【新文速递】2024年7月8日固体力学SCI期刊最新文章

 

今日更新：Journal of the Mechanics and Physics of Solids 5 篇，Mechanics of Materials 1 篇，Thin-Walled Structures 6 篇

Journal of the Mechanics and Physics of Solids

Physics-based discrete models for magneto-mechanical metamaterials

Gabriel Alkuino, Teng Zhang

doi:10.1016/j.jmps.2024.105759

基于物理的磁力学超材料离散模型

Magneto-mechanical metamaterials are emerging smart materials whose mechanical responses can be tailored through structure architecture and magnetic interactions. The latter provides additional freedom in the material design space and leads to novel behaviors due to its nonlocal nature. The enriched functionalities open new possibilities in various applications, such as actuators, energy absorbers, and soft robots. However, the nonlinear and nonlocal coupling between elastic and magnetic forces poses a great challenge in the modeling and simulation of these systems, further hindering theory-based rational design strategies. Here, we focus on a class of magneto-mechanical metamaterials, comprising elastic solids embedded with rigid permanent magnets. The clear separation between elastic and magnetic forces simplifies the design and fabrication process, yet their nonlocal interplay still allows for complex behaviors. We present a simulation framework for such magneto-mechanical metamaterials through combining a lattice spring model for the elastic solid with the dipole model for the magnetic interactions and implement it in the LAMMPS molecular dynamics software. We demonstrate the capabilities of our framework by simulating a few representative structures, including shape-locking lattice metamaterials, a soft cellular solid with controllable buckling, and a metamaterial chain with phase-transforming behavior. For the shape-locking lattice metamaterials, we successfully capture the magnetic-actuation-driven reconfiguration and the nonlinear mechanical response of the curved lattices. For the soft cellular solid, we identify its buckling patterns under external non-uniform magnetic fields and simulate a buckling evolution process consistent with experiments. For the metamaterial chain, we include the strong long-range interactions among the embedded magnets and reproduce the controllable phase transitions in the experiments. Our work provides a simple yet versatile simulation methodology to investigate the nonlinear mechanical behaviors in the presence of strong external and internal magnetic forces, which will facilitate the design and analysis of magneto-mechanical materials. It can also be applied to other magnetic driven smart structures, such as soft robots.

磁机械超材料是一种新兴的智能材料，其机械响应可通过结构架构和磁相互作用进行定制。后者为材料设计提供了额外的自由度，并由于其非局部性而产生新的行为。丰富的功能为致动器、能量吸收器和软机器人等各种应用提供了新的可能性。然而，弹性力和磁力之间的非线性和非局部耦合给这些系统的建模和仿真带来了巨大挑战，进一步阻碍了基于理论的合理设计策略。在此，我们重点研究一类磁力学超材料，包括嵌入刚性永磁体的弹性固体。弹性力和磁力之间的明确分离简化了设计和制造过程，但它们之间的非局部相互作用仍能产生复杂的行为。通过将弹性固体的晶格弹簧模型与磁相互作用的偶极子模型相结合，我们提出了针对此类磁机械超材料的模拟框架，并将其应用于 LAMMPS 分子动力学软件中。我们通过模拟一些具有代表性的结构，包括形状锁定晶格超材料、具有可控屈曲的软蜂窝固体和具有相变行为的超材料链，展示了我们的框架的能力。对于形状锁定晶格超材料，我们成功捕捉到了磁驱动的重新配置和弯曲晶格的非线性机械响应。对于软细胞固体，我们确定了其在外部非均匀磁场下的屈曲模式，并模拟了与实验一致的屈曲演化过程。对于超材料链，我们包含了嵌入磁体之间的强长程相互作用，并重现了实验中的可控相变。我们的工作提供了一种简单而通用的模拟方法，用于研究强内外磁力作用下的非线性力学行为，这将有助于磁力学材料的设计和分析。它还可应用于其他磁驱动智能结构，如软机器人。

A micromagnetic-mechanically coupled phase-field model for fracture and fatigue of magnetostrictive alloys

Shen Sun, Qihua Gong, Yong Ni, Min Yi

doi:10.1016/j.jmps.2024.105767

磁致伸缩合金断裂和疲劳的微磁-机械耦合相场模型

Magnetostrictive alloys are usually brittle materials with micromagnetic structures. Their structural reliability and durability depend on the complex micromagnetic-mechanical coupling at smaller length scales encompassing the evolution of micromagnetic structures. Herein we propose a micromagnetic-mechanically coupled phase-field model for fracture and fatigue behavior of magnetostrictive alloys with evolution of the micromagnetic structure. The thermodynamically-consistent model is derived from microforce theory, laws of thermodynamics, and Coleman–Noll analysis. The evolution of crack phase-field and magnetization-vector order parameters that are fully coupled is governed by history field dependent Allen–Cahn and Landau–Lifshitz–Gilbert equations, respectively. The model is extended to fatigue by introducing a degradation prefactor for the fracture energy as a function of positive elastic energy. One-dimensional analyses are then presented to anatomize the crack driving forces in terms of fully coupled micromagnetic-mechanical and pure mechanical driving force. We demonstrate the model capabilities by finite-element numerical studies on the micromagnetic domain evolution during the crack propagation and the influence of external magnetic field for type-I, type-II, and three-point bending fracture, as well as for the fracture of a single-edge notched specimen with an elliptical inclusion. The simulation result shows that depending on how micromagnetic domains are switched under micromagnetic-mechanical coupling, the magnetic field can enhance or decrease the critical load. In the presence of inclusion with larger fracture toughness, a crack is found to nucleate in the tri-junction of multi-domain micromagnetic structure owing to the high elastic strain around the tri-junction point. It is further found that a suitable magnetic field promoting magnetization-vector rotation around the crack tip could remarkably improve the fracturing load and fatigue life. The results demonstrate the model promising for the study of micromagnetic-mechanically coupled fracture and fatigue in magnetostrictive alloys.

磁致伸缩合金通常是具有微磁结构的脆性材料。它们的结构可靠性和耐久性取决于微磁结构演化过程中较小长度尺度上复杂的微磁-机械耦合。在此，我们针对磁致伸缩合金的断裂和疲劳行为提出了一个微磁-机械耦合相场模型，该模型与微磁结构的演化有关。该模型与热力学相一致，由微力理论、热力学定律和 Coleman-Noll 分析得出。完全耦合的裂纹相场和磁化矢量阶次参数的演变分别受与历史场相关的 Allen-Cahn 和 Landau-Lifshitz-Gilbert 方程的支配。通过引入作为正弹性能量函数的断裂能退化预因子，该模型被扩展到疲劳领域。然后进行一维分析，根据完全耦合的微磁-机械和纯机械驱动力对裂纹驱动力进行解剖。我们通过有限元数值研究证明了该模型的能力，研究了 I 型、II 型和三点弯曲断裂以及带有椭圆夹杂物的单边缺口试样断裂的裂纹扩展过程中的微磁畴演化和外部磁场的影响。模拟结果表明，根据微磁域在微磁-机械耦合下的切换方式，磁场可以增强或减弱临界载荷。在具有较大断裂韧性的内含物存在时，由于三交点周围的弹性应变较大，裂纹会在多域微磁结构的三交点处成核。研究进一步发现，适当的磁场可促进裂纹尖端周围的磁化矢量旋转，从而显著提高断裂载荷和疲劳寿命。研究结果表明，该模型有望用于研究磁致伸缩合金的微磁-机械耦合断裂和疲劳。

An asymptotically consistent morphoelastic shell model for compressible biological structures with finite-strain deformations

Xiang Yu, Xiaoyi Chen

doi:10.1016/j.jmps.2024.105768

具有有限应变变形的可压缩生物结构的渐近一致形态弹性壳模型

We derive an asymptotically consistent morphoelastic shell model to describe the finite deformations of biological tissues using an energy approach. Biological materials may exhibit remarkable compressibility when under large deformations, and we take this factor into account for accurate predictions of their morphoelastic changes. The morphoelastic shell model combines the growth model of Rodriguez et al. and a novel shell model developed by us. We start from the three-dimensional (3D) morphoelastic model and construct the optimal shell energy based on a series expansion around the middle surface. A two-step variational method is applied that retains the leading-order expansion coefficient while eliminating the higher-order ones. The main outcome is a two-dimensional (2D) shell energy depending on the stretching and bending strains of the middle surface. The derived morphoelastic shell model is asymptotically consistent with three-dimensional morphoelasticity and can recover various shell models in literature. Several examples are shown for the verification and illustration.

我们推导出一种渐近一致的形态弹性壳模型，利用能量法描述生物组织的有限变形。生物材料在发生大变形时可能表现出显著的可压缩性，我们将这一因素考虑在内，以准确预测其形态弹性变化。形态弹性壳模型结合了罗德里格斯等人的生长模型和我们开发的新型壳模型。我们从三维（3D）形态弹性模型出发，根据围绕中间表面的序列展开构建最佳壳能。我们采用了一种两步变分法，在消除高阶膨胀系数的同时保留了前阶膨胀系数。主要结果是取决于中间表面拉伸和弯曲应力的二维（2D）壳能。推导出的形态弹性壳模型与三维形态弹性渐近一致，可以恢复文献中的各种壳模型。文中举了几个例子进行验证和说明。

Predicting mechanical properties of mitotic spindles with a minimal constitutive model

Houbo Sun, Jingchen Li, Yuehua Yang, Hongyuan Jiang

doi:10.1016/j.jmps.2024.105770

用最小构成模型预测有丝分裂纺锤体的机械特性

The mitotic spindle, crucial for precise chromosome segregation and cytoplasmic partitioning during cell division, demands stability against forces arising from chromosomal movements and thermal fluctuations. Despite its central role, the mechanical properties of spindles remain largely elusive. In this study, we delve into the mechanical properties of spindles through a comprehensive model encompassing interactions among centrosomes, microtubules, chromosomes, and molecular motors. Our model successfully reproduces the 3D self-assembly of spindles and their responses to mechanical forces. We find that the spindle exhibits viscoelastic properties, responding distinctively to stretch and compression. Rapid stretch induces transient softening of the spindle, while compression leads to temporary hardening. Based on the viscoelastic responses of spindles under constant-force and constant-displacement loadings, we propose a minimal constitutive model for the spindle structure. This constitutive model can not only accurately recapture the viscoelastic responses of spindles under stretch and compression but also predict the mechanical behaviors of spindles under constant-rate loadings and cyclic loadings, which are further verified by simulations. Therefore, our validated constitutive model can replace complex simulations, providing more interesting predictions and guidance for future experiments.

有丝分裂纺锤体对细胞分裂过程中染色体的精确分离和细胞质的分配至关重要，它需要在染色体运动和热波动所产生的力的作用下保持稳定。尽管起着核心作用，但纺锤体的机械特性在很大程度上仍然难以捉摸。在本研究中，我们通过一个包含中心体、微管、染色体和分子马达之间相互作用的综合模型，深入研究了纺锤体的机械特性。我们的模型成功地再现了纺锤体的三维自组装及其对机械力的反应。我们发现纺锤体具有粘弹性，对拉伸和压缩的反应截然不同。快速拉伸会导致纺锤体瞬时软化，而压缩则会导致暂时硬化。根据纺锤体在恒力和恒位移载荷下的粘弹性反应，我们提出了纺锤体结构的最小构成模型。该构成模型不仅能准确再现主轴在拉伸和压缩下的粘弹性响应，还能预测主轴在恒定速率载荷和循环载荷下的力学行为，并通过模拟进一步验证了这些力学行为。因此，我们经过验证的构成模型可以取代复杂的模拟，为未来的实验提供更有趣的预测和指导。

Active interfacial degradation/deposition of an elastic matrix by a fluid inclusion: Theory and pattern formation

Giancarlo Cicconofri, Pau Blanco, Guillermo Vilanova, Pablo Sáez, Marino Arroyo

doi:10.1016/j.jmps.2024.105773

流体夹杂物对弹性基质的主动界面降解/沉积：理论与模式形成

During collective invasion in 3D, cohesive cellular tissues migrate within a fibrous extracellular matrix (ECM). This process requires significant remodeling of the ECM by cells, notably proteolysis at the cell-ECM interface by specialized molecules. Motivated by this problem, we develop a theoretical framework to study the dynamics of a fluid inclusion (modeling the cellular tissue) embedded in an elastic matrix (the ECM), which undergoes surface degradation/deposition. To account for the active nature of this process, we develop a continuum theory based on irreversible thermodynamics, leading to a kinetic relation for the degradation front that locally resembles the force-velocity relation of a molecular motor. We further study the effect of mechanotransduction on the stability of the cell-ECM interface, finding a variety of self-organized dynamical patterns of collective invasion. Our work identifies ECM proteolysis as an active process possibly driving the self-organization of cellular tissues.

在三维集体入侵过程中，具有内聚力的细胞组织会在纤维状细胞外基质（ECM）中迁移。这一过程需要细胞对 ECM 进行大量重塑，特别是在细胞-ECM 界面由特化分子进行蛋白水解。受这一问题的启发，我们建立了一个理论框架来研究嵌入弹性基质（ECM）中的流体包裹体（模拟细胞组织）的动力学，该包裹体会发生表面降解/沉积。为了解释这一过程的主动性质，我们开发了基于不可逆热力学的连续理论，从而得出降解前沿的动力学关系，该关系局部类似于分子马达的力-速度关系。我们进一步研究了机械传导对细胞-ECM 界面稳定性的影响，发现了多种集体入侵的自组织动力学模式。我们的研究发现，ECM 蛋白溶解是一个可能驱动细胞组织自组织的活跃过程。

Mechanics of Materials

Predicting mechanical heterogeneity in glassy polymer nanocomposites via an inverse computational approach based on atomistic molecular simulations and homogenization methods

Malak Barakat, Hilal Reda, Panayiota Katsamba, Hassan Shraim, Vagelis Harmandaris

doi:10.1016/j.mechmat.2024.105082

通过基于原子分子模拟和均质化方法的反向计算方法预测玻璃聚合物纳米复合材料的机械异质性

Probing the mechanical behavior of the region formed between a nanoparticle reinforcement and a polymer matrix in a polymer nanocomposite structure, denoted as the “interphase”, is a main challenge as such regions are difficult to investigate by experimental methods. Here, we accurately characterize the heterogeneous mechanical behavior of polymer nanocomposites, focusing on polymer/nanofiller interphases via a combination of nanomechanical simulations and numerical homogenization techniques. Initially, the global mechanical performance of a glassy poly(ethylene oxide) polymer nanocomposite reinforced with silica nanoparticles is studied using detailed atomistic molecular dynamics simulations for 1.9% and 12.7% silica volume fractions. Next, the polymer/silica interphase thickness is identified by probing the polymer atom-based density distribution profile in the vicinity of the nanofiller at equilibrium. On the basis of this thickness, the interphase is subdivided to check the position-dependent change in mechanical properties. Then, using continuum mechanics and atomistic simulations, we proceed to compute the effective Young’s modulus and Poisson’s ratio of the polymer/nanoparticle interphase as function of the distance from the nanoparticle. In the last step, an inverse numerical homogenization model is proposed to predict the mechanical properties of the interphase on the basis of a comparison criteria with the data from MD. The results were found to be acceptable, raising the possibility of accurately and efficiently predicting interfacial properties in nanostructured materials.

在聚合物纳米复合材料结构中，纳米粒子增强体与聚合物基体之间形成的区域被称为 "相间"，探究该区域的力学行为是一大挑战，因为此类区域很难通过实验方法进行研究。在此，我们结合纳米力学模拟和数值均质化技术，准确描述了聚合物纳米复合材料的异质力学行为，重点关注聚合物/纳米填料间相。首先，通过详细的原子分子动力学模拟，研究了二氧化硅体积分数分别为 1.9% 和 12.7% 的玻璃状聚（环氧乙烷）聚合物纳米复合材料的整体机械性能。接着，通过探测平衡状态下纳米填料附近基于聚合物原子的密度分布曲线，确定了聚合物/二氧化硅相间厚度。在此厚度的基础上，对相间层进行细分，以检查机械性能随位置的变化。然后，利用连续介质力学和原子模拟，我们继续计算聚合物/纳米粒子间相的有效杨氏模量和泊松比与纳米粒子间距离的函数关系。最后，根据与 MD 数据的比较标准，提出了一个逆数值均质化模型来预测相间的机械性能。结果是可接受的，为准确有效地预测纳米结构材料的界面特性提供了可能。

Thin-Walled Structures

Constitutive model of die-cast light-alloy thin-walled parts considering geometric imperfection

Xueqiang Wang, Xin Wang, Lingyang Yuan, Siping Li, Liming Peng

doi:10.1016/j.tws.2024.112158

考虑几何缺陷的轻合金薄壁压铸件的结构模型

Replacing steel with aluminum and shifting from forging to casting have become important means of automotive lightweight. Large integrated die-cast parts are gaining popularity among original equipment manufacturers. Engineers often ignore the influence of geometric imperfection on mechanical properties when simulating strength of thin-walled parts, therefore causing a bias. To investigate the relation between geometric imperfections and mechanical properties of die-cast light alloy, quasi-static tensile tests are conducted on the specimens of JDA1b aluminum alloy and JDM1 magnesium alloy. The specimens exhibit varying geometric imperfection factors (from 0 to 90%) achieved by introducing circular holes with different diameters. The results show that the strength and elongation of JDA1b and JDM1 alloys decrease significantly as the geometric defect factor increases. Even small holes can significantly affect tensile strength. A constitutive model that incorporates the stress limit value and geometric imperfection factors is proposed, which has higher accuracy than the J–C model. Experiments and simulations on a die-cast thin-walled part validated the idea and proposed constitutive model. These findings provide essential insights into the influence of structural holes on the mechanical properties of die-cast light-alloy materials. The proposed constitutive model offers high-precision computational support for simulating the mechanical performance of parts.

以铝代钢、从锻造转向铸造已成为汽车轻量化的重要手段。大型集成压铸件越来越受到原始设备制造商的青睐。工程师在模拟薄壁零件强度时，往往会忽略几何缺陷对机械性能的影响，从而造成偏差。为了研究几何缺陷与压铸轻合金机械性能之间的关系，对 JDA1b 铝合金和 JDM1 镁合金试样进行了准静态拉伸试验。通过引入不同直径的圆孔，试样呈现出不同的几何缺陷系数（从 0 到 90%）。结果表明，随着几何缺陷系数的增加，JDA1b 和 JDM1 合金的强度和伸长率明显下降。即使是小孔也会严重影响拉伸强度。我们提出了一种包含应力极限值和几何缺陷因子的构成模型，其精度高于 J-C 模型。在压铸薄壁零件上进行的实验和模拟验证了这一想法和提出的构成模型。这些发现为了解结构孔对压铸轻合金材料机械性能的影响提供了重要依据。所提出的构成模型为模拟零件的机械性能提供了高精度的计算支持。

Constitutive behavior of asymmetric multi-material honeycombs with bi-level variably-thickened composite architecture

M. Awasthi, S. Naskar, A. Singh, T. Mukhopadhyay

doi:10.1016/j.tws.2024.112183

具有双层可变加厚复合结构的非对称多材料蜂窝的构效行为

Bi-level tailoring of cellular metamaterials involving a dual design space of unit cell and elementary beam level architectures has recently gained traction for the ability to achieve extreme elastic constitutive properties along with modulating multi-functional mechanical behavior in an unprecedented way. This article proposes an efficient analytical approach for the accurate evaluation of all constitutive elastic constants of asymmetric multi-material variably-thickened hexagonal lattices by considering the combined effect of bending, stretching, and shearing deformations of cell walls along with their rigid rotation. A tri-member unit cell is conceptualized, wherein all nine constitutive constants are obtained through the mechanics under one cell wall direction and subsequent repetitive coordinate transformations. We enhance the design space of lattice metamaterials substantially here by introducing multiple exploitable dimensions such as asymmetric geometry, multi-material unit cells and variably-thickened cell walls, wherein the conventional monomaterial auxetic and non-auxetic hexagonal configurations can be analyzed as special cases along with other symmetric and asymmetric lattices such as a range of rectangular and rhombic geometries. The generic analytical approach along with extensive numerical results presented in this paper opens up new avenues for efficient optimized design of the next-generation multi-functional lattices and cellular metamaterials with highly tailored effective elastic properties.

蜂窝超材料的双级定制涉及单元格和基本梁级架构的双重设计空间，最近因其能够以前所未有的方式实现极端弹性构成特性以及调节多功能机械行为而备受关注。本文提出了一种高效的分析方法，通过考虑晶胞壁的弯曲、拉伸和剪切变形及其刚性旋转的综合影响，精确评估非对称多材料可变加厚六边形晶格的所有构成弹性常数。我们构思了一个三元单元格，通过一个单元格壁方向下的力学以及随后的重复坐标变换，获得了所有九个构成常数。在此，我们通过引入多种可利用的维度，如非对称几何形状、多材料单元格和可变加厚的单元壁，大幅提升了晶格超材料的设计空间，其中传统的单材料辅助和非辅助六边形配置可作为特例与其他对称和非对称晶格（如一系列矩形和菱形几何形状）一起进行分析。本文介绍的通用分析方法和大量数值结果为高效优化设计具有高度定制有效弹性特性的下一代多功能晶格和蜂窝超材料开辟了新途径。

Dynamic fracture of hen’s eggshell under impact loading: A combined experimental, theoretical and numerical study

Cong Chen, Xianheng Wang, Yan Liu, Yiran Li, Kaitao Tang, Xinming Qiu

doi:10.1016/j.tws.2024.112192

冲击荷载下母鸡蛋壳的动态断裂：实验、理论和数值综合研究

As a typical biological material from nature, the eggshell possesses a smooth macroscale appearance with various curvatures and hierarchical microscale morphology, which contribute to the superior mechanical properties of this lightweight brittle material. The research on the biomimicry of the eggshell has attracted much attention. For both biological reproduction and the poultry industry, the dynamic fracture of the eggshell is a key issue and quite complex due to the thin-walled structure of the eggshell and the strong fluid-solid interaction between the eggshell and its content. In our work, the dynamic fracture of hen’s eggshells under the impact and the influence of the content are thoroughly investigated experimentally, numerically, and theoretically. The responses of eggshells are similar no matter what the content is and exhibit four stages under the same input kinetic energy. It is found that there are two self-protection mechanisms of an egg when subjected to impact, which serves as significant inspiration for the design of novel structures. Under the influence of curvatures, the non-simultaneous propagation of cracks in the thickness direction induces the hinge pattern and the spider-web-like crack network. In addition to its role in biology, the viscosity of the albumen can provide resistance to damage and protect the eggshell during the impact. It is suggested that exterior curvature and interior content can be optimized to absorb dynamic impact energy when designing a thin-walled structure.

作为一种典型的自然界生物材料，蛋壳具有光滑的宏观外观和不同的曲率，以及分层的微观形态，这些特点造就了这种轻质脆性材料优越的机械性能。蛋壳的生物仿生研究备受关注。对于生物繁殖和家禽业来说，蛋壳的动态断裂是一个关键问题，而且由于蛋壳的薄壁结构和蛋壳及其内容物之间强烈的流固相互作用而相当复杂。在我们的工作中，我们通过实验、数值和理论对母鸡蛋壳在冲击力和内含物影响下的动态断裂进行了深入研究。在输入动能相同的情况下，无论蛋壳的成分如何，蛋壳的反应都是相似的，并呈现出四个阶段。研究发现，鸡蛋在受到冲击时有两种自我保护机制，这对新型结构的设计具有重要启发意义。在曲率的影响下，裂纹在厚度方向上的非同步传播诱发了铰链模式和蛛网状裂纹网络。除了在生物学中的作用外，蛋白的粘度还能在撞击过程中提供抗破坏性并保护蛋壳。建议在设计薄壁结构时优化外部曲率和内部含量，以吸收动态冲击能量。

Nonlinear Free Vibration Analysis of Multi-Directional Functionally Graded Porous Sandwich Plates

Van-Chinh Nguyen, Huu-Quoc Tran, Minh-Tu Tran

doi:10.1016/j.tws.2024.112204

多方向功能分级多孔夹层板的非线性自由振动分析

Multi-directional functionally graded materials (MFGMs) have attracted significant research attention due to their advantages over one-directional FGMs. In MFGM structures, material properties can be tailored to grade in the required direction, overcoming practical problems like excessive temperature gradients or extreme deflections. This paper aims to investigate the nonlinear free vibration of MFG porous sandwich plates to improve their application in sandwich structures. The two outer layers of the plates are composed of three-directional functionally graded material (3D-FGM), with a bi-directional functionally graded material (2D-FGM) core layer. Additionally, the porosity distribution within the material matrix is assumed to be either even or uneven across the plate thickness. A higher-order finite element model based on Shi's plate theory and the von Kármán assumption is developed. The nonlinear free vibration frequencies are determined through the maximum vibrational amplitude using an iterative algorithm with a displacement control strategy. The accuracy and effectiveness of the proposed model are demonstrated through a comparison with published data. The results show that the vibration response is significantly influenced by various parameters. Specifically, increasing the material gradient indexes in the thickness direction enhances the frequency ratio, while increasing the gradient indexes in the length and width directions reduces it. Higher porosity coefficients in the core layer decrease the frequency ratio, whereas higher pore coefficients in the outer layers increase it. The additional knowledge gained from this study can help with future analysis and design procedures related to the nonlinear responses of these complex structures.

多向功能分级材料（MFGMs）因其优于单向功能分级材料而备受研究关注。在多方向功能分级材料结构中，材料特性可按所需方向进行分级，从而克服了温度梯度过大或极端挠度等实际问题。本文旨在研究 MFG 多孔夹层板的非线性自由振动，以改进其在夹层结构中的应用。夹层板的两个外层由三维功能分级材料（3D-FGM）组成，核心层为双向功能分级材料（2D-FGM）。此外，假定材料基体内的孔隙率分布在整个板厚上均匀或不均匀。基于 Shi 的板理论和 von Kármán 假设，建立了一个高阶有限元模型。通过采用位移控制策略的迭代算法，通过最大振幅确定非线性自由振动频率。通过与已公布数据的对比，证明了所提出模型的准确性和有效性。结果表明，振动响应受到各种参数的显著影响。具体来说，增加厚度方向的材料梯度指数会提高频率比，而增加长度和宽度方向的梯度指数则会降低频率比。核心层的孔隙系数越高，频率比越低，而外层的孔隙系数越高，频率比越高。从本研究中获得的更多知识有助于今后对这些复杂结构的非线性响应进行分析和设计。

Fire resistance time prediction and optimization of cold-formed steel walls based on machine learning

Kang Liu, Mingming Yu, Yaqiong Liu, Wei Chen, Zhiyuan Fang, James B.P. Lim

doi:10.1016/j.tws.2024.112207

基于机器学习的冷弯型钢墙体耐火时间预测与优化

Many full-scale experiments and numerical studies have been conducted to determine the fire performance of cold-formed steel (CFS) walls, but these studies are expensive and time consuming. This study proposes a machine learning (ML) based framework aiming at accurately predicting the fire resistance time (FRT) and optimizing the design of CFS walls under ISO 834 fire condition. To overcome the limitation of 32 experimental data points in the literature, a validated numerical method was used to generate 592 data points to expand the dataset of CFS walls, considering different wall configurations, various sheathing board types and thicknesses. The XGBoost (eXtreme Gradient Boosting) model was trained with numerical data and tested with experimental data. The hyperparameter tuning of the XGBoost model was implemented with Bayesian optimization, and it was found that the XGBoost model accurately predicted the FRT of CFS walls, with R2 and MAPE values being 0.933 and 8.46%, respectively. The prediction process of the XGBoost model was interpreted by the SHAP (SHapley Additive exPlanations) method to determine the relative importance of input variables. The NSGA-II algorithm was adopted to optimize the FRT-cost dual-objective of CFS walls and the Pareto front including optimal solutions was emerging. The cost for each solution of Pareto front sets was lower than that in the real dataset at same FRT level. This phenomenon implied that the ML-based optimization framework successfully identified the cost-efficient design process. The proposed ML-based optimization framework offers a promising alternative for engineers to design CFS walls effectively with both mechanical and economic objectives.

为了确定冷弯型钢（CFS）墙体的防火性能，已经进行了许多全尺寸实验和数值研究，但这些研究既昂贵又耗时。本研究提出了一种基于机器学习（ML）的框架，旨在准确预测耐火时间（FRT），并优化 ISO 834 火灾条件下 CFS 墙体的设计。为了克服文献中仅有 32 个实验数据点的局限性，我们使用一种经过验证的数值方法生成了 592 个数据点，以扩大 CFS 墙体的数据集，同时考虑到不同的墙体结构、各种覆面板类型和厚度。利用数值数据对 XGBoost（eXtreme Gradient Boosting）模型进行了训练，并用实验数据进行了测试。XGBoost 模型的超参数调整是通过贝叶斯优化实现的，结果发现 XGBoost 模型准确预测了 CFS 墙体的 FRT，R2 和 MAPE 值分别为 0.933 和 8.46%。XGBoost 模型的预测过程采用 SHAP（SHapley Additive exPlanations）方法进行解释，以确定输入变量的相对重要性。采用 NSGA-II 算法对 CFS 墙体的 FRT 成本双目标进行优化，出现了包括最优解在内的帕累托前沿。在相同 FRT 水平下，帕累托前沿集每个解的成本均低于真实数据集。这一现象表明，基于 ML 的优化框架成功地确定了具有成本效益的设计过程。所提出的基于 ML 的优化框架为工程师有效设计 CFS 墙体提供了一种兼顾机械和经济目标的可行方法。

Mechanical and thermal property analysis and optimization design of hybrid lattice structure based on triply periodic minimal surfaces

Hongling Ye, Fuwei Tian, Weilin He, Sujun Wang

doi:10.1016/j.tws.2024.112203

基于三周期极小面的混合晶格结构的机械和热性能分析及优化设计

Hybrid lattice structures have significant potential in engineering applications owing to their outstanding mechanical and thermal properties. In this paper, an innovative design strategy for hybrid lattice structures is proposed involving the integration of primitive surfaces with truss lattice configurations. This approach allows for the full exploitation of the mechanical and thermal properties inherent in each component, leading to the development of new hybrid lattice structures. Firstly, the quasi-static compression and fluid-solid coupling heat conduction analysis of the hybrid lattice structure is carried out by numerical simulation. Then the effects of surface wall thickness, and truss diameter on the mechanical and thermal properties of the lattice structure are discussed. Additionally, the mechanical performance of the array hybrid lattice structure is evaluated through quasi-static compression experiments. These experimental results are compared with those from the numerical simulations, validating the accuracy of the simulation model. Finally, a multi-objective optimization model targeting specific elastic modulus and heat dissipation performance (indicated by Nusselt number) is established, in response to the demand of aviation and aerospace industries for lightweight, load-bearing, and heat-dissipating multi-functional integrated lattice design. The non-dominated sorting genetic algorithm is utilized to solve the optimal model, and the distribution of feasible solutions and Pareto front are obtained. The results show that the interpenetrating hybrid lattice structure has a greater improvement in mechanical and thermal properties than the primitive surfaces. This research holds significant implications for the design of multi-performance hybrid lattice structures.

混合晶格结构因其出色的机械和热性能，在工程应用中具有巨大潜力。本文提出了混合晶格结构的创新设计策略，涉及原始表面与桁架晶格配置的整合。这种方法可以充分利用每个组件固有的机械和热性能，从而开发出新型混合晶格结构。首先，通过数值模拟对混合晶格结构进行了准静态压缩和流固耦合热传导分析。然后讨论了表面壁厚和桁架直径对晶格结构的机械和热性能的影响。此外，还通过准静态压缩实验评估了阵列混合晶格结构的机械性能。这些实验结果与数值模拟结果进行了比较，验证了模拟模型的准确性。最后，针对航空和航天工业对轻质、承重和散热多功能集成晶格设计的需求，建立了以特定弹性模量和散热性能（用努塞尔特数表示）为目标的多目标优化模型。利用非支配排序遗传算法求解最优模型，得到了可行解的分布和帕累托前沿。结果表明，与原始表面相比，穿插混合晶格结构在机械性能和热性能方面有更大的改善。这项研究对设计高性能混合晶格结构具有重要意义。