen Y, Zhang J, Gu X, et al. 2018. Distinction of corrosion resistance of selective laser melted Al-12Si alloy on different planes. Journal of Alloys and Compounds, 747: 648-658. doi: 10.1016/j.jallcom.2018.03.062
[39]	Cheng L, Liang X, Bai J, Chen Q, Lemon J, To A C. 2019. On utilizing topology optimization to design support structure to prevent residual stress induced build failure in laser powder bed metal additive manufacturing. Additive Manufacturing, 27: 290-30. doi: 10.1016/j.addma.2019.03.001
[40]	Childerhouse T, Hernández-Nava E, Tapoglou N, et al. 2021. The influence of finish machining depth and hot isostatic pressing on defect distribution and fatigue behaviour of selective electron beam melted Ti-6Al-4V. International Journal of Fatigue, 147: 106169. doi: 10.1016/j.ijfatigue.2021.106169
[41]	Chu S, Guo C, Zhang T, Wang Y, et al. 2020. Phase-field simulation of microstructure evolution in electron beam additive manufacturing. The European Physical Journal E, 43: 35. doi: 10.1140/epje/i2020-11952-1
[42]	Dai N, Zhang L, Zhang J, et al. 2016. Distinction in corrosion resistance of selective laser melted Ti-6Al-4V alloy on different planes. Corrosion Science, 111: 703-710. doi: 10.1016/j.corsci.2016.06.009
[43]	Dao M H, Lou J. 2021. Simulations of laser assisted additive manufacturing by smoothed particle hydrodynamics. Computer Methods in Applied Mechanics and Engineering, 373: 113491. doi: 10.1016/j.cma.2020.113491
[44]	Dapogny C, Estevez R, Faure R, Michailidis G. 2019. Shape and topology optimization considering anisotropic features induced by additive manufacturing processes. Computer Methods in Applied Mechanics and Engineering, 344: 626-665. doi: 10.1016/j.cma.2018.09.036
[45]	Denlinger E R, Gouge M, Irwin J, Michaleris P. 2017. Thermomechanical model development and in situ experimental validation of the Laser Powder-Bed Fusion process. Additive Manufacturing, 16: 73-80. doi: 10.1016/j.addma.2017.05.001
[46]	Echeta I, Feng X, Dutton B, et al. 2020. Review of defects in lattice structures manufactured by powder bed fusion. The International Journal of Advanced Manufacturing Technology, 106: 2649. doi: 10.1007/s00170-019-04753-4
[47]	Edwards P, Ramulu M. 2014. Fatigue performance evaluation of selective laser melted Ti-6Al-4V. Materials Science and Engineering: A, 598: 327-337. doi: 10.1016/j.msea.2014.01.041
[48]	Eshenauer H A, Olhoff N. 2001. Topology optimization of continuum structures: A review. Applied Mechanics Reviews, 54: 331-390. doi: 10.1115/1.1388075
[49]	Calignano F. 2018. Investigation of the accuracy and roughness in the laser powder bed fusion process. Virtual and Physical Prototyping, 13: 97-104. doi: 10.1080/17452759.2018.1426368
[50]	Fallah V, Amoorezaei M, Provatas N, Corbin S F, Khajepour A. 2012. Phase-field simulation of solidification morphology in laser powder deposition of Ti-Nb alloys. Acta Materialia, 60: 1633-1646. doi: 10.1016/j.actamat.2011.12.009
[51]	Formanoir D C, Suard M, Dendievel R, et al. 2016. Improving the mechanical efficiency of electron beam melted titanium lattice structures by chemical etching. Additive Manufacturing, 11: 71-76. doi: 10.1016/j.addma.2016.05.001
[52]	Gan Z, Lian Y, Lin S E. 2019. Benchmark study of thermal behavior, surface topography, and dendritic microstructure in selective laser melting of Inconel 625. Integrating Materials and Manufacturing Innovation, 8: 178-193. doi: 10.1007/s40192-019-00130-x
[53]	Gandin C A, Rappaz M. 1997. A 3D cellular automaton algorithm for the prediction of dendritic grain growth. Acta Materialia, 45: 2187-2195. doi: 10.1016/S1359-6454(96)00303-5
[54]	Gao J, Luo Z, Li H, Gao L. 2019a. Topology optimization for multiscale design of porous composites with multi-domain microstructures. Computer Methods in Applied Mechanics and Engineering, 344: 451-476. doi: 10.1016/j.cma.2018.10.017
[55]	Gao J, Luo Z, Li H, Li P, Gao L. 2019b. Dynamic multiscale topology optimization for multi-regional micro-structured cellular composites. Composite Structures, 211: 401-417. doi: 10.1016/j.compstruct.2018.12.031
[56]	Gao J, Luo Z, Xia L, Gao L. 2019c. Concurrent topology optimization of multiscale composite structures in Matlab. Structural and Multidisciplinary Optimization, 60: 2621-2651. doi: 10.1007/s00158-019-02323-6
[57]	Gaynor A T, Guest J K. 2016. Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design. Structural and Multidisciplinary Optimization, 54: 1157-72. doi: 10.1007/s00158-016-1551-x
[58]	Ge P, Zhang Z, Tan Z J, Hu C P, Zhao G Z, Guo X. 2019. An integrated modeling of process-structure-property relationship in laser additive manufacturing of duplex titanium alloy. International Journal of Thermal Sciences, 140: 329-343. doi: 10.1016/j.ijthermalsci.2019.03.013
[59]	Geng L C, Ruan X L, Wu W W, et al. 2019a. Mechanical properties of selective laser sintering (SLS) additive manufactured chiral auxetic cylindrical stent. Experimental Mechanics, 59: 913-925. doi: 10.1007/s11340-019-00489-0
[60]	Geng L, Wu W, Sun L, et al. 2019b. Damage characterizations and simulation of selective laser melting fabricated 3D re-entrant lattices based on in-situ CT testing and geometric reconstruction. International Journal of Mechanical Sciences, 157-158: 231-242. doi: 10.1016/j.ijmecsci.2019.04.054
[61]	Gong X, Chou K. 2015. Phase-field modeling of microstructure evolution in electron beam additive manufacturing. JOM Journal of the Minerals Metals and Materials Society, 67: 1176-1182. doi: 10.1007/s11837-015-1352-5
[62]	Guest J K. 2009. Imposing maximum length scale in topology optimization. Structural and Multidisciplinary Optimization, 37: 463-473. doi: 10.1007/s00158-008-0250-7
[63]	Guo H, Takezawa A, Honda M, et al. 2020. Finite element simulation of the compressive response of additively manufactured lattice structures with large diameters. Computational Materials Science, 175: 109610. doi: 10.1016/j.commatsci.2020.109610
[64]	Guo X, Cheng G D. 2010. Recent development in structural design and optimization. Acta Mechanica Sinica, 26: 807-823. doi: 10.1007/s10409-010-0395-7
[65]	Guo X, Zhang W, Zhong W. 2014. Explicit feature control in structural topology optimization via level set method. Computer Methods in Applied Mechanics and Engineering, 272: 354-378. doi: 10.1016/j.cma.2014.01.010
[66]	Guo X, Zhou J, Zhang W, Du Z, Liu C, Liu Y. 2017. Self-supporting structure design in additive manufacturing through explicit topology optimization. Computer Methods in Applied Mechanics and Engineering, 323: 27-63. doi: 10.1016/j.cma.2017.05.003
[67]	Hanks B, Berthel J, Frecker M, et al. 2020. Mechanical properties of additively manufactured metal lattice structures: Data review and design interface. Additive Manufacturing, 35: 101301. doi: 10.1016/j.addma.2020.101301
[68]	Hashemi S M, Parvizi S, Baghbanijavid H, Tan A T L, et al. 2021. Computational modelling of process-structure-property-performance relationships in metal additive manufacturing: A review. International Materials Reviews, DOI: 10.1080/09506608.2020.1868889
[69]	He X, Wang T, Wang X, et al. 2019. Fatigue behavior of direct laser deposited Ti-6.5Al-2Zr-1Mo-1V titanium alloy and its life distribution model. Chinese Journal of Aeronautics, 31: 2124-2135.
[70]	He Z Z, Wang F C, Zhu Y B, et al. 2017. Mechanical properties of copper octet-truss nanolattices. Journal of the Mechanics and Physics of Solids, 101: 133-149. doi: 10.1016/j.jmps.2017.01.019
[71]	Herriott C, Li X, Kouraytem N, Tari V, Tan W, et al. 2019. A multi-scale, multi-physics modeling framework to predict spatial variation of properties in additive-manufactured metals. Modelling and Simulation in Materials Science and Engineering, 27: 025009. doi: 10.1088/1361-651X/aaf753
[72]	Hu R, Chen X, Yang G, Gong S, Pang S. 2018. Metal transfer in wire feeding-based electron beam 3D printing: Modes, dynamics, and transition criterion. International Journal of Heat and Mass Transfer, 126: 877-887. doi: 10.1016/j.ijheatmasstransfer.2018.06.033
[73]	Hu Y N, Wu S C, Wu Z K, et al. 2020. A new approach to correlate the defect population with the fatigue life of selective laser melted Ti-6Al-4V alloy. International Journal of Fatigue, 136: 105584. doi: 10.1016/j.ijfatigue.2020.105584
[74]	Huang H, Ma N, Chen J, Feng Z, Murakawa H. 2020. Toward large-scale simulation of residual stress and distortion in wire and arc additive manufacturing. Additive Manufacturing, 34: 101248. doi: 10.1016/j.addma.2020.101248
[75]	Huang X, Xie Y M. 2008. Optimal design of periodic structures using evolutionary topology optimization. Structural and Multidisciplinary Optimization, 36: 597-606. doi: 10.1007/s00158-007-0196-1
[76]	Huang X, Zhou S W, Xie Y M, Li Q. 2013. Topology optimization of microstructures of cellular materials and composites for macrostructures. Computational Materials Science, 67: 397-407. doi: 10.1016/j.commatsci.2012.09.018
[77]	Jia H, Lei H, Wang P, et al. 2020. An experimental and numerical investigation of compressive response of designed Schwarz Primitive triply periodic minimal surface with non-uniform shell thickness. Extreme Mechanics Letters, 37: 100671. doi: 10.1016/j.eml.2020.100671
[78]	Jones D R, Fensin S J, Dippo O, et al. 2016. Spall fracture in additive manufactured Ti-6Al-4V. Journal of Applied Physics, 120: 135902. doi: 10.1063/1.4963279
[79]	Khairallah S A, Anderson A T, Rubenchik A, King W E. 2016. Laser powder-bed fusion additive manufacturing: Physics of complex melt flow and formation mechanisms of pores, spatter, and denudation zones. Acta Materialia, 108: 36-45. doi: 10.1016/j.actamat.2016.02.014
[80]	Khairallah S A, Anderson A. 2014. Mesoscopic simulation model of selective laser melting of stainless steel powder. Journal of Materials Processing Technology, 214: 2627-2636. doi: 10.1016/j.jmatprotec.2014.06.001
[81]	Khairallah S A, Martin A A, Lee J R I, Guss G, et al. 2020. Controlling interdependent meso-nanosecond dynamics and defect generation in metal 3D printing. Science, 368: 660-665. doi: 10.1126/science.aay7830
[82]	Korner C, Attar E, Heinl P. 2011. Mesoscopic simulation of selective beam melting processes. Journal of Materials Processing Technology, 211: 978-987. doi: 10.1016/j.jmatprotec.2010.12.016
[83]	Korner C, Markl M, Koepf J A. 2020. Modeling and simulation of microstructure evolution for additive manufacturing of metals: A critical review. Metallurgical and Materials Transactions A, 51: 4970-4983. doi: 10.1007/s11661-020-05946-3
[84]	Kurz W. Fisher D J. 1981. Dendrite growth at the limit of stability: Tip radius and spacing. Acta Materialia, 29: 11-20. doi: 10.1016/0001-6160(81)90082-1
[85]	Langelaar M. 2016. Topology optimization of 3D self-supporting structures for additive manufacturing. Additive Manufacturing, 12: 60-70. doi: 10.1016/j.addma.2016.06.010
[86]	Laurencon M, Resseguier T, Loison D, et al. 2019. Effects of additive manufacturing on the dynamic response of AlSi10Mg to laser shock loading. Materials Science and Engineering A, 748: 407-417. doi: 10.1016/j.msea.2019.02.001
[87]	Latture R M, Begley M R, Zok F W. 2019. Defect sensitivity of truss strength. Journal of the Mechanics and Physics of Solids, 124: 489-504. doi: 10.1016/j.jmps.2018.10.019
[88]	Le V-D, Pessard E, Morel F, et al. 2019. Interpretation of the fatigue anisotropy of additively manufactured TA6V alloys via a fracture mechanics approach. Engineering Fracture Mechanics, 214: 410-426. doi: 10.1016/j.engfracmech.2019.03.048
[89]	Le V-D, Pessard E, Morel F, et al. 2020. Fatigue behaviour of additively manufactured Ti-6Al-4V alloy: The role of defects on scatter and statistical size effect. International Journal of Fatigue, 140: 105811. doi: 10.1016/j.ijfatigue.2020.105811
[90]	Lee Y S, Zhang W. 2016. Modeling of heat transfer, fluid flow and solidification microstructure of Nickel-base superalloy fabricated by laser powder bed fusion. Additive Manufacturing, 12: 178-188. doi: 10.1016/j.addma.2016.05.003
[91]	Lei H, Li C, Zhang X, et al. 2020. Deformation behavior of heterogeneous multi-morphology lattice core hybrid structures. Additive Manufacturing, 37: 101674.
[92]	Leuders S, Thöne M, Riemer A, et al. 2013. On the mechanical behaviour of titanium alloy TiAl6V4 manufactured by selective laser melting: Fatigue resistance and crack growth performance. International Journal of Fatigue, 48: 300-307. doi: 10.1016/j.ijfatigue.2012.11.011
[93]	Lhuissier P, Bataillon X, Maestre C, et al. 2020. In situ 3D X-ray microtomography of laser-based powder-bed fusion (L-PBF)—A feasibility study. Additive Manufacturing, 34: 101271. doi: 10.1016/j.addma.2020.101271
[94]	Li H, Gao L, Li H, Li X, Tong H. 2021. Full-scale topology optimization for fiber-reinforced structures with continuous fiber paths. Computer Methods in Applied Mechanics and Engineering, 377: 113668. doi: 10.1016/j.cma.2021.113668
[95]	Li H, Gao L, Li H, Tong H. 2020. Spatial-varying multi-phase infill design using density-based topology optimization. Computer Methods in Applied Mechanics and Engineering, 372: 113354. doi: 10.1016/j.cma.2020.113354
[96]	Li H, Luo Z, Gao L, Walker P. 2018. Topology optimization for functionally graded cellular composites with metamaterials by level sets. Computer Methods in Applied Mechanics and Engineering, 328: 340-64. doi: 10.1016/j.cma.2017.09.008
[97]	Li H, Luo Z, Zhang N, Gao L, Brown T. 2016. Integrated design of cellular composites using a level-set topology optimization method. Computer Methods in Applied Mechanics and Engineering, 309: 453-75. doi: 10.1016/j.cma.2016.06.012
[98]	Li P, Wang Z, Petrinic N, et al. 2014. Deformation behavior of stainless steel microlattice structures by selective laser melting. Materials Science and Engineering: A, 614: 116-121. doi: 10.1016/j.msea.2014.07.015
[99]	Li P. 2015. Constitutive and failure behavior in selective laser melted stainless steel for microlattice structures. Materials Science and Engineering: A, 622: 114-120. doi: 10.1016/j.msea.2014.11.028
[100]	Li S, Yuan S, Zhu J, Wang C, Li J, Zhang W. 2020. Additive manufacturing-driven design optimization: Building direction and structural topology. Additive Manufacturing, 36: 101406. doi: 10.1016/j.addma.2020.101406
[101]	Lian Y, Gan Z, Yu C, Kats D, Liu W K, Wagner G J. 2019. A cellular automaton finite volume method for microstructure evolution during additive manufacturing. Materials and Design, 169: 107672. doi: 10.1016/j.matdes.2019.107672
[102]	Lian Y, Lin S, Yan W, Liu W K, Wager J W. 2018. A parallelized three-dimensional cellular automaton model for grain growth during additive manufacturing. Computational Mechanics, 61: 543-558. doi: 10.1007/s00466-017-1535-8
[103]	Liu C, Du Z, Zhu Y, Zhang W, Zhang X, Guo X. 2020. Optimal design of shell-graded-infill structures by a hybrid MMC-MMV approach. Computer Methods in Applied Mechanics and Engineering, 369: 113187. doi: 10.1016/j.cma.2020.113187
[104]	Liu H, Zong H, Shi T, Xia Q. 2020. M-VCUT level set method for optimizing cellular structures. Computer Methods in Applied Mechanics and Engineering, 367: 113154. doi: 10.1016/j.cma.2020.113154
[105]	Liu J, To A C. 2017. Deposition path planning-integrated structural topology optimization for 3D additive manufacturing subject to self-support constraint. Computer-Aided Design, 91: 27-45. doi: 10.1016/j.cad.2017.05.003
[106]	Liu J, Yu H. 2020. Self-support topology optimization with horizontal overhangs. Journal of Manufacturing Science and Engineering, 142: 091003. doi: 10.1115/1.4047352
[107]	Liu J. 2019. Piecewise length scale control for topology optimization with an irregular design domain. Computer Methods in Applied Mechanics and Engineering, 351: 744-765. doi: 10.1016/j.cma.2019.04.014
[108]	Liu L, Kamm P, García-Moreno F, et al. 2017. Elastic and failure response of imperfect three-dimensional metallic lattices: The role of geometric defects induced by Selective Laser Melting. Journal of the Mechanics and Physics of Solids, 107: 160-184. doi: 10.1016/j.jmps.2017.07.003
[109]	Liu L, Yan J, Cheng G. 2008. Optimum structure with homogeneous optimum truss-like material. Computers & Structures, 86: 1417-25.
[110]	Liu P W, Wang Z, Xiao Y H, Lebensohn R A, et al. 2020. Integration of phase-field model and crystal plasticity for the prediction of process-structure-property relation of additively manufactured metallic materials. International Journal of Plasticity, 128: 102670. doi: 10.1016/j.ijplas.2020.102670
[111]	Liu S, Li Q, Chen W, Tong L, Cheng G. 2015. An identification method for enclosed voids restriction in manufacturability design for additive manufacturing structures. Frontiers of Mechanical Engineering, 10: 126-137. doi: 10.1007/s11465-015-0340-3
[112]	Liu X, Wada T, Suzuki A, et al. 2021. Understanding and suppressing shear band formation in strut-based lattice structures manufactured by laser powder bed fusion. Materials & Design, 199: 109416.
[113]	Liu Z, Liu P, Lu W, Lu Y, Qing Z-X, Wang H-M. 2018. Fatigue properties of Ti-6.5Al-3.5Mo-1.5Zr-0.3Si alloy produced by direct laser deposition. Materials Science and Engineering: A, 716: 140-149. doi: 10.1016/j.msea.2018.01.016
[114]	Lou R, Li H, Zhong J, Zhang C, Fang D. 2021. A transient updated Lagrangian finite element formulation for bond formation in fused deposition modeling process. Journal of the Mechanics and Physics of Solids, 152: 104450. doi: 10.1016/j.jmps.2021.104450
[115]	Lozanovski B, Downing D, Tino R, et al. 2020a. Non-destructive simulation of node defects in additively manufactured lattice structures. Additive Manufacturing, 36: 101593. doi: 10.1016/j.addma.2020.101593
[116]	Lozanovski B, Downing D, Tino R, et al. 2021. Image-based geometrical characterization of nodes in additively manufactured lattice structures. 3D Printing and Additive Manufacturing, 8: 51-68. doi: 10.1089/3dp.2020.0091
[117]	Lozanovski B, Downing D, Tran P, et al. 2020b. A Monte Carlo simulation-based approach to realistic modelling of additively manufactured lattice structures. Additive Manufacturing, 32: 101092. doi: 10.1016/j.addma.2020.101092
[118]	Luo Y W, Zhang B, Feng X, et al. 2021. Pore-affected fatigue life scattering and prediction of additively manufactured Inconel 718: An investigation based on miniature specimen testing and machine learning approach. Materials Science and Engineering: A, 802: 140693. doi: 10.1016/j.msea.2020.140693
[119]	Luo Y, Sigmund O, Li Q, Liu S. 2020. Additive manufacturing oriented topology optimization of structures with self-supported enclosed voids. Computer Methods in Applied Mechanics and Engineering, 372: 113385. doi: 10.1016/j.cma.2020.113385
[120]	McDowell D L, Gall K, Horstemeyer M F, et al. 2003. Microstructure-based fatigue modeling of cast A356-T6 alloy. Engineering Fracture Mechanics, 70: 49-80. doi: 10.1016/S0013-7944(02)00021-8
[121]	Melancon D, Bagheri Z S, Johnston R B, et al. 2017. Mechanical characterization of structurally porous biomaterials built via additive manufacturing: experiments, predictive models, and design maps for load-bearing bone replacement implants. Acta Biomaterialia, 63: 350-368. doi: 10.1016/j.actbio.2017.09.013
[122]	Mirzendehdel A M, Rankouhi B, Suresh K. 2018. Strength-based topology optimization for anisotropic parts. Additive Manufacturing, 19: 104-113. doi: 10.1016/j.addma.2017.11.007
[123]	Molaei, R., Fatemi, A., Sanaei, N., et al. 2020. Fatigue of additive manufactured Ti-6Al-4V, Part II: The relationship between microstructure, material cyclic properties, and component performance. International Journal of Fatigue, 132: 105363. doi: 10.1016/j.ijfatigue.2019.105363
[124]	Moustafa A R, Dinwiddie R B, Pawlowski A E, et al. 2018. Mesostructure and porosity effects on the thermal conductivity of additively manufactured interpenetrating phase composites. Additive Manufacturing, 22: 223-229. doi: 10.1016/j.addma.2018.05.018
[125]	Murakami Y. 2019. 18-Additive manufacturing: effects of defects //Murakami Y. Metal Fatigue (Second Edition). Academic Press, P453-483
[126]	Nurel B, Nahmany M, Frage N, et al. 2018. Split Hopkinson pressure bar tests for investigating dynamic properties of additively manufactured AlSi10Mg alloy by selective laser melting. Additive Manufacturing, 22: 823-833. doi: 10.1016/j.addma.2018.06.001
[127]	Olakanmi E O, Cochrane R F, Dalgarno K W. 2015. A review on selective laser sintering/melting (SLS/SLM) of aluminium alloy powders: Processing, microstructure, and properties. Progress in Materials Science, 74: 401-477. doi: 10.1016/j.pmatsci.2015.03.002
[128]	Ou W, Mukherjee T, Knapp G L, Wei Y, DebRoy T. 2018. Fusion zone geometries, cooling rates and solidification parameters during wire arc additive manufacturing. International Journal of Heat and Mass Transfer, 127: 1084-1094. doi: 10.1016/j.ijheatmasstransfer.2018.08.111
[129]	Ozdemir Z, Hernandez-Nava E, Tyas A, et al. 2016. Energy absorption in lattice structures in dynamics: Experiments. International Journal of Impact Engineering, 89: 49-61. doi: 10.1016/j.ijimpeng.2015.10.007
[130]	Ozturk T, Rollett A D. 2018. Effect of microstructure on the elasto-viscoplastic deformation of dual phase titanium structures. Computational Mechanics, 61: 55-70. doi: 10.1007/s00466-017-1467-3
[131]	Park J, Kangaroo J-H, Oh C-S. 2020. Phase-field simulations and microstructural analysis of epitaxial growth during rapid solidification of additively manufactured AlSi10Mg alloy. Materials and Design, 195: 108985. doi: 10.1016/j.matdes.2020.108985
[132]	Poulsen T A. 2003. A new scheme for imposing a minimum length scale in topology optimization. International Journal for Numerical Methods in Engineering, 57: 741-760. doi: 10.1002/nme.694
[133]	Qian X. 2017. Undercut and overhang angle control in topology optimization: A density gradient based integral approach. International Journal for Numerical Methods in Engineering, 111: 247-272. doi: 10.1002/nme.5461
[134]	Qiu W, Jin P, Jin S, Wang C, Xia L, Zhu J, Shi T. 2020. An evolutionary design approach to shell-infill structures. Additive Manufacturing, 34: 101382. doi: 10.1016/j.addma.2020.101382
[135]	Radman A, Huang X, Xie Y M. 2012. Topology optimization of functionally graded cellular materials. Journal of Materials Science, 48: 1503-1510.
[136]	Rappaz M, Gandin C A. 1993. Probabilistic modelling of microstructure formation in solidification processes. Acta metal Material, 41: 345-360. doi: 10.1016/0956-7151(93)90065-Z
[137]	Razavi M, Berto F. 2019. Directed energy deposition versus wrought Ti-6Al-4V: A comparison of microstructure, fatigue behavior, and notch sensitivity. Advanced Engineering Materials, 21: 1900220. doi: 10.1002/adem.201900220
[138]	Rigon D, Meneghetti G. 2020. An engineering estimation of fatigue thresholds from a microstructural size and Vickers hardness: application to wrought and additively manufactured metals. International Journal of Fatigue, 139: 105796. doi: 10.1016/j.ijfatigue.2020.105796
[139]	Rodgers T M, Madison J D, Tikare V. 2017. Simulation of metal additive manufacturing microstructure using kinetic Monte Carlo. Computational Materials Science, 135: 78-89. doi: 10.1016/j.commatsci.2017.03.053
[140]	Rodgers T M, Moser D, Abdeljawad F, Jackson O D U, et al. 2021. Simulation of powder bed metal additive manufacturing microstructures with coupled finite difference-Monte Carlo method. Additive Manufacturing, 41: 101953. doi: 10.1016/j.addma.2021.101953
[141]	Rodrigues H, Guedes J M, Bendsoe M P. 2002. Hierarchical optimization of material and structure. Structural and Multidisciplinary Optimization, 24: 1-10. doi: 10.1007/s00158-002-0209-z
[142]	Romano S, Brandão A, Gumpinger J, et al. 2017. Qualification of AM parts: Extreme value statistics applied to tomographic measurements. Materials & Design, 131: 32-48.
[143]	Ruiz D G S, Jeffers J R T, Ghouse S. 2020. A validated finite element analysis procedure for porous structures. Materials & Design, 189: 108546.
[144]	Russell M A, Souto-Iglesias A, Zohdi T I. 2018. Numerical simulation of laser fusion additive manufacturing processes using the SPH method. Computer Methods in Applied Mechanics and Engineering, 341: 163-187. doi: 10.1016/j.cma.2018.06.033
[145]	Sanaei N, Fatemi A. 2021. Defects in additive manufactured metals and their effect on fatigue performance: A state-of-the-art review. Progress in Materials Science, 117: 100724. doi: 10.1016/j.pmatsci.2020.100724
[146]	Sheridan L, Gockel J E, Scott-Emuakpor O E. 2021. Stress-defect-life interactions of fatigued additively manufactured alloy 718. International Journal of Fatigue, 143: 106033. doi: 10.1016/j.ijfatigue.2020.106033
[147]	Sigmund O. 2007. Morphology-based black and white filters for topology optimization. Structural and Multidisciplinary Optimization, 33: 401-424. doi: 10.1007/s00158-006-0087-x
[148]	Sing S L, Yeong W Y, Wiria F E. 2016. Selective laser melting of titanium alloy with 50 wt% tantalum: Microstructure and mechanical properties. Journal of Alloys and Compounds, 660: 461-470. doi: 10.1016/j.jallcom.2015.11.141
[149]	Sivapuram R, Dunning P D, Kim H A. 2016. Simultaneous material and structural optimization by multiscale topology optimization. Structural and Multidisciplinary Optimization, 54: 1267-1281. doi: 10.1007/s00158-016-1519-x
[150]	Smith T R, Sugar J D, Schoenung J M, et al. 2019. Relationship between manufacturing defects and fatigue properties of additive manufactured austenitic stainless steel. Materials Science and Engineering: A, 765: 138268. doi: 10.1016/j.msea.2019.138268
[151]	Sterling A J, Torries B, Shamsaei N, et al. 2016. Fatigue behavior and failure mechanisms of direct laser deposited Ti-6Al-4V. Materials Science and Engineering: A, 655: 100-112. doi: 10.1016/j.msea.2015.12.026
[152]	Suard M, Lhuissier P, Dendievel R, et al. 2014. Towards stiffness prediction of cellular structures made by electron beam melting (EBM). Powder Metallurgy, 57: 190-195. doi: 10.1179/1743290114Y.0000000093
[153]	Suard M, Martin G, Lhuissier P, et al. 2015. Mechanical equivalent diameter of single struts for the stiffness prediction of lattice structures produced by Electron Beam Melting. Additive Manufacturing, 8: 124-131. doi: 10.1016/j.addma.2015.10.002
[154]	Suard M, Plancher E, Martin G, et al. 2020. Surface defects sensitivity during the unfolding of corrugated struts made by powder-bed additive manufacturing. Advanced Engineering Materials, 22: 2000315. doi: 10.1002/adem.202000315
[155]	Takezawa A, To A C, Chen Q, Liang X, Dugast F, Zhang X, Kitamura M. 2020. Sensitivity analysis and lattice density optimization for sequential inherent strain method used in additive manufacturing process. Computer Methods in Applied Mechanics and Engineering, 370: 113231. doi: 10.1016/j.cma.2020.113231
[156]	Tan J H K, Sing S L, Yeoong W Y. 2020. Microstructure modeling for metallic additive manufacturing: A review. Virtual and Physical Prototyping, 15: 87-105. doi: 10.1080/17452759.2019.1677345
[157]	Tian Y, Gora W S, Cabo A P, et al. 2018. Material interactions in laser polishing powder bed additive manufactured Ti6Al4V components. Additive Manufacturing, 20: 11-22. doi: 10.1016/j.addma.2017.12.010
[158]	Torries B, Sterling A J, Shamsaei N, et al. 2016. Utilization of a microstructure sensitive fatigue model for additively manufactured Ti-6Al-4V. Rapid Prototyping Journal, 22: 817-825. doi: 10.1108/RPJ-11-2015-0168
[159]	Wan H, Wang Q, Jia C, et al. 2016. Multi-scale damage mechanics method for fatigue life prediction of additive manufacture structures of Ti-6Al-4V. Materials Science and Engineering: A, 669: 269-278. doi: 10.1016/j.msea.2016.05.073
[160]	Wang H, Liao H, Fan Z, Fan J, Stainier L, Li X, Li B. 2020. The Hot Optimal Transportation Meshfree (HOTM) method for materials under extreme dynamic thermomechanical conditions. Computer Methods in Applied Mechanics and Engineering, 364: 112958. doi: 10.1016/j.cma.2020.112958
[161]	Wang P, Lei H, Zhu X, et al. 2019. Influence of manufacturing geometric defects on the mechanical properties of AlSi10Mg alloy fabricated by selective laser melting. Journal of Alloys and Compounds, 789: 852-859. doi: 10.1016/j.jallcom.2019.03.135
[162]	Wang P, Zhou H, Zhang L, et al. 2020. In situ X-ray micro-computed tomography study of the damage evolution of prefabricated through-holes in SLM-Printed AlSi10Mg alloy under tension. Journal of Alloys and Compounds, 821: 153576. doi: 10.1016/j.jallcom.2019.153576
[163]	Wang S, Zhu L, Dun Y. Yang Z, His Fuh J Y, Yan W. 2021. Multi-physics modeling of direct energy deposition process of thin-walled structures: Defect analysis. Computational Mechanics, 67: 1229-1242. doi: 10.1007/s00466-021-01992-9
[164]	Wang T, He X, Wang J, et al. 2021. Detail fatigue rating method based on bimodal weibull distribution for DED Ti-6.5Al-2Zr-1Mo-1V titanium alloy. Chinese Journal of Aeronautics, 40: 1-13.
[165]	Wang X, He X, Wang T, et al. 2019. Internal pores in DED Ti-6.5Al-2Zr-Mo-V alloy and their influence on crack initiation and fatigue life in the mid-life regime. Additive Manufacturing, 28: 373-393. doi: 10.1016/j.addma.2019.05.007
[166]	Wang Y, Chen F, Wang M Y. 2017. Concurrent design with connectable graded microstructures. Computer Methods in Applied Mechanics and Engineering, 317: 84-101. doi: 10.1016/j.cma.2016.12.007
[167]	Wang Y, Gao J, Kang Z. 2018. Level set-based topology optimization with overhang constraint: Towards support-free additive manufacturing. Computer Methods in Applied Mechanics and Engineering, 339: 591-614. doi: 10.1016/j.cma.2018.04.040
[168]	Wang Y, Wang M Y, Chen F. 2016a. Structure-material integrated design by level sets. Structural and Multidisciplinary Optimization, 54: 1145-1156. doi: 10.1007/s00158-016-1430-5
[169]	Wang Y, Zhang L, Wang M Y. 2016b. Length scale control for structural optimization by level sets. Computer Methods in Applied Mechanics and Engineering, 305: 891-909. doi: 10.1016/j.cma.2016.03.037
[170]	Wang Z, Yan W, Liu W K, Liu M. 2019. Powder-scale multi-physics modeling of multi-layer multi-track selective laser melting with sharp interface capturing method. Computational Mechanics, 63: 649-661. doi: 10.1007/s00466-018-1614-5
[171]	Wei H L, Knapp G L, Mukherjee T, DebRoy T. 2019. Three-dimensional grain growth during multi-layer printing of a nickel based alloy Inconel 718. Additive Manufacturing, 25: 448-459. doi: 10.1016/j.addma.2018.11.028
[172]	Wei H L, Mukherjee T, Zhang W, Zuback J S, Knapp G L, De A, DebRoy T. 2021. Mechanistic models for additive manufacturing of metallic components. Progress in Materials Science, 116: 100703. doi: 10.1016/j.pmatsci.2020.100703
[173]	Wessels H, Bode T, Weibenfels C, Wriggers P, Zohdi T I. 2019. Investigation of heat source modeling for selective laser melting. Computational Mechanics, 63: 949-970. doi: 10.1007/s00466-018-1631-4
[174]	Wu J, Clausen A, Sigmund O. 2017. Minimum compliance topology optimization of shell-infill composites for additive manufacturing. Computer Methods in Applied Mechanics and Engineering, 326: 358-375. doi: 10.1016/j.cma.2017.08.018
[175]	Wu J, Aage N, Westermann R, Sigmund O. 2018. Infill optimization for additive manufacturing—Approaching bone-like porous structures. IEEE Trans Vis Comput Graph, 24: 1127-1140. doi: 10.1109/TVCG.2017.2655523
[176]	Wu J, Wang W, Gao X. 2021. Design and optimization of conforming lattice structures. IEEE Trans Vis Comput Graph, 27: 43-56. doi: 10.1109/TVCG.2019.2938946
[177]	Wu Z, Wu S, Bao J, et al. 2021. The effect of defect population on the anisotropic fatigue resistance of AlSi10Mg alloy fabricated by laser powder bed fusion. International Journal of Fatigue, 151: 106317. doi: 10.1016/j.ijfatigue.2021.106317
[178]	Wu Z, Xia L, Wang S, Shi T. 2019. Topology optimization of hierarchical lattice structures with substructuring. Computer Methods in Applied Mechanics and Engineering, 345: 602-617. doi: 10.1016/j.cma.2018.11.003
[179]	Xia L, Breitkopf P. 2014. Concurrent topology optimization design of material and structure within FE² nonlinear multiscale analysis framework. Computer Methods in Applied Mechanics and Engineering, 278: 524-542. doi: 10.1016/j.cma.2014.05.022
[180]	Xiao M, Liu X, Zhang Y, Gao L, Gao J, Chu S. 2021. Design of graded lattice sandwich structures by multiscale topology optimization. Computer Methods in Applied Mechanics and Engineering, 384: 113949. doi: 10.1016/j.cma.2021.113949
[181]	Xie C, Wu S, Yu Y, et al. 2021. Defect-correlated fatigue resistance of additively manufactured Al-Mg4.5Mn alloy with in situ micro-rolling. Journal of Materials Processing Technology, 291: 117039. doi: 10.1016/j.jmatprotec.2020.117039
[182]	Xin H, Correia J A F O, Veljkovic M, et al. 2021. Probabilistic strain-fatigue life performance based on stochastic analysis of structural and WAAM-stainless steels. Engineering Failure Analysis, 127: 105495. doi: 10.1016/j.engfailanal.2021.105495
[183]	Xiong F, Huang C, Kafka O L, Lian Y, Yan W, Chen M, Fang D. 2021. Grain growth prediction in selective electron beam melting of Ti-6Al-4V with a cellular automaton method. Materials & Design, 199: 109410.
[184]	Xiong Y, Yao S, Zhao Z L, Xie Y M. 2020. A new approach to eliminating enclosed voids in topology optimization for additive manufacturing. Additive Manufacturing, 32: 101006. doi: 10.1016/j.addma.2019.101006
[185]	Xu T, Cui Y, Ma S, Wang J, Liu C. 2021. Exploring the inclined angle limit of fabricating unsupported rods structures by pulse hot-wire arc additive manufacturing. Journal of Materials Processing Technology, 295: 117160. doi: 10.1016/j.jmatprotec.2021.117160
[186]	Xue Y, Pascu A, Horstemeyer M F, et al. 2010. Microporosity effects on cyclic plasticity and fatigue of LENS^TM-processed steel. Acta Materialia, 58: 4029-4038. doi: 10.1016/j.actamat.2010.03.014
[187]	Xue L, Xiao J, Nie Z, et al. 2021. Dynamic response of Ti-6.5Al-1Mo-1V-2Zr-0.1B alloy fabricated by wire arc additive manufacturing. Materials Science & Engineering A, 800: 140310.
[188]	Yadollahi A, Mahtabi M J, Khalili A, et al. 2018. Fatigue life prediction of additively manufactured material: Effects of surface roughness, defect size, and shape. Fatigue & Fracture of Engineering Materials & Structures, 41: 1602-1614.
[189]	Yan S, Huang Y, Zhao D, Niu F, Ma G, Wu D. 2019. 3D printing of nano-scale Al2O3-ZrO2 eutectic ceramic: Principle analysis and process optimization of pores. Additive Manufacturing, 28: 120-126. doi: 10.1016/j.addma.2019.04.024
[190]	Yan W, Lian Y, Yu C, Kafka O L, Liu Z, Liu W K, Wagner G J. 2018a. An integrated process-structure-property modeling framework for additive manufacturing. Computer Methods in Applied Mechanics and Engineering, 339: 184-204. doi: 10.1016/j.cma.2018.05.004
[191]	Yan W, Qian Y, Ge W, Lin S. Liu W K, Lin F, Wagner G J. 2018b. Meso-scale modeling of multiple-layer fabrication process in selective electron beam melting: Inter-layer/track voids formation. Materials and Design, 141: 210-219. doi: 10.1016/j.matdes.2017.12.031
[192]	Yang M, Wang L, Yan W. 2021. Phase-field modeling of grain evolutions in additive manufacturing from nucleation, growth, to coarsening. Npj Computational Materials, 7: 56. doi: 10.1038/s41524-021-00524-6
[193]	Zaretsky E, Stern A, Frage N. 2017. Dynamic response of AlSi10Mg alloy fabricated by selective laser melting. Materials Science and Engineering A, 688: 364-370. doi: 10.1016/j.msea.2017.02.004
[194]	Zhan Z, Li H. 2021. Machine learning based fatigue life prediction with effects of additive manufacturing process parameters for printed SS 316L. International Journal of Fatigue, 142: 105941. doi: 10.1016/j.ijfatigue.2020.105941
[195]	Zhang H, Wang Y, Kang Z. 2019. Topology optimization for concurrent design of layer-wise graded lattice materials and structures. International Journal of Engineering Science, 138: 26-49. doi: 10.1016/j.ijengsci.2019.01.006
[196]	Zhang Q, Xie J, London T, et al. 2019. Estimates of the mechanical properties of laser powder bed fusion Ti-6Al-4V parts using finite element models. Materials & Design, 169: 107678.
[197]	Zhang W, Li D, Zhang J, Guo X. 2016. Minimum length scale control in structural topology optimization based on the Moving Morphable Components (MMC) approach. Computer Methods in Applied Mechanics and Engineering, 311: 327-55. doi: 10.1016/j.cma.2016.08.022
[198]	Zhang W, Sun S. 2006. Scale-related topology optimization of cellular materials and structures. International Journal for Numerical Methods in Engineering, 68: 993-1011. doi: 10.1002/nme.1743
[199]	Zhang W, Zhou L. 2018. Topology optimization of self-supporting structures with polygon features for additive manufacturing. Computer Methods in Applied Mechanics and Engineering, 334: 56-78. doi: 10.1016/j.cma.2018.01.037
[200]	Zhang Z D, Ibhadode O, Ali U, Dibia C F, Rahnama P, Bonakdar A, Toyserkani E. 2020. Topology optimization parallel-computing framework based on the inherent strain method for support structure design in laser powder-bed fusion additive manufacturing. International Journal of Mechanics and Materials in Design, 16: 897-92. doi: 10.1007/s10999-020-09494-x
[201]	Zhao S, Yuan K, Guo W, et al. 2020. A comparative study of laser metal deposited and forged Ti-6Al-4V alloy: Uniaxial mechanical response and vibration fatigue properties. International Journal of Fatigue, 136: 105629. doi: 10.1016/j.ijfatigue.2020.105629
[202]	Zheng M, Wei L, Chen J, et al. 2019. A novel method for the molten pool and porosity formation modeling in selective laser melting. International Journal of Heat and Mass Transfer, 140: 1091-1105. doi: 10.1016/j.ijheatmasstransfer.2019.06.038
[203]	Zhou M, Lazarov B S, Wang F, Sigmund O. 2015. Minimum length scale in topology optimization by geometric constraints. Computer Methods in Applied Mechanics and Engineering, 293: 266-282. doi: 10.1016/j.cma.2015.05.003
[204]	Zhou Y, Nomura T, Saitou K. 2019. Multicomponent topology optimization for additive manufacturing with build volume and cavity free constraints. Journal of Computing and Information Science in Engineering, 19: 021011. doi: 10.1115/1.4042640
[205]	Zhu J, Zhou H, Wang C, Zhou L, Yuan S, Zhang W. 2021. A review of topology optimization for additive manufacturing: Status and challenges. Chinese Journal of Aeronautics, 34: 91-110.