【新文速递】2025年1月2日固体力学SCI期刊最新文章

 

今日更新：International Journal of Solids and Structures 1 篇，International Journal of Plasticity 4 篇，Thin-Walled Structures 6 篇

International Journal of Solids and Structures

Non-local orthotropic damage-plastic model for 3D printed materials

Denis Linardi, Elisabetta Monaldo, Sonia Marfia

doi:10.1016/j.ijsolstr.2024.113210

3D打印材料的非局部正交各向异性损伤塑性模型

A non-local orthotropic damage and plasticity phenomenological model for 3D printed materials is presented. The model specifically refers to 3D printed structural elements realized with an extrusion-based technique and made with thermoplastic materials. The structural behaviour of the 3D printed component is described with a laminate finite element model based on the first-order shear deformation theory. Each layer of the laminate is described with a non-local orthotropic damage and plastic model. Indeed, the overall mechanical response of 3D printed materials is significantly influenced by plasticity and damage mechanisms that can lead to a range of failure modes from brittle-like to ductile. The proposed orthotropic damage model is based on the introduction of three different damage parameters. Each of them describes a specific damage mechanism, i.e. fiber breakage, fiber detachment and delamination, that is clearly visible from the analysis of the 3D printed samples subjected to experimental tests. Some applications are carried out and the numerical results are compared with experimental results available in literature, highlighting the effectiveness of the proposed modelling technique.

提出了3D打印材料的非局部正交各向异性损伤和塑性现象学模型。该模型具体指的是采用基于挤出技术并由热塑性材料制成的3D打印结构元件。 采用基于一阶剪切变形理论的层合有限元模型描述了3D打印部件的结构行为。用非局部正交各向异性损伤和塑性模型描述了层合板的每一层。事实上，3D打印材料的整体力学响应受到塑性和损伤机制的显著影响，这可能导致从脆性到延性的一系列失效模式。提出的正交各向异性损伤模型是在引入三种不同损伤参数的基础上建立的。每一种都描述了一种特定的损伤机制，即纤维断裂、纤维脱离和分层，这从经过实验测试的3D打印样品的分析中可以清楚地看到。将数值结果与文献中的实验结果进行了比较，强调了所提出的建模技术的有效性。

International Journal of Plasticity

Multiscale modeling of the damage and fracture behaviours of TA15 titanium alloy with trimodal microstructure

M.Y. Fei, P.F. Gao, Z.N. Lei, H.W. Li, M. Zhan, M.W. Fu

doi:10.1016/j.ijplas.2024.104238

TA15钛合金三模态组织损伤断裂行为的多尺度模拟

Trimodal microstructure, consisting of equiaxed α (αp), lamellar α (αl), and transformed β (βt), has become an ideal target microstructure of titanium alloys. However, the complex microstructure morphologies and the differences in mechanical property among the three constituent phases of the trimodal microstructure significantly influence its microscopic crack propagation behaviour and further affect its fracture toughness. To address this issue, a multiscale finite element (FE) model, including a microscopic crack propagation (micro-CP) model and a macroscopic fracture toughness (macro-FT) model, was established for analysis and prediction of the damage fracture behaviour and property of the trimodal microstructure. In this model, the deformation, damage and fracture behaviours of the trimodal microstructure at both micro and macro scales were described by bridging the constitutive laws of constituent phases and deformation responses. In tandem with this, the micro-CP model adopted a macro-micro nested structure, and the macro-FT model was developed based on a virtual fracture toughness test. Using the established multiscale FE model, the dependence of microscopic crack propagation and macroscopic fracture behaviours on the constituent phases of the trimodal microstructure was revealed. It is found that both αp and αl improved the path tortuosity and energy consumption of microscopic crack propagation, and αl decreased the microscopic crack propagation rate simultaneously. In addition, αp and αl contributed to the fracture toughness of the trimodal microstructure from both the intrinsic toughening mechanism (suppressing the heterogeneous deformation and damage and then decreasing the strength and increasing the plasticity) and the extrinsic toughening mechanism (increasing the tortuosity and energy consumption of crack propagation). The research provided an in-depth understanding of the damage and fracture behaviours of TA15 titanium alloy with the trimodal microstructure.

由等轴α（αp）、层片α（αl）和转变β（βt）组成的三相微结构已成为钛合金的理想目标微结构。然而，这种复杂微结构的形态以及三相成分之间机械性能的差异显著影响其微观裂纹扩展行为，并进一步影响其断裂韧性。为解决这一问题，建立了包含微观裂纹扩展（micro-CP）模型和宏观断裂韧性（macro-FT）模型的多尺度有限元（FE）模型，用于分析和预测三相微结构的损伤断裂行为和性能。在该模型中，通过连接各组成相的本构定律和变形响应，描述了三相微结构在微观和宏观尺度上的变形、损伤和断裂行为。同时，micro-CP 模型采用了宏观-微观嵌套结构，而 macro-FT 模型则是基于虚拟断裂韧性测试开发的。利用已建立的多尺度有限元模型，揭示了三相微结构的组成相对于微观裂纹扩展和宏观断裂行为的影响。研究发现，αp 和 αl 均提高了微观裂纹扩展的路径曲折度和能量消耗，同时 αl 还降低了微观裂纹扩展速率。此外，αp 和 αl 从内在增韧机制（抑制异质变形和损伤，从而降低强度并提高塑性）和外在增韧机制（增加裂纹扩展的曲折度和能量消耗）两方面提高了三相微结构的断裂韧性。该研究为具有三相微结构的 TA15 钛合金的损伤和断裂行为提供了深入的理解。

A thermodynamically consistent phase-field model for frictional fracture in rocks

Sijia Liu, Yunteng Wang

doi:10.1016/j.ijplas.2024.104220

岩石摩擦断裂的热力学一致相场模型

Frictional fracture phenomena in geological media are often closely related to fault instability in earthquakes and slip surface formation in geohazards. In this work, we propose a new phase-field model for capturing frictional fractures in pressure-sensitive geomaterials. Our model has three novel features: (i) a thermodynamically consistent energetic interface for contact and friction conditions; (ii) incorporation of a level set function to couple phase-field evolution and frictional-contact slips; and (iii) a transition from stored energy to yielding for describing different plastic-like frictional stick–slip fractures. Based on the energy conservation law and a variational inequality of virtual work, we formulate the governing equations for frictional fractures, including the dynamic equilibrium equation, phase-field evolution law, and most importantly, frictional interface plastic-like driving forces. We also present a robust numerical technique to handle the spatiotemporal formation and evolution of frictional fractures in rocks. We validate the model by simulating several benchmark examples. Our model is shown to reproduce both frictional stick and slip phenomena in rocks. We also apply this model to study the effect of confining pressure on frictional crack initiation and propagation in rocks, which helps us better understand the deep mechanisms of frictional fracture.

地质介质中的摩擦断裂现象往往与地震中的断层失稳和地质灾害中的滑面形成密切相关。在这项工作中，我们提出了一种新的相场模型，用于捕获压力敏感岩土材料中的摩擦裂缝。我们的模型具有三个新特征：(i)接触和摩擦条件下的热力学一致的能量界面；（ii）结合一个水平集函数来耦合相场演化和摩擦接触滑移；(3)从存储能量到屈服的过渡，用于描述不同的类塑性粘滑摩擦裂缝。基于能量守恒定律和虚功的变分不等式，建立了摩擦断裂的控制方程，包括动力学平衡方程、相场演化定律，以及最重要的摩擦界面类塑性驱动力。我们还提出了一种强大的数值技术来处理岩石中摩擦裂缝的时空形成和演化。我们通过模拟几个基准示例来验证模型。我们的模型被证明可以再现岩石中的摩擦粘和滑动现象。我们还应用该模型研究了围压对岩石摩擦裂纹萌生和扩展的影响，这有助于我们更好地理解摩擦破裂的深层机制。

Advancing material simulations: Physics-Informed Neural Networks and Object-Oriented Crystal Plasticity Finite Element Methods

Shahriyar Keshavarz, Yuwei Mao, Andrew C.E. Reid, Ankit Agrawal

doi:10.1016/j.ijplas.2024.104221

先进的材料模拟：物理信息神经网络和面向对象的晶体塑性有限元方法

An innovative method for predicting the behavior of crystalline materials is presented by integrating Physics-Informed Neural Networks (PINNs) with an object-oriented Crystal Plasticity Finite Element (CPFE) code within a large deformation framework. The CPFE platform is utilized to generate reference data for training the PINNs, ensuring precise and fast predictions of material responses. The object-oriented design of the CPFE system facilitates the coherent incorporation of complex constitutive models and numerical methods, enhancing simulation flexibility and scalability. To demonstrate the adaptability of this approach, two problems are addressed: a fundamental power-law and a complex dislocation density-based constitutive models for predicting the behavior of Ni3Al-based alloys. Both models are implemented within an object-oriented CPFE system powered by its flexible plug-in architecture. The resulting PINN model accurately captures intricate deformation mechanisms in crystalline materials, as validated through comparisons with CPFE simulations and experimental data. This work offers a promising alternative for efficient and accurate material behavior prediction, paving the way for advanced simulations in materials science.

本文提出了一种创新方法，通过将物理信息神经网络（PINNs）与面向对象的晶体塑性有限元（CPFE）代码集成在一个大变形框架内，来预测晶体材料的行为。CPFE 平台用于生成训练 PINNs 的参考数据，从而确保对材料响应进行精确且快速的预测。CPFE 系统的面向对象设计有助于将复杂的本构模型和数值方法进行一致整合，从而提高模拟的灵活性和可扩展性。为了展示该方法的适应性，解决了两个问题：一个是基本的幂律模型，另一个是基于位错密度的复杂本构模型，用于预测 Ni3Al 基合金的行为。这两个模型均在由其灵活的插件架构支持的面向对象 CPFE 系统中实现。通过与 CPFE 模拟和实验数据的比较验证，所得的 PINN 模型能够准确捕捉晶体材料中复杂的变形机制。这项工作为高效且准确地预测材料性能提供了一种很有前景的替代方案，为材料科学中的高级模拟铺平了道路。

Modeling inter- and intra-granular dislocation transport using crystal plasticity

Subhendu Chakraborty, Abigail Hunter, D.J. Luscher

doi:10.1016/j.ijplas.2024.104222

利用晶体塑性模拟晶间和晶内位错输运

This work presents the development of a crystal plasticity material model that incorporates both dislocation transport within grains and dislocation transfer across grain boundaries. This model has been implemented in the open-source finite element code MOOSE. In addition, a novel geometry-based criterion is developed to determine the direction of dislocation transfer across grain boundaries. The transfer criterion incorporates the geometric features of the grain boundary, such as the grain boundary plane normal, and its misorientation, which is accounted for through the orientation of the incoming and outgoing slip systems. The model is tested with several cases, including a copper single crystal, bi-crystal, and polycrystal. The development of the transfer criterion, implementation of the model, and its application to these test cases are discussed in detail.

这项工作提出了晶体塑性材料模型的发展，该模型结合了晶粒内的位错传递和跨晶界的位错传递。该模型已在开源有限元代码MOOSE中实现。此外，提出了一种新的基于几何的判据来确定位错跨晶界转移的方向。传递准则结合了晶界的几何特征，如晶界平面法向及其取向偏差，这是通过进出滑动系统的取向来解释的。该模型在几种情况下进行了测试，包括铜单晶，双晶和多晶。详细讨论了转移准则的开发、模型的实现及其在这些测试用例中的应用。

Thin-Walled Structures

Novel resonator concept for improved performance of locally resonant based metamaterials

F.A. Pires, R.F. Boukadia, M. Wandel, C. Thomas, E. Deckers, W. Desmet, C. Claeys

doi:10.1016/j.tws.2024.112866

改进局部共振基超材料性能的新谐振器概念

In the context of noise control engineering, locally resonant metamaterials (LRMs) have gained significant research attention over the past two decades due to their ability to combine lightweight, compact design with excellent noise and vibration insulation performance in targeted frequency ranges, known as stop bands. This paper proposes a novel resonator concept that achieves a high modal effective mass (MEF) for out-of-plane bending, aiming to widen the stop bands in LRMs. First, the dynamic motion of an idealized double-lever system, which inspired the resonator design, is analyzed. Then, a realizable resonator design is presented, along with an optimization scheme that maximizes the MEF, achieving values as high as 96.5%. The proposed resonator concept is used to develop an LRM solution to enhance the acoustic insulation performance of a structure relevant to the aerospace industry, yielding improvements of up to 9 dB in the frequency band of interest. Experimental results demonstrate that the designed LRM solution significantly improves the vibro-acoustic response of the system. Future work will consider additional aspects of the optimization process, including manufacturing constraints, costs, and robustness.

在噪声控制工程的背景下，局部谐振超材料（lrm）在过去的二十年中获得了重要的研究关注，因为它们能够将轻质，紧凑的设计与在目标频率范围内（称为阻挡带）的优异噪声和振动绝缘性能相结合。本文提出了一种新的谐振器概念，实现了高模态有效质量（MEF）的面外弯曲，旨在扩大lrm中的阻带。首先，分析了理想双杠杆系统的动态运动，该系统启发了谐振器的设计。然后，提出了一个可实现的谐振器设计，以及一个最大化MEF的优化方案，使MEF达到高达96.5%的值。提出的谐振器概念用于开发LRM解决方案，以增强与航空航天工业相关的结构的隔音性能，在感兴趣的频带内产生高达9 dB的改进。实验结果表明，所设计的LRM方案显著改善了系统的声振响应。未来的工作将考虑优化过程的其他方面，包括制造限制、成本和鲁棒性。

Torsional Restraint of Roof Sheeting on Cold-Formed Steel Hat Sections

John Papangelis, Chong Li, Liao Yi, Fangyuan Yue

doi:10.1016/j.tws.2024.112882

冷弯型钢顶板的抗扭约束

Cold-formed steel hat sections are commonly used as thin-walled beams to support thin profiled roof sheeting. Cold-formed steel sections are usually thinner than hot-rolled sections and have modes of failure which are not commonly encountered in hot-rolled structural steel design. The individual plate elements in cold-formed steel hat sections are normally thin compared with their width and so local and distortional buckling may occur before section yielding. In addition, cold-formed steel hat sections may undergo flexural-torsional buckling because of their low torsional stiffness. For cold-formed steel hat sections which may fail by flexural-torsional buckling, the roof sheeting provides a torsional restraint which can increase the flexural-torsional buckling capacity. Previous research has focused on determining the torsional restraint provided by roof sheeting to C and Z section purlins but no research has been done for hat sections. This paper describes a unique test procedure to determine the value of the torsional restraint provided by roof sheeting on hat sections for 12 different combinations of hat sections and roof sheeting profiles. Three tests for each combination were performed, resulting in a total of 36 tests. The results show that the torsional restraint increases as the depth or thickness of the hat section is increased and also when the sheeting thickness increases. A finite element flexural-torsional buckling analysis is also described for analysing hat sections with elastic continuous restraints, such as those provided by roof sheeting. The finite element analysis is validated with the theoretical solution for the flexural-torsional buckling of hat sections with torsional restraint and diaphragm shear restraint. An example is described to demonstrate the effect of torsional restraint and diaphragm shear restraint on the flexural-torsional buckling of hat sections subjected to uniformly distributed load. It is shown that including these restraints in the analysis will result in a significant increase in the flexural-torsional buckling load and the design load capacity.

冷弯型钢帽截面通常用作薄壁梁来支撑薄型屋面板。冷弯型钢通常比热轧型钢更薄，并且具有热轧型钢设计中不常见的失效模式。冷弯型钢帽截面中的单个板单元通常比其宽度薄，因此在截面屈服之前可能发生局部扭曲屈曲。此外，冷弯型钢帽截面由于其扭转刚度低，可能发生弯扭屈曲。对于可能受弯扭屈曲破坏的冷弯型钢帽型钢，顶板提供了扭转约束，可以增加弯扭屈曲能力。以往的研究主要集中在确定顶板对C、Z截面檩条的抗扭约束上，但对C、Z截面檩条的抗扭约束尚未进行研究。本文描述了一种独特的测试程序，用于确定12种不同的帽型和车顶板型的组合，车顶板对帽型提供的扭转约束值。对每种组合进行了三次测试，总共进行了36次测试。结果表明，扭转约束随帽段深度或厚度的增加而增大，随板层厚度的增加而增大。有限元弯扭屈曲分析也描述了分析具有弹性连续约束的帽段，例如由屋面板提供的那些。通过有限元分析验证了具有扭转约束和膜片剪切约束的帽形截面弯曲-扭转屈曲的理论解。通过算例验证了扭转约束和膜片剪切约束对均布荷载作用下帽形截面弯扭屈曲的影响。结果表明，在分析中加入这些约束将导致弯扭屈曲载荷和设计载荷能力的显著增加。

Nonlinear Vibration-acoustic Analysis of the Coupled System of Flexible Cylindrical Shell Foundation and HSLDS Vibration Isolator

Junfeng Liu, Jingjun Lou, Kai Chai, Qingchao Yang

doi:10.1016/j.tws.2024.112896

柔性圆柱壳基础与HSLDS隔振器耦合系统的非线性振动-声分析

This paper is concerned with the vibration and acoustic radiation problems of the coupled system of mass oscillator, high-static-low-dynamic stiffness (HSLDS) isolator and flexible stiffened cylindrical shell immersed in an infinite acoustic medium. A frequency domain numerical calculation method is proposed. The HSLDS isolator is fitted by odd-order polynomials, and the periodic solution of the deformation of the HSLDS isolator spring is expanded into a superimposed harmonic function. The dynamic stiffness matrix of the stiffened cylindrical shell is established by the wave propagation method, and the force of the external acoustic fluid on the shell is introduced by the Helmholtz boundary integral equation, and the acoustic radiation calculation is carried out. Based on the force and displacement continuity conditions and the interface compatibility conditions between the structure and the acoustic medium, the dynamic stiffness matrix of the mass-spring-damper system, the stiffened cylindrical shell and the external fluid coupling is established, and the harmonic balance method and Newton-like solver are used to solve it. By comparing the solutions of the finite element method and the boundary element method, the accuracy of the method is verified, and the predicted results are in good agreement with the reference results. The effects of circumferential wave modes and the number of axially discrete 3-node elements of cylindrical shells on the vibration and radiated acoustic response of nonlinear coupling systems are studied. The effects of HSLDS isolators, damping and the amplitude of external loads on the vibration and acoustic radiation behavior of the coupling system are studied, and the influences of HSLD isolators on shell vibration and acoustic radiation propagation are analyzed, which can provide useful guidance for the vibration isolation design and optimization of underwater rigid-flexible coupling systems.

研究了质量振子、高静低动刚度（HSLDS）隔振器和柔性加筋圆柱壳在无限大声介质中的耦合系统的振动和声辐射问题。提出了一种频域数值计算方法。采用奇阶多项式对HSLDS隔振器进行拟合，将HSLDS隔振器弹簧变形的周期解展开为叠加谐波函数。采用波传播法建立加劲圆柱壳的动力刚度矩阵，采用亥姆霍兹边界积分方程引入外声流体对壳体的作用力，并进行声辐射计算。基于力和位移连续条件和结构与声介质界面相容条件，建立了质量-弹簧-阻尼器系统、加劲圆柱壳和外部流体耦合的动态刚度矩阵，并采用谐波平衡法和类牛顿求解器对其进行求解。通过比较有限元法和边界元法的解，验证了该方法的准确性，预测结果与参考结果吻合较好。研究了圆柱壳的周向波模态和轴向离散3节点单元数对非线性耦合系统振动和辐射声响应的影响。研究了HSLD隔振器、阻尼和外载荷幅值对耦合系统振动和声辐射特性的影响，分析了HSLD隔振器对壳体振动和声辐射传播的影响，为水下刚柔耦合系统的隔振设计和优化提供了有益的指导。

Impact properties and damage assessment of unidirectional aramid/carbon fiber hybrid reinforced polymer composites

Xiaogang Liu, Weichen Kong, Siqi Song, Anni Wang

doi:10.1016/j.tws.2024.112898

单向芳纶/碳纤维杂化增强聚合物复合材料的冲击性能及损伤评估

To improve the impact resistance of unidirectional carbon fiber-reinforced polymer (CFRP) composites, unidirectional aramid/carbon fiber hybrid-reinforced polymer (A/CFHRP) composites were developed. Through a series of low-speed impact tests, ultrasonic scanning, CT scanning, and post-impact compression tests, the study examined the impact response, damage modes, and severity of damage in A/CFHRP composites with varying fiber volume ratios. Additionally, the residual properties after impact were assessed. The findings revealed that the incorporation of aramid fibers significantly enhances the impact resistance of CFRP. As the aramid fiber content increased, the specific energy absorption of A/CFHRP initially increased and then decreased, indicating an upper limit to the improvement in impact resistance provided by aramid, which is dependent on the impact energy. The maximum specific energy absorption of A/CFHRP is 46% higher than that of CFRP. The introduction of aramid fibers transforms the damage mode of CFRP from brittle fracture to interlayer delamination and interface debonding, thereby preserving higher structural integrity and superior post-impact residual performance. After 10J impact energy, the strength retention rate of A/CFRP after impact is 81.2% higher than that of CFRP; after 50J impact energy, the strength retention rate of A/CFRP after impact is 37.4% higher than that of CFRP

为了提高单向碳纤维增强聚合物（CFRP）复合材料的抗冲击性能，研制了单向芳纶/碳纤维混合增强聚合物（A/CFHRP）复合材料。通过一系列低速冲击试验、超声扫描、CT扫描和冲击后压缩试验，研究了不同纤维体积比下a /CFHRP复合材料的冲击响应、损伤模式和损伤严重程度。此外，还对冲击后的残余性能进行了评估。结果表明，芳纶纤维的掺入显著提高了CFRP的抗冲击性。随着芳纶纤维含量的增加，A/CFHRP的比能量吸收率先升高后降低，说明芳纶提高抗冲击性能的能力有一个上限，这取决于冲击能量。A/CFHRP的最大比能量吸收比CFRP高46%。芳纶纤维的引入使CFRP的损伤模式从脆性断裂转变为层间分层和界面脱粘，从而保持了较高的结构完整性和优异的冲击后残留性能。10J冲击能量后，A/CFRP的强度保持率比CFRP高81.2%；50J冲击能量后，A/CFRP的强度保持率比CFRP高37.4%

Material performance, manufacturing methods, and engineering applications in aviation of Carbon fiber reinforced polymers: A comprehensive review

Xiangyu Xu, Gongqiu Peng, Baoyan Zhang, Fenghui Shi, Liang Gao, Junpeng Gao

doi:10.1016/j.tws.2024.112899

碳纤维增强聚合物材料性能、制造方法及其在航空工程中的应用综述

Carbon fiber reinforced polymers (CFRP) is becoming the predominant material in the aviation industry due to its excellent performance including light weight, high specific strength, high specific modulus, excellent fatigue fracture resistance, corrosion resistance, strong design flexibility, and suitability for the overall molding of large components. The application parts of CFRP are almost all over the aircrafts, such as wings, tails, fuselages, landing gears, engines and other parts. The proportion of fiber reinforced polymer matrix composites (PMCs) has become an essential indicator of aircrafts in practical engineering applications. This paper provides an overview of the background and evolution of CFRPs followed by an introduction to the material properties of carbon fibers (CFs) and different resin matrices. Subsequently, the principle and characteristics of the commonly used manufacturing methods of CFRP are presented. Next, the material performance of both thermosetting and thermoplastic CFRP are provided. Finally, the applications in aviation and the developing trends of CFRP are described. This review aims to offer researchers a comprehensive reference on the material performance and applications of CFRP within the aviation field while providing valuable insights for future PMC advancements.

碳纤维增强聚合物（CFRP）具有重量轻、比强度高、比模量高、抗疲劳断裂、耐腐蚀、设计柔韧性强、适合大型部件整体成型等优点，正成为航空工业的主导材料。CFRP的应用部件几乎遍及飞机的各个部位，如机翼、尾翼、机身、起落架、发动机等部件。在实际工程应用中，纤维增强聚合物基复合材料（PMCs）的比例已成为飞机性能的重要指标。本文概述了碳纤维纤维的背景和发展，然后介绍了碳纤维（CFs）和不同树脂基体的材料特性。随后，介绍了碳纤维增强塑料的常用制造方法的原理和特点。其次，介绍了热固性和热塑性CFRP的材料性能。最后介绍了碳纤维布在航空领域的应用及发展趋势。本综述旨在为研究人员提供碳纤维增强塑料在航空领域的材料性能和应用的综合参考，同时为未来碳纤维增强塑料的发展提供有价值的见解。

From the Yoshimura origami pattern to foldable structures: Exploration of crease design

Zhitong Fei, Dongyang Xu, Yanzhi Zhao, Zhen Han, Linquan Song, Ruibao Ma, Yulin Guo

doi:10.1016/j.tws.2024.112888

从吉村折纸图案到可折叠结构：折痕设计的探索

Crease design is crucial to the function and application scope of origami projects; however, for the Yoshimura origami pattern, the connection between origami two-dimensional (2D) creases and three-dimensional (3D) forms has not been established, which greatly limits the research and application of origami structures. In this paper, a crease design theory for the Yoshimura origami pattern is proposed to create 3D foldable origami structures. Afterward, the flat origami folding process is described, and the corresponding end trajectory equations are derived from a crease chain folding analysis performed on the element block and the expansion block. Next, the positional and angular constraint equations for single-variable, double-variable, and triple-variable foldable forms with only element blocks are systematically discussed. Finally, a detailed folding simulation analysis is performed based on the positional and angular constraint equations, and the foldable form family diagrams with the corresponding angular value intersection curve constraints are summarized. The theory is verified by finite element programs and experiments. This work provides an effective theory for the design of origami creases and new ideas and methods for the study of the Yoshimura pattern and other origami patterns.

折痕设计对折纸项目的功能和应用范围至关重要；然而，对于吉村折纸图案，折纸二维（2D）折痕与三维（3D）折痕之间的联系尚未建立，这极大地限制了折纸结构的研究和应用。本文提出了一种吉村折纸图案的折痕设计理论，用于创建三维可折叠折纸结构。然后，描述了平面折纸的折叠过程，并通过对单元块和膨胀块进行折痕链折叠分析，推导了相应的末端轨迹方程。其次，系统地讨论了单变量、双变量和三变量仅包含单元块的可折叠形式的位置和角度约束方程。最后，基于位置约束方程和角度约束方程进行了详细的折叠仿真分析，总结了具有相应角值相交曲线约束的可折叠形式族图。通过有限元程序和实验对理论进行了验证。本工作为折纸折痕的设计提供了有效的理论依据，也为吉村图案等折纸图案的研究提供了新的思路和方法。