【新文速递】2023年9月30日固体力学SCI期刊最新文章

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今日更新：International Journal of Solids and Structures 2 篇，Journal of the Mechanics and Physics of Solids 1 篇，Computer Methods in Applied Mechanics and Engineering 1 篇，Thin-Walled Structures 2 篇

International Journal of Solids and Structures

Computation of the crack opening displacement in the phase-field model

Chen Lin, Wang Zhao, Li Bin, de Borst René

doi:10.1016/j.ijsolstr.2023.112496

相场模型中裂缝张开位移的计算

The phase-field model treats discrete cracks in a smeared sense by a regularisation technique. It holds attractive properties: there is no need to consider cracks as geometric discontinuities, and it avoids remeshing around crack tips. The method has been employed in the analysis of brittle and cohesive fracture problems. In the brittle fracture model, a Griffith-like energy functional is used in the simulation, while in the cohesive fracture model, the fracturing problem exploits a displacement jump governed energy functional. Obviously, the displacement jump is crucial in the cohesive fracture model and in certain other applications, e.g. for hydraulic fracturing. In the current study, the approximated form of the crack opening displacement is derived for the brittle and cohesive fracture models. In both models, the crack opening displacement is associated with a line integral normal to the crack, but different factors in front of the integral apply. The derived integrals are verified analytically in a one-dimensional setting and numerically in multi-dimensional set-ups, featuring straight and curved cracks.

相场模型通过正则化技术，在抹平的意义上处理离散裂缝。它具有以下诱人的特性：无需将裂纹视为几何不连续性，而且避免了裂纹尖端周围的重合。该方法已被用于分析脆性和内聚性断裂问题。在脆性断裂模型中，模拟使用了类似格里菲斯的能量函数，而在内聚断裂模型中，断裂问题利用了受位移跃迁支配的能量函数。显然，位移跃迁在内聚压裂模型和某些其他应用（如水力压裂）中至关重要。在当前的研究中，针对脆性和内聚性断裂模型推导出了裂缝张开位移的近似形式。在这两种模型中，裂缝张开位移都与裂缝法线积分有关，但积分前的系数不同。推导出的积分在一维环境下进行了分析验证，在多维环境下进行了数值验证，包括直线和曲线裂缝。

Simple tension three ways

Murphy J.G.

doi:10.1016/j.ijsolstr.2023.112497

三种简单的拉力方式

The consequences of using a principal Cauchy stress formulation of simple tension of cuboid specimens are explored within the context of incompressible isotropic materials, with the prototypical neo-Hookean material used to illustrate the main ideas. When simple tension is defined in this way it is shown that there are three natural Cartesian forms for the Cauchy stress: the conventional form, a plane stress form and a uniform stress form. A deformation consistent with each of these forms is obtained for the neo-Hookean material and it is shown that that there are some counter-intuitive effects. It is also shown that the plane stress form of simple tension could alternatively describe the effect of applying equal and opposite forces to opposite edges of a cuboid specimen, with the uniform stress form describing the effect of applying these forces to opposite corners of a cuboid.

在不可压缩各向同性材料的背景下，探讨了对立方体试样的简单拉伸使用主考赫应力公式的后果，并使用新胡克材料原型来说明主要观点。以这种方式定义简单拉伸时，可以发现考奇应力有三种自然的笛卡尔形式：传统形式、平面应力形式和均匀应力形式。对于新胡肯材料，可以得到与上述每种形式一致的变形，并证明存在一些反直觉效应。研究还表明，简单拉伸的平面应力形式可替代描述在长方体试样的相对边缘施加等效和相反力的效果，而均匀应力形式则描述在长方体的相对角上施加这些力的效果。

Journal of the Mechanics and Physics of Solids

A nanofibril network model of biological silks

Yan Yi, Shao Yue, Zhao Hong-Ping, Feng Xi-Qiao, Deng Zi-Chen

doi:10.1016/j.jmps.2023.105448

生物丝的纳米纤维网络模型

Biological silks produced by, for examples, spiders and silkworms exhibit exceptional mechanical properties, including high strength, toughness, and extensibility, which arise from their optimized hierarchical structures. Understanding the relationship between their structures and properties is crucial for the design of bioinspired materials. However, it remains a challenge to recapitulate their macroscopic mechanical behaviors of biological silks with a micromechanical model that integrates the physical mechanisms of deformation and failure, such as molecular unfolding and nanofibrous remodeling. In this paper, we propose a nanofibril network (NFN) model to analyze the deformation, damage, and fracture processes of biological silks. The NFN model reveals how molecular unfolding affects the deformation and fracture of biological silks at the nanofibril scale. It is observed that molecular unfolding consecutively occurs, evolving into band or elliptical morphologies with increasing tensile strain. Intermolecular hydrogen bonds tend to stabilize the expansion of unfolding zones. The NFN model also unveils how the instability of molecular unfolding is suppressed by nanofibrous architecture and how intermolecular hydrogen bonds interact with intramolecular unfolding to toughen the biological silk. This work provides a theoretical tool for studying and designing biomimetic nanofibrous materials.

由蜘蛛和家蚕等生产的生物丝具有优异的机械性能，包括高强度、韧性和延展性，这些都源于其优化的分层结构。了解其结构与性能之间的关系对于设计生物启发材料至关重要。然而，如何通过微观力学模型再现生物蚕丝的宏观力学行为仍是一个挑战，该模型整合了变形和失效的物理机制，如分子展开和纳米纤维重塑。在本文中，我们提出了一种纳米纤维网（NFN）模型来分析生物蚕丝的变形、损伤和断裂过程。NFN 模型揭示了分子折叠如何在纳米纤维尺度上影响生物蚕丝的变形和断裂。据观察，随着拉伸应变的增加，分子连续发生解折，并演变成带状或椭圆形形态。分子间氢键倾向于稳定解折区的扩展。NFN 模型还揭示了纳米纤维结构如何抑制分子解折的不稳定性，以及分子间氢键如何与分子内解折相互作用以增强生物蚕丝的韧性。这项工作为研究和设计仿生物纳米纤维材料提供了理论工具。

Computer Methods in Applied Mechanics and Engineering

The quad layout immersion: A mathematically equivalent representation of a surface quadrilateral layout

Shepherd Kendrick M., Hiemstra René R., Hughes Thomas J.R.

doi:10.1016/j.cma.2023.116445

四边形布局沉浸：表面四边形布局的数学等价表示法

Quadrilateral layouts on surfaces are essential for defining quadrilateral meshes, for fitting splines for engineering design and analysis, and for texture mapping in computer graphics. Previous work has characterized such layouts as a special mapping with extensive integer constraints, as a special metric on a surface, or as a meromorphic quartic differential with finite trajectories. In this work, a surface quadrilateral layout is alternatively characterized as a special immersion of a cut representation of the surface into the Euclidean plane. We call this a quad layout immersion. This characterization, while posed in smooth topology, naturally generalizes to piecewise-linear representations. As such, it mathematically describes and generalizes integer grid maps, which represent the current state-of-the-art. Due to its generality, the proposed representation supports a range of different computational methods to extract quadrilateral layouts. This is demonstrated by several computational examples, including the extraction of quadrilateral layouts on a 1996 Dodge Neon.

曲面上的四边形布局对于定义四边形网格、工程设计和分析中的花键拟合以及计算机图形学中的纹理映射至关重要。以往的工作将这种布局描述为具有广泛整数约束的特殊映射、表面上的特殊度量或具有有限轨迹的单态四微分。在本研究中，曲面四边形布局的另一个特征是将曲面的切面表示特殊浸入欧几里得平面。我们称之为四边形布局浸入。这种表征虽然是在光滑拓扑中提出的，但可以自然地推广到片断线性表征中。因此，它在数学上描述并概括了代表当前最先进技术的整数网格映射。由于其通用性，所提出的表示法支持一系列不同的计算方法来提取四边形布局。几个计算实例证明了这一点，包括提取 1996 年道奇霓虹汽车上的四边形布局。

Thin-Walled Structures

Elastic effect on the final deflection of rigid-plastic square plates under pulse loading

Hu Qingjie, Zhu Ling, Yu T.X.

doi:10.1016/j.tws.2023.111238

脉冲加载下刚塑方形板最终挠度的弹性效应

Rigid-perfectly plastic (R-PP) models are widely employed in the study of structural impact dynamics. However, due to the complexity of dynamic elastic-plastic behavior and the limitations of numerical simulation, it is of great significance to evaluate the elastic effect on the structural response to pulse loading. This paper examines the validity of the R-PP theoretical solutions on large deflection of pulse-loaded square plates. First, by exploring the characteristic of “plastic membrane” and considering the effect of membrane forces and bending moments on energy dissipation, an energy ratio R and a characteristic time ratio are precisely defined. Then based on the R-PP complete solutions recently developed for square plates under rectangular pressure pulse, the discrepancies in final deflection and in saturated impulse between the R-PP theoretical predictions and the elastic-perfectly plastic (E-PP) simulation results are evaluated and elaborated. It is revealed that the discrepancy in final deflection is dependent on the dimensionless stiffness ζplate and the dimensionless pulse magnitude λ. Moreover, the discrepancies in final deflection are compared between square plates and beams via a thorough analysis of key parameters, indicating that most characteristics of the elastic effect are similar for both cases, i.e., the R-PP solutions for both square plates and beams can reliably provide theoretical predictions for engineering applications if energy ratios R>5, with no limitation on the pulse duration. With the same geometric and material parameters, however, the energy ratio R of square plates is about twice that of beams, the discrepancy in final deflection of plates is larger than that of beams, but the absolute value of the discrepancy in final deflection for the clamped square plates remains in the order of 1/(1.5R) and can be bounded by 1/[4λ(λ-1)].

刚性-完全塑性（R-PP）模型被广泛应用于结构冲击动力学研究中。然而，由于动态弹塑性行为的复杂性和数值模拟的局限性，评估弹性效应对脉冲加载结构响应的影响具有重要意义。本文研究了脉冲加载方形板大挠度的 R-PP 理论解的有效性。首先，通过探讨 "塑性膜 "的特性，并考虑膜力和弯矩对能量耗散的影响，精确定义了能量比 R 和特性时间比。然后，基于最近开发的矩形压力脉冲下方形板的 R-PP 完整解决方案，评估并阐述了 R-PP 理论预测与弹性全塑（E-PP）模拟结果之间在最终挠度和饱和冲量方面的差异。结果表明，最终挠度的差异取决于无量纲刚度 ζplate 和无量纲脉冲幅度 λ 有关。此外，通过对关键参数的深入分析，比较了方形板和横梁最终挠度的差异，表明两种情况下弹性效应的大部分特征是相似的，即如果能量比 R>5 且脉冲持续时间不受限制，方形板和横梁的 R-PP 解决方案都能为工程应用提供可靠的理论预测。然而，在几何和材料参数相同的情况下，方形板的能量比 R 约为梁的两倍，板的最终挠度偏差大于梁的最终挠度偏差，但夹紧方形板的最终挠度偏差的绝对值仍保持在 1/(1.5R)的数量级，并可由 1/[4λ(λ-1)]限定。

Postfire performance of pultruded wood-cored GFRP sandwich beams

Zhang Lingfeng, Liu Weiqing, Omar Ahmed Ahmad, Ling Zhibin, Yang Dongdong, Liu Yan

doi:10.1016/j.tws.2023.111240

拉挤木芯 GFRP 夹层梁的火后性能

Wood-cored sandwich components have been extensively used in constructions of buildings and bridges. However, the existing studies on the postfire behavior of these components are very limited. This study aims to quantitatively evaluate the postfire residual properties of the pultruded wood-cored GFRP sandwich (PWGS) beams. This paper mainly comprises three parts: (i) review of fire experiment of the PWGS beams; (ii) postfire bending experiments conducted on the PWGS beams with different fire scenarios and (iii) numerical study on thermal and postfire thermomechanical responses. It was found the failure modes mainly depended on the number of exposed sides and the fire damage degree. For the three-sided fire-exposed specimens (except for the one with a 25 mm-thick calcium silica board), the progressive tension rapture of the charred fibers was the dominant failure mode. The other specimens, however, exhibited the brittle in-plane shear failure of the web. Moreover, after cooling down from 250 оC to 20 оC, the GFRP and wood exhibited 68 % and 35 % of recoveries of elastic modulus respectively. A three-dimensional thermal model with kinetic thermophysical sub-models considering heat transfer, water evaporation and decomposition was developed. The developed thermal model accurately predicted the temperature responses and charring profiles. Furthermore, a thermomechanical model considering the material damage was developed to accurately predict the elastic modulus distribution, postfire residual bending capacity and failure modes. This study provides the basis for the retrofit and the reinforcement of the fire-damaged PWGS beams. In the future, study on the fire resistance of the PWGS components in fire will be required.

木芯夹层构件已广泛应用于建筑物和桥梁的建造中。然而，现有关于这些构件火灾后行为的研究非常有限。本研究旨在定量评估拉挤木芯 GFRP 夹层（PWGS）梁的火灾后残余特性。本文主要包括三个部分：(i) PWGS 梁的火灾实验回顾；(ii) 在不同火灾情况下对 PWGS 梁进行的火灾后弯曲实验；(iii) 热响应和火灾后热力学响应的数值研究。研究发现，破坏模式主要取决于暴露面的数量和火灾破坏程度。对于三面受火的试样（厚度为 25 毫米的硅钙板试样除外），烧焦纤维的渐进拉伸骤变是主要的破坏模式。而其他试样则表现为腹板的脆性平面剪切破坏。此外，从 250 ℃ 冷却到 20 ℃ 后，GFRP 和木材的弹性模量分别恢复了 68% 和 35%。开发的三维热模型包含动力学热物理子模型，考虑了热传导、水分蒸发和分解。所开发的热模型准确地预测了温度响应和炭化曲线。此外，还开发了一个考虑材料损伤的热力学模型，以准确预测弹性模量分布、火灾后的残余抗弯能力和破坏模式。这项研究为火灾损坏的 PWGS 梁的改造和加固提供了依据。今后，还需要对 PWGS 组件在火灾中的耐火性能进行研究。

来源：复合材料力学仿真Composites FEM

【新文速递】2023年9月25日固体力学SCI期刊最新文章

今日更新：Journal of the Mechanics and Physics of Solids 2 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 2 篇Journal of the Mechanics and Physics of SolidsDynamic homogenization of heterogeneous piezoelectric media: A polarization approach using infinite-body Green’s functionLee Jeong-Ho, Zhang Zhizhou, Gu Grace X.doi:10.1016/j.jmps.2023.105442异质压电介质的动态均质化：使用无限体格林函数的极化方法Dynamic homogenization theories are powerful tools for describing and understanding the behavior of heterogeneous media such as composites and metamaterials. However, a major challenge in the homogenization theory is determining Green’s function of these media, which makes it difficult to predict their effective constitutive relations, particularly for the finite-size and/or non-periodic media in real-world applications. In this paper, we present a formulation for finding the elastodynamic effective constitutive relations for general heterogeneous media, including finite-size and non-periodic ones, via a polarization approach based on the Hashin–Shtrikman principle along with Green’s identities. Our proposed formulation relies on the infinite-body Green’s function of a homogeneous reference medium, making it free from the difficulty of determining Green’s function even for the homogenization of finite-size and/or non-periodic media. Additionally, we demonstrate the universal applicability of this formulation for both random and deterministic heterogeneous media. This work contributes to a better understanding of the homogenization theory and the design of next-generation metamaterials that require the accurate prediction of effective material characteristics for dynamic wave manipulation under desired operating environments.动态均质化理论是描述和理解复合材料和超材料等异质介质行为的有力工具。然而，均质化理论的一个主要挑战是确定这些介质的格林函数，这使得预测它们的有效构成关系变得十分困难，特别是对于实际应用中的有限尺寸和/或非周期介质。在本文中，我们根据哈申-施特里克曼原理和格林常数，通过极化方法提出了一种计算方法，用于计算一般异质介质（包括有限尺寸和非周期性介质）的弹性动力有效构成关系。我们提出的公式依赖于均质参考介质的无穷体格林函数，因此即使是有限尺寸和/或非周期介质的均质化，也能摆脱确定格林函数的困难。此外，我们还证明了这一公式对随机和确定性异质介质的普遍适用性。这项工作有助于更好地理解均质化理论和设计下一代超材料，这些超材料需要准确预测有效材料特性，以便在所需的工作环境下进行动态波操纵。Modeling heterogeneity and permeability evolution in a compaction band using a phase-field approachIp Sabrina C.Y., Borja Ronaldo I.doi:10.1016/j.jmps.2023.105441利用相场方法模拟压实带中的异质性和渗透性演变Compaction bands are tabular zones of localized compressive deformation associated with porosity and permeability reduction. Depending on their orientation, compaction bands can act as barriers to fluid flow, and can be detrimental to fluid production in oil and gas reservoirs, as well as in CO2sequestration. The process of permeability reduction and the development of excess pore pressures during compaction band formation in a heterogeneous rock mass are not fully understood. Furthermore, few studies have modeled compaction band formation considering coupled hydromechanical processes. In this study, we propose a coupled hydromechanical, phase-field approach for capturing the formation and propagation of compaction bands in heterogeneous porous media. Breakage mechanics is adopted to characterize the free energy function in the intact and damaged material. The resulting phase-field variable provides a measure of the degree of grain crushing. Permeability reduction in the zone of compaction localization is modeled using the Kozeny-Carman equation accounting for microstructural evolution. Numerical simulations demonstrate the ability of the model to capture compaction band formation, porosity reduction, and permeability evolution under drained and undrained conditions. The results highlight the role of effective confining pressure, drainage conditions, and material parameters on the styles of compaction bands that form.压实带是与孔隙度和渗透率降低有关的局部压缩变形的片状区域。根据其走向，压实带可成为流体流动的障碍，不利于油气藏以及二氧化碳储层的流体生产封存。人们对异质岩体中压实带形成过程中渗透率降低和孔隙压力过大的过程还不完全了解。此外，很少有研究在模拟压实带形成时考虑耦合的水文机械过程。在本研究中，我们提出了一种耦合水力学相场方法，用于捕捉异质多孔介质中压实带的形成和传播。采用破裂力学来描述完整和受损材料中的自由能函数。由此产生的相场变量提供了晶粒破碎程度的度量。压实局部区域的渗透性降低采用 Kozeny-Carman 方程建模，该方程考虑了微结构演变。数值模拟证明了该模型能够捕捉到排水和非排水条件下的压实带形成、孔隙度降低和渗透性演变。结果凸显了有效约束压力、排水条件和材料参数对压实带形成方式的作用。International Journal of PlasticityModeling a sample size-dependency of martensitic phase transformation using a mesoscale frameworkVasoya Manish, Lagoudas Dimitris C.doi:10.1016/j.ijplas.2023.103760利用中尺度框架模拟马氏体相变的样品尺寸依赖性Predicting a sample size-dependency of the constitutive response of any material system when it is being used in nano- and micro-scale devices, such as NEMS and MEMS, is very crucial for their design process. This also includes the shape memory alloys (SMAs), where predicting a sample size-dependency of the phase transformation process is the key aspect. Many experimental studies with micropillar compression tests showed an increase in critical stress to transformation and an increase in transformation hardening as the sample size decreases below a critical size. In this work, we have employed and extended a recently developed mesoscale framework to model such size effects in SMAs. A plane strain tensile SMA strip of finite width is analyzed within a small deformation framework. The martensitic transformation regions are modeled as Eshelby inclusions in an austenite phase matrix. Circular potential nucleation sites are considered with a square packing for their spatial locations and with nucleation stress assigned to each site from a Gaussian distribution. The combination of the Gaussian distribution of nucleation stress and the size of the nucleation site represents the underlying SMA material microstructure. Our numerical analysis, with varying values of the aspect ratio between the strip width and the nucleation site size, provides a critical value of the aspect ratio characterizing a transitioning length scale between a bulk vs. a sample size-dependent phase transformation behavior. At the transition, the critical stress to phase transformation and the transformation hardening increase drastically as the aspect ratio decreases below its critical value. The limitations of these predictions are discussed with existing literature on experimental observations, and some perspectives to improve the model are stated.当任何材料系统用于纳米和微米尺度设备（如 NEMS 和 MEMS）时，预测其构成响应的样品尺寸依赖性对其设计过程至关重要。这也包括形状记忆合金（SMA），其中预测相变过程的样品尺寸依赖性是关键环节。许多微柱压缩试验研究表明，当样品尺寸减小到临界尺寸以下时，转变的临界应力会增加，转变硬化也会增加。在这项工作中，我们采用并扩展了最近开发的中尺度框架，以模拟 SMA 中的这种尺寸效应。在小变形框架内分析了有限宽度的平面应变拉伸 SMA 带。马氏体转变区域被模拟为奥氏体相基体中的埃舍尔比夹杂物。考虑了圆形潜在成核点，其空间位置采用正方形包装，每个成核点的成核应力采用高斯分布。成核应力的高斯分布与成核点大小的组合代表了 SMA 材料的基本微观结构。我们的数值分析采用了条带宽度与成核点尺寸之间不同的纵横比值，从而得出了纵横比的临界值，该值表征了体积与样品尺寸相关相变行为之间的过渡长度尺度。在过渡阶段，当纵横比减小到临界值以下时，相变的临界应力和转变硬化会急剧增加。我们结合现有的实验观察文献讨论了这些预测的局限性，并提出了一些改进模型的观点。Thin-Walled StructuresNumerical and theoretical prediction of foreign object damage on AM355 simulated blade validated by ballistic impact testsZhang Hongbo, Hu Dayong, Ye Xubin, Chen Xin, He Yuhuaidoi:10.1016/j.tws.2023.111230通过弹道冲击试验验证 AM355 模拟叶片上异物损伤的数值和理论预测Foreign object damage (FOD) of aeroengine blade was a critical concern in aeroengine maintenance due to its potential impact on airworthiness. This study investigated FOD of simulated blades made of high-strength steel AM355 through a combination of experiments, finite element (FE) simulations, and theoretical analysis. Firstly, mechanical tests were conducted, including the quasi-static tensile tests at different triaxialities and temperatures, as well as Split-Hopkinson pressure bar (SHPB) tests. Experimental results showed that AM355 was sensitive to strain rate, with a 30.7% increase in yield strength observed at a strain rate of 3864 s−1. Then, a Johnson–Cook (J-C) model with failure criterion was developed and validated through FE analysis. The mechanical performance of AM355 was compared to that of TC4. Lastly, FOD tests accompanied by corresponding numerical simulations were conducted via the laboratory air gun device and the developed J-C model. The predicted notch morphologies and sizes agreed well with experimental observations, with the notch depth linearly increased with the increase of the projectile velocity. Finally, a FOD theory prediction model was developed through a spring-mass model based on Winkler's elastic-plastic foundation. The theoretical predictions were in good agreement with the numerical and experimental results, providing valuable insights for FOD assessment of real aeroengine blades.航空发动机叶片的异物损伤（FOD）对适航性有潜在影响，是航空发动机维护中的一个重要问题。本研究通过实验、有限元（FE）模拟和理论分析相结合的方法，对高强度钢 AM355 制成的模拟叶片的 FOD 进行了研究。首先，进行了机械试验，包括不同三轴度和温度下的准静态拉伸试验，以及斯普利特-霍普金森压力棒（SHPB）试验。实验结果表明，AM355 对应变速率很敏感，在应变速率为 3864 s-1 时，屈服强度提高了 30.7%。随后，通过有限元分析建立并验证了具有失效准则的约翰逊-库克（J-C）模型。将 AM355 的机械性能与 TC4 进行了比较。最后，通过实验室气枪装置和所开发的 J-C 模型进行了 FOD 测试和相应的数值模拟。预测的缺口形态和大小与实验观察结果非常吻合，缺口深度随射弹速度的增加而线性增加。最后，通过基于温克勒弹塑性基础的弹簧-质量模型，建立了 FOD 理论预测模型。理论预测结果与数值和实验结果十分吻合，为实际航空发动机叶片的 FOD 评估提供了宝贵的见解。Effect of evolutionary anisotropic hardening on the prediction of deformation and forming load in incremental sheet forming simulationLee Hyung-Rim, Lee Myoung-Gyu, Park Namsudoi:10.1016/j.tws.2023.111231进化各向异性硬化对增量板材成形模拟中变形和成形载荷预测的影响The incremental sheet forming (ISF) process typically accompanies large plastic strain without fracture exceeding uniform elongation or ultimate tensile strength (UTS) in the uniaxial tensile test. Therefore, ISF features improved formability compared to the conventional stamping process. Meanwhile, numerous studies have focused on modeling and simulation of formability in ISF where anisotropic yield function is one of the key constitutive laws for predicting sheet deformation. However, the conventional yield function is defined based on anisotropy of initial yielding, while the ISF modeling requires the deformation behavior at large strains beyond the UTS. In this study, an evolutionary anisotropic plasticity model is investigated based on Hill's 48 yield function combined with the non-associated flow rule; i.e., e-NAFR Hill's 48. The e-NAFR Hill's 48 model is implemented to the vectorized user-defined material subroutine in the commercial finite element software ABAQUS/Explicit. Then, the proposed FE model is applied to the forming of truncated cone, pyramid, and clover shaped single point incremental forming (SPIF) of an aluminum alloy 6014-T4 sheet. The simulated part profile, thickness variation, and forming force are compared with those of experiments. The evolutionary constitutive model shows an average accuracy of 99.15% in thickness prediction and 94.22% accuracy in forming force, demonstrating the importance of evolutionary sheet anisotropy in the SPIF process.增量板材成形（ISF）工艺通常会产生较大的塑性应变，但不会在单轴拉伸试验中出现超过均匀伸长率或极限拉伸强度（UTS）的断裂。因此，与传统冲压工艺相比，ISF 具有更好的成形性。同时，许多研究都集中在 ISF 成型性的建模和模拟上，其中各向异性屈服函数是预测板材变形的关键构成法则之一。然而，传统的屈服函数是基于初始屈服的各向异性来定义的，而 ISF 建模则需要超出 UTS 的大应变变形行为。在本研究中，研究了基于希尔 48 屈服函数与非关联流动规则相结合的进化各向异性塑性模型，即 e-NAFR 希尔 48。e-NAFR Hill's 48 模型在商业有限元软件 ABAQUS/Explicit 的矢量化用户定义材料子程序中实现。然后，将所提出的有限元模型应用于铝合金 6014-T4 板材的截顶锥形、金字塔形和四叶草形单点增量成形（SPIF）。模拟的零件轮廓、厚度变化和成形力与实验结果进行了比较。进化构成模型在厚度预测方面的平均准确率为 99.15%，在成形力方面的平均准确率为 94.22%，证明了板材各向异性进化在 SPIF 过程中的重要性。来源：复合材料力学仿真Composites FEM