今日更新:Journal of the Mechanics and Physics of Solids 2 篇,Mechanics of Materials 1 篇,International Journal of Plasticity 2 篇,Thin-Walled Structures 3 篇
Hyperelastic modeling based on generalized Landau invariants and multi-stage calibration
Jiashen Guan, Xin Li, Hongyan Yuan, Ju Liu
doi:10.1016/j.jmps.2025.106338
基于广义朗道不变量和多级标定的超弹性建模
Hyperelastic modeling has long faced two challenges, that is, the non-uniqueness of fitted parameters and limited predictive capability. In this work, we propose a new modeling framework in conjunction with a multi-stage fitting method. In the model construction, we generalize Landau invariants by introducing the generalized strains and use them as the building blocks for the model family. The models are mathematically concise yet sufficiently general, encompassing the Ogden model and the hyperelasticity of Hill’s class as special cases. A new micro-to-macro transition is proposed using the generalized strain, and the generalized Landau invariants emerge naturally from the homogenization procedure, providing a clear micromechanical interpretation. This enables the construction of a suite of models with micromechanical foundation. A key feature is the emergence of a pseudo-universal relation derived from the generalized invariants, which forms the basis of the multi-stage fitting method. It enables the separated calibration of the invariant parameters and material modulus in the fitting. The proposed strategy demonstrates strong predictive performance in that it accurately predicts biaxial mechanical responses using parameters identified from a single pure shear test. This robustness is further confirmed through a three-dimensional benchmark involving non-homogeneous strain. In addition, the multi-stage method yields mathematically sound models that maintain convex energy contours, a property correlated with predictive reliability. Several models within the proposed framework also demonstrate competitive fitting and prediction accuracy compared to state-of-the-art models using the same number of parameters. This work establishes a new paradigm for constitutive modeling by unifying theoretical development with a robust calibration methodology. The proposed approach promotes the practical applicability of hyperelastic models and offers a promising foundation for modeling more complex material behaviors.
长期以来,超弹性模型一直面临着拟合参数的非唯一性和预测能力有限两大挑战。在这项工作中,我们提出了一个新的建模框架,结合多阶段拟合方法。在模型构建中,我们通过引入广义应变来推广朗道不变量,并将其作为模型族的构建单元。这些模型在数学上是简洁的,但又足够普遍,包括奥格登模型和希尔类的超弹性作为特殊情况。利用广义应变提出了一种新的微观到宏观的转变,广义朗道不变量从均匀化过程中自然产生,提供了清晰的微观力学解释。这使得构建一套具有微力学基础的模型成为可能。一个关键特征是由广义不变量衍生出的伪普遍关系的出现,它构成了多阶段拟合方法的基础。实现了拟合过程中不变参数和材料模量的分离标定。所提出的策略显示出强大的预测性能,因为它可以准确地预测双轴力学响应,使用从单个纯剪切试验中确定的参数。通过涉及非均匀应变的三维基准进一步证实了这种鲁棒性。此外,多阶段方法产生数学上合理的模型,保持凸能量轮廓,这是与预测可靠性相关的特性。与使用相同数量参数的最先进模型相比,所提出框架中的几个模型也显示出具有竞争力的拟合和预测精度。这项工作建立了一个新的范式本构建模统一的理论发展与稳健的校准方法。该方法提高了超弹性模型的实际适用性,为更复杂的材料行为建模提供了良好的基础。
Modeling finite viscoelasticity based on the Green–Naghdi kinematic assumption and generalized strains
Ju Liu, Chongran Zhao, Jiashen Guan
doi:10.1016/j.jmps.2025.106346
基于Green-Naghdi运动学假设和广义应变的有限粘弹性建模
We propose a modeling framework for finite viscoelasticity, inspired by the kinematic assumption made by Green and Naghdi in plasticity. This approach fundamentally differs from the widely used multiplicative decomposition of the deformation gradient, as the intermediate configuration, a concept that remains debated, becomes unnecessary. The advent of the concept of generalized strains allows the Green–Naghdi assumption to be employed with different strains, offering a flexible mechanis m to separate elastic and viscous deformation. This leads to a constitutive theory in which the kinematic separation is adjustable and can be calibrated. For quadratic configurational free energy, the framework yields a suite of finite linear viscoelasticity models governed by linear evolution equations. Notably, these models recover established models, including those by Green and Tobolsky (1946) and Simo (1987), when the Seth-Hill strain is chosen with the strain parameter being -2 and 2, respectively. It is also related to the model of Miehe and Keck (2000) when the strain is of the Hencky type. We further extend the approach by adopting coercive strains, which allows us to define an elastic deformation tensor locally. This facilitates modeling the viscous branch using general forms of the configurational free energy, and we construct a micromechanical viscoelastic model as a representative instantiation. The constitutive integration algorithms of the proposed models are detailed. We employ the experimental data of VHB 4910 to examine the proposed models, which demonstrate their effectiveness and potential advantages in the quality of fitting and prediction. Three-dimensional finite element an alysis is also conducted to assess the influence of different strains on the viscoelastic behavior.
我们提出了一种有限粘弹性建模框架,其灵感源自格林和纳吉迪在塑性理论中所做的运动学假设。这种方法与广泛使用的变形梯度乘法分解截然不同,因为中间构型这一仍存在争议的概念变得不再必要。广义应变概念的出现使得格林 - 纳吉迪假设能够与不同应变一起使用,从而提供了一种灵活的机制来分离弹性变形和粘性变形。这导致了一种本构理论,在其中运动学分离是可调的,并且可以进行校准。对于二次构型自由能,该框架产生了一组由线性演化方程支配的有限线性粘弹性模型。值得注意的是,当选择塞斯 - 希尔应变且应变参数分别为 -2 和 2 时,这些模型恢复了已建立的模型,包括格林和托博尔斯基(1946 年)以及西莫(1987 年)的模型。当应变是亨奇类型时,它也与米赫和凯克(2000 年)的模型相关。我们进一步拓展了该方法,采用强制应变,这使我们能够局部定义弹性变形张量。这有助于使用构型自由能的一般形式来建模粘性分支,并构建了一个微观力学粘弹性模型作为代表性实例。详细介绍了所提出模型的本构积分算法。我们采用 VHB 4910 的实验数据来检验所提出的模型,结果表明它们在拟合和预测质量方面具有有效性和潜在优势。还进行了三维有限元分析,以评估不同应变对粘弹性行为的影响。
General load-depth relations for spherical, conical, and flat-ended cylindrical indentations of soft elastic layers: From ultra-thin-film to half-space
Weike Yuan, Yue Ding, Jianjun Bian, Gangfeng Wang
doi:10.1016/j.mechmat.2025.105502
软弹性层的球形、锥形和平端圆柱形压痕的一般载荷深度关系:从超薄膜到半空间
The thickness dependency of the mechanical response of layered structures challenges the applicability of classical Hertz-Sneddon contact mechanics in the indentation measurements of soft thin specimens. Although various modified theories have been reported for the contact of very thin or relatively thick elastic layers placed on a rigid substrate, unified ana lytical solutions covering the complete spectrum of layer thickness are still missing. Here, we establish explicit expressions of the load-depth relations for spherical, conical, and flat-ended cylindrical indentations of soft layers of arbitrary thickness. Two fundamental boundary conditions between the elastic layer and the rigid support are considered: (1) connected without friction and (2) perfectly bonded. Crucially, the derived relations demonstrate mathematical continuity from the ultra-thin-film limit to the half-space limit, which offer accurate yet convenient-to-use formulae for determining elastic modu li of thin materials via indentations, particularly for soft layers exhibiting intermediate thickness ranges. The validity of our general relations is confirmed through excellent agreements with experimental data and existing solutions within certain ranges.
层状结构力学响应的厚度依赖性对经典赫兹-斯奈登接触力学在软质薄试件压痕测量中的适用性提出了挑战。尽管对于放置在刚性衬底上的非常薄或相对厚的弹性层的接触已经报道了各种修正的理论,但仍然缺乏覆盖层厚度完整谱的统一解析解。本文建立了任意厚度软层的球形、锥形和平端圆柱形压痕的载荷-深度关系的显式表达式。考虑弹性层与刚性支撑之间的两个基本边界条件:(1)无摩擦连接;(2)完美粘结。至关重要的是,推导的关系证明了从超薄膜极限到半空间极限的数学连续性,这为通过压痕确定薄材料的弹性模量提供了准确而方便使用的公式,特别是对于具有中等厚度范围的软层。我们的一般关系的有效性是通过在一定范围内与实验数据和现有解决方案的良好一致性来证实的。
A crystal plasticity-informed data-driven model for magnesium alloys
Ding Tang, Shikun Qi, Kecheng Zhou, May Haggag, Xiaochuan Sun, Dayong Li, Huamiao Wang, Peidong Wu
doi:10.1016/j.ijplas.2025.104480
镁合金晶体塑性信息数据驱动模型
In the past few years, data-driven models based on artificial neural network (ANN) have been successfully developed and applied to investigate the macro- and micro-mechanical behaviors of various materials. However, these data-driven models are either too complex in structure or lack interpretable physical insights. In the present work, a crystal plasticity-informed data-driven (CPIDD) model is proposed, which updates the microstructural information and parameters associated with the macroscopic constitutive model using a parallel ANN structure, and combines conventional constitutive equations to obtain the stress-strain response, ensuring efficient and stable calculations. In conjunction with the finite element (FE) method, the FE-CPIDD model simulates the micro- and macro-mechanical behaviors of magnesium (Mg) alloys under uniaxial loading, non-proportional loading, four-point bending and unloading. The comparison between the simulations and available experiments (or crystal plasticity simulations) demonstrates the accuracy and effectiveness of the proposed CPIDD model. Using Mg alloys as a representative case, the CPIDD model provides an operational and extensional tool for the design, fabrication, manufacturing, and service of the metallic components.
近年来,基于人工神经网络(ANN)的数据驱动模型已被成功开发,并应用于研究各种材料的宏观和微观力学行为。然而,这些数据驱动的模型要么结构过于复杂,要么缺乏可解释的物理见解。本文提出了一种基于晶体塑性的数据驱动(CPIDD)模型,该模型利用并行神经网络结构更新微观结构信息和与宏观本构模型相关的参数,并结合传统的本构方程获得应力应变响应,保证了计算的高效和稳定。结合有限元法,建立了FE- cpidd模型,模拟了镁合金在单轴加载、非比例加载、四点弯曲和卸载下的微观和宏观力学行为。通过与已有实验(或晶体塑性模拟)的比较,验证了所提CPIDD模型的准确性和有效性。CPIDD模型以镁合金为代表,为金属部件的设计、制造、制造和服务提供了一种可操作和可扩展的工具。
Experimental an alysis and modeling of anisotropic ductile damage in non-proportional extreme low-cycle biaxial loading with shear-tension histories
Zhichao Wei, Guoxi Mao, Steffen Gerke, Sebastian Münstermann, Michael Brünig
doi:10.1016/j.ijplas.2025.104474
具有剪切-拉伸历史的非比例极低周双轴加载的各向异性延性损伤实验分析与建模
This paper discusses the ductile damage and fracture behavior based on newly designed and performed non-proportional, non-reverse, extremely low-cycle experiments. In contrast to most extremely low-cycle experiments, which involve reverse loading histories or are restricted to a limited s mall plastic strain range, this study proposes novel non-proportional tension-to-shear (TS) and shear-to-tension (ST) loading patterns. Different combinations of displacement increments are applied within individual cyclic loading patterns, ensuring that specimen failure is governed by ductile damage and fracture under large plastic deformations. Numerical calculations are based on an advanced cyclic plastic-damage constitutive model with combined hardening laws. A novel non-proportionality parameter incorporating the effective back stress tensor is introduced into the combined hardening formulation to account for non-proportional hardening, allowing for a more accurate characterization of plastic behavior under non-proportional cyclic loading conditions. Digital image correlation (DIC) is used to ana lyze the global load–displacement curves and local strain fields, enabling comparison with the numerical results at both macroscopic and microscopic levels. Scanning electron microscope (SEM) and light optical microscope (LOM) images were taken from the fracture surfaces as well as both fractured and unfractured notch areas of the specimen, respectively. A novel quantitative an alysis was introduced to evaluate the obtained SEM images using a convolutional neural network (CNN) approach, whereas LOM images were ana lyzed with the open-source software ImageJ. The present work highlights that non-proportional loading histories and shear-tension cyclic loading sequences with various plastic amplitudes significantly influence on the material’s plastic and ductile damage behavior.
本文基于新设计和实施的非比例、非反向、极低循环试验,讨论了塑性损伤和断裂行为。与大多数涉及反向加载历史或局限于有限的小塑性应变范围的极低循环实验相反,本研究提出了新的非比例拉伸-剪切(TS)和剪切-张力(ST)加载模式。在不同的循环加载模式中应用不同的位移增量组合,确保试样的破坏是由大塑性变形下的延性损伤和断裂控制的。数值计算基于具有复合硬化规律的先进循环塑性损伤本构模型。结合有效背应力张量的一种新的非比例参数被引入到组合硬化公式中,以考虑非比例硬化,允许更准确地表征非比例循环加载条件下的塑性行为。采用数字图像相关(DIC)技术对整体荷载-位移曲线和局部应变场进行分析,实现了宏观和微观水平上与数值结果的对比。扫描电镜(SEM)和光学显微镜(LOM)分别对试样的断口表面以及断裂和未断裂的缺口区域进行了成像。采用一种新颖的定量分析方法,利用卷积神经网络(CNN)方法对获得的SEM图像进行评估,而LOM图像则使用开源软件ImageJ进行分析。非比例加载历史和不同塑性幅值的剪切-拉伸循环加载序列对材料的塑性和延性损伤行为有显著影响。
On the Magnetically Tunable Free Damped-Vibration of L-Shaped Composite Spherical Panels Made of GPL-Reinforced Magnetorheological Elastomers: An Element-Based GDQ Approach
Peijun Zhang, Zhen Wang, Huaigu Tian, Xiaojian Xi, Xiaogang Liu
doi:10.1016/j.tws.2025.113987
gpl增强磁流变弹性体l型复合球面板的磁可调自由阻尼振动:基于单元的GDQ方法
In practical engineering applications, curved structures rarely conform to idealized rectangular or circular planforms and often involve far more intricate geometries. Among these, L-shaped spherical panels have emerged as a structurally significant form, found in subsystem interfaces, aerospace fuselage junctions, complex biomedical shells, and multifunctional architectural surfaces. This study explores the free damped-vibration behavior of such panels constructed from a graphene platelet (GPL)-reinforced magnetorheological elastomer (MRE) nanocomposite. Unlike conventional elastic matrices, the MRE base material exhibits time- and field-dependent viscoelastic behavior, influenced by both magnetic field intensity and ferromagnetic content. This behavior is mathematically formulated through an experimentally validated generalized Kelvin–Voigt-type model, tailored to represent the storage and dissipation characteristics of the matrix under dynamic excitation. The reinforcing particles are graded through the panel thickness. The effective elastic properties of the composite are homogenized using the Halpin–Tsai micromechanical model, accounting for the influence of GPL content and sizes. To address the geometric complexity, a hybrid element-based GDQ (generalized differential quadrature) approach is developed. The L-shaped spherical panel is subdivided into rectangular elements, each governed by equations derived using Hamilton’s principle, first-order shear deformation theory, and Sander’s strain-displacement relations. Discretization via quadrature nodes enables the GDQ method to transform the governing PDEs into an efficient algebraic system. The global system is constructed by enforcing both displacement and force continuity at shared nodes and applying appropriate boundary conditions. The proposed framework achieves excellent accuracy in capturing frequencies and loss factors, demonstrating its capability for efficient dynamic an alysis of non-standard. In addition to validating the accuracy of the proposed approach against benchmark problems, the study reveals distinct mode-switching and mode-jumping phenomena triggered by changes in geometric parameters—highlighting the sensitivity of vibrational behavior to panel shape and reinforcing the need for precise modeling in advanced s mart structures.
在实际工程应用中,弯曲结构很少符合理想的矩形或圆形平面,而且往往涉及更复杂的几何形状。其中,l形球形板已成为一种结构上重要的形式,用于子系统接口、航空航天机身连接处、复杂的生物医学外壳和多功能建筑表面。本研究探讨了由石墨烯血小板(GPL)增强磁流变弹性体(MRE)纳米复合材料构建的这种面板的自由阻尼振动行为。与传统的弹性基体不同,MRE基材料表现出与时间和场相关的粘弹性行为,受磁场强度和铁磁含量的影响。这种行为是通过实验验证的广义kelvin - voigt型模型在数学上表述的,该模型专门用于表示矩阵在动态激励下的存储和耗散特性。增强颗粒按面板厚度分级。考虑GPL含量和尺寸的影响,采用Halpin-Tsai微观力学模型对复合材料的有效弹性性能进行均匀化。为了解决几何复杂性,提出了一种基于混合单元的广义微分求积方法。l形球形面板被细分为矩形单元,每个单元由Hamilton原理、一阶剪切变形理论和Sander应变-位移关系导出的方程控制。通过正交节点的离散化使GDQ方法能够将控制偏微分方程转化为有效的代数系统。全局系统是通过在共享节点上强制位移和力的连续性并应用适当的边界条件来构建的。该框架在捕获频率和损耗因子方面具有很高的精度,证明了其对非标动态分析的有效性。除了针对基准问题验证所提出方法的准确性外,该研究还揭示了几何参数变化引发的不同模式切换和模式跳跃现象,突出了面板形状对振动行为的敏感性,并加强了对高级智能结构精确建模的需求。
Enhanced Interlaminar Fracture Toughness of CFRP Using UHMWPE Fiber Veils Modified with Polydopamine and Graphene Oxide
Xuming Yao, Junzhen Chen, Guoyu Yang, Jialiang Li, Shuo Cheng, Jianjun Jiang
doi:10.1016/j.tws.2025.113990
用聚多巴胺和氧化石墨烯改性超高分子量聚乙烯纤维增强CFRP的层间断裂韧性
Carbon fiber-reinforced polymer (CFRP) laminates are prone to delamination due to their inherently low interlaminar fracture toughness. This study, for the first time, investigates the use of ultra-high molecular weight polyethylene fiber (PE) veils to enhance the interlaminar fracture toughness of CFRP and explores the influence of polydopamine (PDA) and graphene oxide (GO) on their toughening efficacy. PE, PDA-modified PE (PPE), and GO/PDA-modified PE (GPPE) veils with an areal density of 10 g/m2 were fabricated using a wet-laying technique and subsequently introduced as interlayers in unidirectional CFRP laminates via a prepreg hot-pressing process. Mode I and Mode II interlaminar fracture toughness (GIc and GIIc) of the CFRPs were evaluated using double cantilever beam and end-notched flexure tests, respectively. The results demonstrated that while all three PE veils improved the interlaminar fracture toughness compared to the pristine CFRP laminates without interlayers, the incorporation of the GPPE veil yielded the largest increase in GIc and GIIc by 90.7% and 69.8%, respectively. Ana lysis of the toughening mechanis ms revealed that PDA modification improved the interfacial adhesion between the PE fibers and the epoxy matrix, promoting fiber bridging and pull-out. The introduction of GO further contributed to the toughness through additional nanoscale mechanis ms such as crack deflection and pinning, exhibiting a synergistic effect with PDA. This research presents an effective strategy for developing high-toughness CFRPs.
碳纤维增强聚合物(CFRP)层压板由于其固有的低层间断裂韧性而容易发生分层。本研究首次研究了使用超高分子量聚乙烯纤维(PE)薄膜增强CFRP的层间断裂韧性,并探讨了聚多巴胺(PDA)和氧化石墨烯(GO)对其增韧效果的影响。采用湿铺技术制备了面密度为10 g/m2的PE、pda改性PE (PPE)和GO/ pda改性PE (GPPE)薄膜,随后通过预浸料热压工艺将其作为单向CFRP层压板的中间层。采用双悬臂梁和端缺口弯曲试验分别对cfrp的I型和II型层间断裂韧性(GIc和GIIc)进行了评估。结果表明,虽然与未添加中间层的CFRP复合材料相比,三种PE层膜都提高了层间断裂韧性,但GPPE层膜的掺入使GIc和GIc分别增加了90.7%和69.8%,增幅最大。增韧机理分析表明,PDA改性提高了PE纤维与环氧基之间的界面附着力,促进了纤维的桥接和拉拔。氧化石墨烯的引入通过额外的纳米级机制(如裂纹偏转和钉住)进一步提高了韧性,与PDA表现出协同效应。本研究提出了一种开发高韧性碳纤维复合材料的有效策略。
Global buckling behaviour and design of stainless steel hexagonal hollow section columns
Yukai Zhong, Ziyi Wang, Ou Zhao
doi:10.1016/j.tws.2025.113986
不锈钢六角空心截面柱整体屈曲行为及设计
Owing to their high load-carrying capacity, ease of constructability and superior corrosion resistance, stainless steel polygonal hollow section members have great potential to be used in practical engineering. However, the absence of relevant design codes hinders their engineering applications. To address this issue, this paper conducts experimental and numerical studies on the flexural buckling behaviour and resistances of stainless steel hexagonal hollow section columns. A testing programme was carried out on ten column specimens designed with different cross-section dimensions and member lengths, together with tensile coupon tests and initial geometric imperfection measurements. A numerical modelling programme was then performed to develop and validate finite element models based on the test results. The validated FE models were adopted to carry out parametric studies to generate further numerical data to supplement the test data, which were then employed for the evaluations of design rules set out in the European code, American specification and ASCE standard. The evaluation results generally revealed that the European code and American specification resulted in an acceptable level of accuracy and consistency in predicting the flexural buckling resistances of stainless steel hexagonal hollow section columns, although some resistances of columns with low member slendernesses were overestimated, while the ASCE standard provided rather unsafe resistance predictions. Finally, a revised ASCE design buckling curve was proposed.
不锈钢多边形空心截面构件具有承载能力高、易施工、耐腐蚀等优点,在实际工程中具有很大的应用潜力。然而,相关设计规范的缺失阻碍了其工程应用。为了解决这一问题,本文对不锈钢六角空心截面柱的屈曲行为和抗力进行了试验和数值研究。对10个不同截面尺寸和构件长度的柱试件进行了试验,并进行了张拉副试验和初始几何缺陷测量。然后执行数值模拟程序,根据测试结果开发和验证有限元模型。采用验证的有限元模型进行参数化研究,生成进一步的数值数据来补充试验数据,然后将这些数据用于欧洲规范、美国规范和ASCE标准的设计规则评估。评价结果表明,欧洲规范和美国规范对不锈钢六角形空心截面柱抗弯屈曲抗力的预测精度和一致性可接受,但对构件细长度较低的部分柱的抗弯屈曲抗力估计过高,而ASCE标准的抗弯屈曲抗力预测不安全。最后,提出了修正的ASCE设计屈曲曲线。