【新文速递】2023年11月1日固体力学SCI期刊最新文章

今日更新：International Journal of Solids and Structures 1 篇，Journal of the Mechanics and Physics of Solids 1 篇，Mechanics of Materials 1 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 4 篇

International Journal of Solids and Structures

Fracture toughness improvement due to crack deflection and crack trapping by elliptical voids or particles

Brescakovic Drazen, Kolednik Otmar

doi:10.1016/j.ijsolstr.2023.112551

椭圆形空隙或颗粒的裂纹偏转和裂纹捕集提高了断裂韧性

The paper investigates how voids and particles can be used to deflect and arrest cracks in order to enhance the failure stress and the fracture toughness of intrinsically brittle materials. This is done by investigating crack propagation near single elliptical voids and particles that are located in an elastic matrix material. The shapes of the inhomogeneities are varied, but their cross section is held constant. Uniaxial and biaxial loading conditions are considered and also the Young’s modulus ratio between particle and matrix material is varied. The crack trajectories near the material inhomogeneities are evaluated by applying a computationally very efficient approach, the crack trajectory interpolation (CTI) method, which has been introduced in an earlier work of the authors. With this method, critical distances are determined where an approaching crack runs into an elliptical void and gets trapped. Similarily, zones for crack arrest and crack deflection near stiff particles are found. Combinations of particles and voids are studied, too. A damage-based approach is used to investigate the improvements in failure stress and fracture toughness when a crack runs into a void. The results show that voids and particles that are elongated perpendicular to the crack plane are most useful for crack arrest. The trapping distances increase with increasing ellipticity of the inhomogeneities. However, the improvement in failure stress is highest for voids with moderate ellipticity. The results of this paper will be used to find optimum arrangements of voids or particle-void combinations for the design of structural components with increased fracture toughness.

本文研究了如何利用空隙和颗粒来偏转和阻止裂纹，从而提高固有脆性材料的破坏应力和断裂韧性。具体方法是研究位于弹性基体材料中的单个椭圆形空隙和颗粒附近的裂纹扩展。不均匀体的形状各不相同，但横截面保持不变。考虑了单轴和双轴加载条件，并改变了颗粒和基体材料之间的杨氏模量比。通过采用一种计算效率极高的方法--裂纹轨迹插值（CTI）法，对材料不均匀性附近的裂纹轨迹进行了评估。利用这种方法，可以确定临近裂缝进入椭圆空隙并被困住的临界距离。同样，还能在坚硬颗粒附近找到裂纹捕捉区和裂纹偏转区。此外，还研究了颗粒和空隙的组合。采用基于损伤的方法研究了当裂纹进入空隙时，破坏应力和断裂韧性的改善情况。结果表明，垂直于裂纹平面拉长的空隙和颗粒最有助于阻止裂纹的产生。随着非均质物椭圆度的增加，捕获距离也会增加。然而，中等椭圆度的空隙对破坏应力的改善最大。本文的研究结果将用于寻找空隙或颗粒-空隙组合的最佳排列方式，以设计具有更高断裂韧性的结构部件。

Journal of the Mechanics and Physics of Solids

A simple quantitative model of neuromodulation, Part I: Ion flow through neural ion channels

Werneck Linda, Han Mertcan, Yildiz Erdost, Keip Marc-André, Sitti Metin, Ortiz Michael

doi:10.1016/j.jmps.2023.105457

神经调节的简单定量模型，第一部分：通过神经离子通道的离子流

We develop a simple model of ionic current through neuronal membranes as a function of membrane potential and extracellular ion concentration. The model combines a simplified Poisson-Nernst–Planck (PNP) model of ion transport through individual ion channels with channel activation functions calibrated from ad hoc in-house experimental data. The simplified PNP model is validated against bacterial gramicidin A ion channel data. The calibrated model accounts for the transport of calcium, sodium, potassium, and chloride and exhibits remarkable agreement with the experimentally measured current–voltage curves for the differentiated human neural cells. All relevant data and code related to the ion flow models are available at Werneck et al. (2023).

我们建立了一个简单的神经元膜离子电流模型，它是膜电位和细胞外离子浓度的函数。该模型将通过单个离子通道进行离子传输的简化泊松-恩斯特-普朗克（PNP）模型与根据内部特别实验数据校准的通道激活函数相结合。根据细菌霉素 A 离子通道数据对简化的 PNP 模型进行了验证。校准后的模型考虑了钙、钠、钾和氯离子的传输，并与实验测量的分化人类神经细胞的电流-电压曲线显示出显著的一致性。与离子流模型相关的所有数据和代码可在 Werneck 等人（2023 年）的网站上查阅。

Mechanics of Materials

Real-time Bayesian model calibration method for C/SiC mechanical behavior considering model bias

Gao Bo, Yang Qiang, Chen Siyao, Wang Pengyuan, Meng Songhe

doi:10.1016/j.mechmat.2023.104847

考虑模型偏差的 C/SiC 力学行为实时贝叶斯模型校准方法

The mechanical behavior of C/SiC composites has significant nonlinear and dispersion. To obtain the real mechanical behavior of C/SiC composites in actual structure, a real-time calibration method for mechanical behavior of C/SiC composites based on the dynamic Bayesian network (DBN) is proposed. The epistemic uncertainty of the mechanical behavior is introduced in the form of model bias. The method comprises offline and online phases. Firstly, the surrogate model of the mechanical behavior is built based on the proper orthogonal decomposition and the Gaussian process model offline. Then, based on the DBN, model parameters can be continuously calibrated by the sensor data online. The validity of the method is verified by the uniaxial tensile test of C/SiC composites. The results show that the proposed method can real-time accurately calibrate and predict the mechanical behavior of all the C/SiC samples and the introduction of the model bias is of great significance.

C/SiC 复合材料的力学行为具有明显的非线性和分散性。为了获得 C/SiC 复合材料在实际结构中的真实力学行为，提出了一种基于动态贝叶斯网络（DBN）的 C/SiC 复合材料力学行为实时校准方法。力学行为的认识不确定性以模型偏差的形式引入。该方法包括离线和在线两个阶段。首先，根据适当的正交分解和离线高斯过程模型建立机械行为的代理模型。然后，在 DBN 的基础上，通过传感器数据对模型参数进行在线持续校准。C/SiC 复合材料的单轴拉伸试验验证了该方法的有效性。结果表明，所提出的方法可以实时准确地校准和预测所有 C/SiC 样品的力学行为，模型偏差的引入具有重要意义。

International Journal of Plasticity

Data-driven multiscale modelling of granular materials via knowledge transfer and sharing

Qu Tongming, Zhao Jidong, Guan Shaoheng, Feng Y.T.

doi:10.1016/j.ijplas.2023.103786

通过知识转让和共享建立数据驱动的颗粒材料多尺度模型

Machine learning approaches have found immense potential to revolutionise the constitutive modelling of granular materials. However, data scarcity poses a significant challenge to this emerging paradigm. This study aims to tackle this issue by presenting two transfer learning-based strategies that harness well-established constitutive knowledge and similar material data to reduce data demands for data-driven material modelling. The first approach utilises phenomenological constitutive models to generate massive synthetic data which reflect the targeted material behaviour to train a base model. This base model is then repurposed for a new task based on numerical simulation data via transfer learning. The other approach involves using available material data to train a base model, which is then applied to other new materials that are similar but with limited data. The proposed transfer learning methods are tested on both particle-scale simulations of representative volume elements (RVEs) and hierarchical multiscale modelling of boundary value problems (BVPs) of granular materials. The trained data-driven material model is embedded in numerical simulations with the finite element method (FEM) to validate its accuracy, efficiency, and stability. The results demonstrate that transfer learning can effectively achieve high-quality machine learning predictions with limited data. The transfer learning strategy presented in this study is expected to be widely applicable to small data-driven material modelling.

机器学习方法具有巨大的潜力，可以彻底改变颗粒材料的构成建模。然而，数据稀缺给这一新兴模式带来了巨大挑战。本研究旨在通过介绍两种基于迁移学习的策略来解决这一问题，这两种策略利用成熟的构造知识和类似的材料数据来减少数据驱动材料建模的数据需求。第一种方法利用现象学构造模型生成反映目标材料行为的大量合成数据，以训练基础模型。然后，基于数值模拟数据，通过迁移学习将该基础模型重新用于新任务。另一种方法是利用现有的材料数据训练基础模型，然后将其应用于其他类似但数据有限的新材料。所提出的迁移学习方法在代表性体积元素（RVE）的颗粒尺度模拟和颗粒材料边界值问题（BVP）的分层多尺度建模中进行了测试。训练好的数据驱动材料模型被嵌入到有限元法（FEM）的数值模拟中，以验证其准确性、效率和稳定性。结果表明，迁移学习可以在数据有限的情况下有效地实现高质量的机器学习预测。本研究提出的迁移学习策略有望广泛应用于小型数据驱动材料建模。

Thin-Walled Structures

Fatigue tests and design of Q460 CHS-CHS T-joints under axial loading and in-plane bending

Hu Chao, Cheng Rui, Wang Yuhang, Chen Yang, Yang Zhou, Liu Yusen

doi:10.1016/j.tws.2023.111305

轴向加载和平面弯曲条件下 Q460 CHS-CHS T 型接头的疲劳试验和设计

Previous research has primarily focused on stress concentration factors (SCFs) and fatigue life of tubular joints made from low-strength steel (nominal yield strength of 235-360 MPa). The fatigue behavior of high-strength tubular joints remains insufficiently studied. In this study, a total of sixteen CHS-CHS T-joints fabricated from Q460 steel were designed, eight of which were subjected to axial load and eight of which were under in-plane bending. Static and fatigue tests were conducted to analyze the distribution of hot spot stress, fatigue crack propagation, and fatigue failure modes. The experimental results showed that the crack initiation consistently occurred at location of maximum hot spot stress for all specimens. The maximum SCFs were concentrated at the saddle (90°) for specimens under axial loads and around the position of 22.5° for those under in-plane bending. The modified SCF design formula for in-plane bending was proposed based on regression analysis. Prior to crack initiation, all specimens exhibited a relatively slow stiffness degradation due to cumulative damage from fatigue loading. Through least squares analysis of the test data, the fatigue design Srhs-N curve for Q460 CHS-CHS T-joints was developed. The proposed Srhs-N curve is capable of accurately predicting the fatigue life of Q460 CHS-CHS T-joint subject to axial loads and in-plane bending. Comparison with previous research and existing design guidelines shows that under the same stress amplitude level, the fatigue lives of CHS-CHS T-joints subjected to axial loading of Q460 steel are comparable to that of low-strength steel (WFG36Z). Under in-plane bending, the fatigue lives for Q460 steel are higher than that for low-strength steels (C350L0, t<4mm).

以往的研究主要集中在低强度钢（名义屈服强度为 235-360 兆帕）管状接头的应力集中系数（SCF）和疲劳寿命方面。对高强度管状接头的疲劳行为研究仍然不足。在这项研究中，共设计了 16 个由 Q460 钢制造的 CHS-CHS T 形接头，其中 8 个承受轴向载荷，8 个承受平面弯曲。通过静态和疲劳试验分析了热点应力分布、疲劳裂纹扩展和疲劳失效模式。实验结果表明，所有试样的裂纹起始点均位于热斑应力最大的位置。轴向载荷下试样的最大 SCF 集中在鞍部（90°），而平面弯曲下试样的最大 SCF 则集中在 22.5° 位置附近。根据回归分析提出了平面内弯曲的修正 SCF 设计公式。在裂纹萌发之前，由于疲劳载荷的累积损伤，所有试样都表现出相对缓慢的刚度退化。通过对试验数据进行最小二乘法分析，得出了 Q460 C 的疲劳设计 Srhs-N 曲线。所提出的 Srhs-N 曲线能够准确预测 Q460 CHS-CHS T 型接头在轴向载荷和平面弯曲作用下的疲劳寿命。与之前的研究和现有的设计指南比较表明，在相同的应力振幅水平下，Q460 钢的 CHS-CHS T 型接头在承受轴向载荷时的疲劳寿命与低强度钢（WFG36Z）相当。在平面弯曲情况下，Q460 钢的疲劳寿命高于低强度钢（C350L0，t<4mm）。

A new trigonometric shear deformation plate theory for free vibration analysis of FGM plates with two-directional variable thickness

Hoang Vu Ngoc Viet, Thanh Pham Trung

doi:10.1016/j.tws.2023.111310

用于双向可变厚度 FGM 板自由振动分析的新三角剪切变形板理论

The present research aims to propose a new trigonometric shear deformation plate theory (TSDPT) for free vibration analysis of functionally graded plates with two-directional variable thickness. Trigonometric functions are utilized to determine the distribution of transverse shear stress in the new TSDPT. The thickness variation follows three distinct patterns: linear, concave, and convex. The governing equations of the composite plates are derived via the new theory and the Hamilton's principle. Then, via the Galerkin's method, the current study establishes a solution for determining natural frequencies of variable-thickness FGM plates. The obtained outcomes of FGM plates are calculated by using the MATLAB program. To confirm the accuracy of the current computational model, we conducted comparisons between the obtained results and data previously reported in the open literature. The results obtained from the new theory are compared not only for the case of a plate made of isotropic material but also in comparison to a plate made of functionally graded material. In both scenarios, the proposed theory showcases superior performance when juxtaposed against classical plate theory (CPT), first-order shear deformation plate theory (FSDPT), and other shear deformation plate theories, displaying significantly reduced error rates. Furthermore, graphical representations of the influences of three-parameter stiffness of Kerr foundation, boundary conditions, geometrical parameters, two different FGMs, FGM index, and mode numbers on the vibrational behaviours of FGM plates are provided.

本研究旨在提出一种新的三角剪切变形板理论（TSDPT），用于分析厚度双向可变的功能分级板的自由振动。在新的 TSDPT 中，三角函数被用来确定横向剪应力的分布。厚度变化遵循三种不同的模式：线性、凹形和凸形。通过新理论和汉密尔顿原理推导出复合板的控制方程。然后，通过伽勒金方法，本研究建立了确定可变厚度 FGM 板固有频率的解决方案。所获得的 FGM 板结果通过 MATLAB 程序进行计算。为了证实当前计算模型的准确性，我们将获得的结果与之前公开文献中报道的数据进行了比较。新理论得出的结果不仅与各向同性材料制成的板材进行了比较，还与功能分级材料制成的板材进行了比较。在这两种情况下，与经典板理论（CPT）、一阶剪切变形板理论（FSDPT）和其他剪切变形板理论相比，所提出的理论都表现出卓越的性能，误差率显著降低。此外，还提供了克尔地基三参数刚度、边界条件、几何参数、两种不同的 FGM、FGM 指数和模数对 FGM 板振动行为影响的图示。

A corotational isogeometric assumed natural strain shell element in updated Lagrangian formulation for general geometric nonlinear analysis of thin-walled structures

Han Qinghua, Wu Chao, Liu Mingjie, Wu Hao

doi:10.1016/j.tws.2023.111311

用于薄壁结构一般几何非线性分析的更新拉格朗日公式中的相关等几何假定自然应变壳元素

A new general geometric nonlinear curved quadrilateral shell element, which can handle large displacements and large rotations, is presented in this paper. It is formulated based on the incremental virtual work equation in updated Lagrangian formulation for general large displacement analysis. The kinematics of shell element is described using non-uniform B-spline patch, which results in the element displacement field with higher order continuity and the element performance more resistive to shear locking and membrane locking. In order to perfectly avoid such membrane locking and shear locking behaviors, the assumed in-plane membrane strain field and the assumed transverse shear strain field for the incremental covariant Green-Lagrange strain are constructed as linear combinations of non-uniform B-spline basis functions with degrees lower than those adopted by the original displacement field interpolation. In addition, based on Euler parameters, the corotational procedure available for high order isogeometric shell element is developed to extract the strain-producing deformational displacements and rotations and to update the element stresses and realistic internal force vectors. The accuracy and robustness of proposed shell element are demonstrated through the solutions of various benchmark problems.

本文介绍了一种新的通用几何非线性曲面四边形壳元素，它可以处理大位移和大旋转。它是根据更新的拉格朗日公式中的增量虚功方程制定的，适用于一般的大位移分析。壳元素的运动学采用非均匀 B-样条贴片描述，这使得元素位移场具有更高阶的连续性，元素性能更能抵抗剪切锁定和膜锁定。为了完美避免这种膜锁定和剪切锁定行为，将增量协变格林-拉格朗日应变的假定平面内膜应变场和假定横向剪切应变场构建为非均匀 B 样条基函数的线性组合，其度数低于原始位移场插值所采用的度数。此外，在欧拉参数的基础上，开发了适用于高阶等几何壳元素的相关程序，以提取产生应变的变形位移和旋转，并更新元素应力和现实内力矢量。通过对各种基准问题的求解，证明了所提出的壳元素的准确性和稳健性。

A novel beam element with nine DOFs per node for resolving the warping-distortion compatibility in analysis of frames and curved beams made of I-sections

Liu Y.Z., Yang Y.B., Liu X.H., Guo D.Z., Xu H.

doi:10.1016/j.tws.2023.111314

一种新型梁元素，每个节点有九个 DOFs，用于在分析由工字截面组成的框架和弯曲梁时解决翘曲-变形兼容性问题

Warping-distortion coupling is common in frames and curved beams made of I-sections, which tends to decrease significantly the lateral and torsional resistance of structures. Traditionally, it has been difficult to consider such effects in structural analysis, because the warping and distortional degrees of freedom (DOFs) of two connected elements at a common joint cannot be easily transformed to a common coordinate system for global stiffness assembly. The purpose of this paper is to conquer such a problem. By introducing the symmetric and anti-symmetric distortion modes, in addition to the warping and conventional six DOFs, this paper develops a new theory that consists of nine DOFs per node for the two-node I-beam element. The three deformational DOFs of the cross-section, i.e., the symmetric distortion, anti-symmetric distortion and warping, can be regarded as three mechanical couples relating to the twisting, shearing and bending, respectively, of the two flanges in the opposite sense. This allows all the DOFs of the connected elements at a common joint to be easily transformed to the global coordinates for stiffness assembly. As a result, the warping-distortion compatibility problem that occurs in frames and curved beams is resolved. In the exemplar studies, the present beam element has been demonstrated to be capable of producing results that are in excellent agreement with those of the shell element for the lateral deformation of angled frames with unstiffened and stiffened joints and of curved beams with various boundary conditions. It is also observed that the cross-sectional distortion effect becomes more manifest in curved I-beams of high curvature or of high flange-to-web rigidity ratio.

翘曲变形耦合在工字截面框架和曲线梁中很常见，往往会显著降低结构的抗侧和抗扭能力。传统上，在结构分析中很难考虑到这种效应，因为在一个共同的连接点上，两个连接元素的翘曲和扭曲自由度（DOFs）不容易转换到一个共同的坐标系中进行全局刚度装配。本文旨在解决这一问题。除了翘曲和传统的六个 DOF 外，本文还引入了对称和反对称变形模式，从而为双节点工字钢元素建立了一种新理论，即每个节点包含九个 DOF。横截面的三个变形 DOF，即对称变形、反对称变形和翘曲，可视为分别与两个翼缘的扭转、剪切和弯曲相关的三个相反意义的机械耦合。这样，在一个共同的连接点上，连接元素的所有 DOFs 都可以很容易地转换为刚度装配的全局坐标。因此，在框架和弯曲梁中出现的翘曲变形兼容性问题得以解决。在示例研究中，对于具有未加固和加固连接的角形框架以及具有各种边界条件的曲线梁的横向变形，本梁元素的结果与壳元素的结果非常一致。此外，我们还发现，截面变形效应在高曲率或高翼缘刚度比的弯曲工字钢中表现得更为明显。