International Journal of Solids and Structures最新文献_第2页

Bending-column woven mesh structure based on body-centered cubic structure 基于体心立方结构的弯柱编织网结构

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-05-01 Epub Date: 2026-02-08 DOI: 10.1016/j.ijsolstr.2026.113892

Lan Chen , Zhiheng Zhang , Yibo Huang , Xinzhou Zhang , Lijia Fang , Haisheng Zhao , Xudong Ren

Truss lattice structures have garnered significant attention due to their simple topological configurations and exceptional resistance to deformation and energy absorption capabilities. This paper proposes a design methodology for woven lattice structures based on bending struts to overcome the limitations of traditional body-centered cubic (BCC) lattices in stiffness enhancement and buckling control. The structure exhibits high flexibility during initial deformation to mitigate stress concentration, while enhancing stiffness through strut self-contact during large deformations. Using selective laser melting technology to fabricate 316 L stainless steel specimens, combined with experiments and simulations, we systematically analyze the mechanical behavior of BCC, flexible lattice, and woven lattice structures. Results indicate that woven structures outperform BCC lattices in both specific energy absorption and plateau stress. The FBCC-F exhibits a plateau stress of 52.72 MPa, approximately 90% higher than BCC, with specific energy absorption improved by about 80%. FBCC-C exhibits superior stability and impact resistance at high strain rates. When rod diameters exceed 0.76 mm, its strain response is minimally affected, while self-contact effects mitigate fracture tendencies in thicker rods, demonstrating excellent relative density adaptability. The proposed bending strut design strategy holds promise for expanding the application potential of truss lattices in practical engineering scenarios such as impact resistance and large deformation protection.

桁架晶格结构由于其简单的拓扑结构和卓越的抗变形和能量吸收能力而引起了人们的极大关注。针对传统体心立方结构在刚度增强和屈曲控制方面的局限性，提出了一种基于弯曲杆的编织网格结构设计方法。结构在初始变形时表现出高柔韧性，以减轻应力集中，同时在大变形时通过支柱自接触提高刚度。采用选择性激光熔化技术制备316l不锈钢试样，结合实验和模拟，系统分析了BCC、柔性晶格和编织晶格结构的力学行为。结果表明，编织结构在比能量吸收和高原应力方面都优于BCC晶格。FBCC-F的平台应力为52.72 MPa，比BCC高约90%，比能吸收提高约80%。FBCC-C在高应变率下表现出优异的稳定性和抗冲击性。当杆径超过0.76 mm时，其应变响应受影响最小，而自接触效应可缓解较厚杆的断裂倾向，表现出优异的相对密度适应性。提出的弯曲支撑设计策略有望扩大桁架格架在抗冲击和大变形防护等实际工程场景中的应用潜力。

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引用次数: 0

Modulating energy storage properties in layered paraelectric/ferroelectric/paraelectric composites via thickness and strain engineering 通过厚度和应变工程调制层状拟电/铁电/拟电复合材料的储能性能

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-05-01 Epub Date: 2026-02-11 DOI: 10.1016/j.ijsolstr.2026.113897

Zihe Wang , Chengwen Bin , Sizheng Zheng , Jie Wang

Ferroelectric capacitors hold great promise for energy storage applications due to their rapid charge/discharge rates and high breakdown strength. However, the relatively low density and efficiency of energy storage limit their practical application, and it is necessary to develop methods to improve their performance. In this study, we introduce a synergistic modulation of layer thickness and strain to enhance the energy storage density and efficiency of paraelectric/ferroelectric/paraelectric (SrTiO₃/PbTiO₃/SrTiO₃) composite multilayer structure. Phase field simulations reveal that the layered composites exhibit superior energy storage properties when the thickness of paraelectric (PE) layer exceeds that of ferroelectric (FE) layers in the studied range of thickness. Under different in-plane strains, larger tensile strains are found to enhance the energy storage performance by effectively reducing the remnant polarization. Furthermore, by carefully adjusting the layer thickness and applied strain, the layered composites exhibit tunable hysteresis loops of polarization versus electric field, including ferroelectric, antiferroelectric-like, and paraelectric-like characteristics. When the layer thickness and strain modulate synergistically, the sensitivity of the composite’s energy storage performance to strain becomes more pronounced as the thickness of the FE layer increases. Consequently, the optimal thicknesses of the FE and PE layers increase as the applied tensile strain increases. This modulation approach for the SrTiO₃/PbTiO₃/SrTiO₃ composite can also be extended to other layered PE/FE/PE systems, providing valuable guidance for optimizing the energy storage performance through either independent or synergistic adjustment of layer thickness and strain.

铁电电容器由于其快速的充放电速率和高击穿强度而在储能应用中具有很大的前景。然而，相对较低的储能密度和效率限制了其实际应用，有必要开发提高其性能的方法。在这项研究中，我们引入了层厚度和应变的协同调制，以提高对电/铁电/对电（SrTiO3/PbTiO3/SrTiO3）复合多层结构的储能密度和效率。相场模拟结果表明，当准电层厚度在研究范围内超过铁电层厚度时，层状复合材料表现出优异的储能性能。在不同的面内应变下，较大的拉伸应变可以有效减少残余极化，从而提高储能性能。此外，通过仔细调整层厚度和施加应变，层状复合材料表现出可调谐的极化滞后回路，包括铁电性、反铁电性和类准电性。当层厚和应变协同调制时，随着层厚的增加，复合材料储能性能对应变的敏感性更加明显。因此，FE和PE层的最佳厚度随着外加拉伸应变的增加而增加。这种SrTiO3/PbTiO3/SrTiO3复合材料的调制方法也可以推广到其他层状PE/FE/PE体系，为通过单独或协同调节层厚和应变来优化储能性能提供了有价值的指导。

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引用次数: 0

Optimizing membrane–substrate buckling to control surface deformation pattern 优化膜-衬底屈曲控制表面变形模式

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-05-01 Epub Date: 2026-02-12 DOI: 10.1016/j.ijsolstr.2026.113898

Wei Zhou, Robert Hewson, Matthew Santer

Buckling of membrane–substrate structures can result in complex deformation patterns on their top surfaces. Traditionally, control over these patterns has relied on altering the material or thickness ratios of the system, which imposes considerable constraints on design flexibility. Inspired by studies on Winkler foundation optimization, this work presents a novel framework for tailoring membrane–substrate buckling modes via topology optimization. In this approach, the material distribution within the substrate is optimized to tune the mechanical response, while filtering and projection techniques are incorporated to enhance manufacturability. Post-processing of the optimized layout yields a physically realizable structure that preserves the desired mechanical behavior. A two-dimensional case study demonstrates that the optimized design successfully generates the prescribed deformation pattern without modifying material properties or thickness ratios, thus enabling precise control over buckling-induced surface morphologies. Experimental validation using fabricated prototypes subjected to compression further confirms that the observed buckling modes closely match the targeted patterns, underscoring the practical effectiveness of the proposed method.

膜基结构的屈曲会导致其顶部表面产生复杂的变形模式。传统上，对这些图案的控制依赖于改变系统的材料或厚度比，这对设计灵活性施加了相当大的限制。受Winkler基础优化研究的启发，本文提出了一种通过拓扑优化来裁剪膜-基底屈曲模式的新框架。在这种方法中，基板内的材料分布被优化以调整机械响应，同时结合过滤和投影技术以提高可制造性。优化布局的后处理产生了物理上可实现的结构，保留了所需的机械性能。二维案例研究表明，优化设计成功地生成了规定的变形模式，而不改变材料性能或厚度比，从而能够精确控制屈曲引起的表面形貌。利用预制原型进行压缩实验验证，进一步证实了所观察到的屈曲模式与目标模式紧密匹配，强调了所提出方法的实际有效性。

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引用次数: 0

Ductile-to-brittle transition in high-strength steel: Experiments and damage-coupled constitutive modeling 高强度钢的韧脆转变：实验与损伤耦合本构模型

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-05-01 Epub Date: 2026-02-10 DOI: 10.1016/j.ijsolstr.2026.113896

Zhichao Wei, Guoxi Mao, Dongsong Li, Berk Tekkaya, Sophie Stebner, Sebastian Münstermann

This paper focuses on the experimental and numerical analysis of the ductile-to-brittle behavior of the high-strength low-alloy (HSLA) steel. Different uniaxial experiments, using samples manufactured from 2 mm thick sheet metal and covering a wide range of stress states, were conducted to identify the elastic, plastic, and ductile damage and fracture loci, and the details of the experimental–numerical hybrid identification strategy are discussed. In addition, a series of sub-sized V-notch Charpy tests from room temperature to -196°C were performed to investigate the ductile-to-brittle transition behavior. For numerical simulations, a modified Bai and Wierzbicki stress-state-dependent yield condition considering isotropic damage by incorporating a scalar damage variable is used to capture the elastic–plastic-damage behavior. The damage evolution is driven by energy dissipation. An extended stress-triaxiality-dependent Johnson–Cook-type damage and fracture model is developed by incorporating the Lode angle parameter to capture the initiation of ductile damage and fracture more accurately. Moreover, a novel temperature-dependent stress-based criterion is introduced to model brittle fracture. The proposed damage and fracture continuum framework accurately captures and predicts the ductile-to-brittle material behavior and can serve as an alternative to the traditional fracture toughness method for characterizing fracture behavior.

本文对高强度低合金（HSLA）钢的延脆行为进行了试验和数值分析。在不同的单轴实验中，采用2mm厚的金属板，覆盖了不同的应力状态，以识别弹性、塑性和延性损伤和断裂位点，并讨论了实验-数值混合识别策略的细节。此外，在室温至-196℃范围内进行了一系列小尺寸v型缺口Charpy试验，以研究其韧脆转变行为。在数值模拟中，采用考虑各向同性损伤的修正的Bai和Wierzbicki应力状态相关屈服条件，加入标量损伤变量来描述弹塑性损伤行为。损伤演化是由能量耗散驱动的。通过纳入Lode角参数，建立了扩展的应力-三轴依赖的johnson - cook型损伤和破裂模型，以更准确地捕获韧性损伤和破裂的起始。此外，还引入了一种新的基于温度相关应力的脆性断裂准则。所提出的损伤和断裂连续体框架可以准确地捕获和预测材料的韧性-脆性行为，可以替代传统的断裂韧性方法来表征断裂行为。

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引用次数: 0

Enhancing elastic energy focusing in multimode strain regions via Bayesian optimization of gradient-index phononic crystals for energy harvesting 利用梯度折射率声子晶体的贝叶斯优化增强多模应变区的弹性能量聚焦

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-22 DOI: 10.1016/j.ijsolstr.2026.113871

Wabi Demeke , Sangryun Lee , Wonju Jeon , Seunghwa Ryu

Metamaterials composed of gradient-index (GRIN) phononic crystals (PnCs), which contain unit cells whose sizes vary perpendicular to the direction of wave propagation, serve as a means of focusing elastic waves for energy harvesting. Owing to the finite wavelength of the propagating wave, GRIN PnCs localize the wave within a finite-sized region, which experiences multimodal strains instead of focusing on a single focal point with a single mode of strain. Consequently, the energy harvesting of elastic waves across a localized, finite region has recently gained research interest. This is due to the advantage of harvesting more energy through a properly designed piezoelectric energy harvester (PEH) that is larger than the wavelength of the elastic wave. However, the design of unit cells in GRIN PnC has been predominantly limited to simple shapes. This study introduces random hole shapes in GRIN PnC to enhance the intensity of elastic energy localization across targeted finite-sized region, utilizing a data-efficient surrogate model through Bayesian optimization (BO). Additionally, the developed BO method identifies a unit cell design that offers wave focusing intensity comparable to that of benchmark deep neural network (DNN)-based optimization, while requiring only 5.9% of the dataset. This advancement in wave localization significantly enhances the wave localization intensity in the target region by 36% and improves power generation by up to 1.5 times compared to GRIN PnC design with simple circular hole.

由梯度指数（GRIN）声子晶体（pnc）组成的超材料，其包含大小垂直于波传播方向变化的单元胞，可作为聚焦弹性波的能量收集手段。由于传播波的波长有限，GRIN pnc将波定位在有限尺寸的区域内，该区域经历多模态应变，而不是聚焦在单一焦点上，具有单一应变模态。因此，弹性波在局部有限区域的能量收集最近引起了人们的研究兴趣。这是由于通过适当设计的比弹性波波长更大的压电能量收集器（PEH）收集更多能量的优势。然而，GRIN PnC中单元胞的设计主要局限于简单的形状。本研究通过贝叶斯优化（BO），利用数据高效的替代模型，在GRIN PnC中引入随机空穴形状，以增强目标有限尺寸区域的弹性能量局部化强度。此外，开发的BO方法确定了一种单元格设计，提供与基准深度神经网络（DNN）优化相当的波聚焦强度，而只需要5.9%的数据集。与具有简单圆孔的GRIN PnC设计相比，这一波定位技术的进步将目标区域的波定位强度显著提高了36%，发电量提高了1.5倍。

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引用次数: 0

Adaptive stiffness–prestress sensitivity of morphing tensegrities 变形张拉整体的自适应刚度-预应力敏感性

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-31 DOI: 10.1016/j.ijsolstr.2026.113878

Hao Hong, Hua Deng

The adaptivity of tensegrities in tuning the sensitivity of structural stiffness to prestress through active deformation is investigated in this paper. Unlike conventional structures with a full-rank elastic stiffness matrix, tensegrities feature an elastic stiffness matrix containing a null space due to their inherent mechanism characteristics. The stiffness components within this null space are entirely contributed by the geometrical stiffness induced by prestress; this constitutes an advantage of tensegrities in stiffness adjustment. This paper reveals that with respect to prestress, the sensitivity of structural stiffness components that resist a specified external load depends on the projection of the load onto the null space of the elastic stiffness matrix. Accordingly, the “null space proportion” is defined to quantify this projection and serves as an indicator for tuning stiffness–prestress sensitivity. The null space of the elastic stiffness matrix theoretically corresponds to the space of the mechanism displacement modes and is determined solely by the geometry of tensegrities. A strategy is proposed for tuning the stiffness–prestress sensitivity according to the established incremental relationship between the eigenvectors within this null space and the vector of member rest lengths. This strategy can either increase or suppress this sensitivity through the active deformation of tensegrities via member length actuation. Two illustrative examples, including a 6-bar 24-cable tensegrity and a 4-layer modular tensegrity robotic arm, are presented to verify the validity of the proposed strategy. The tunable stiffness–prestress sensitivity highlights an essential aspect of the adaptivity of tensegrities.

本文研究了张拉体通过主动变形调节结构刚度对预应力敏感性的自适应性。与传统结构的全秩弹性刚度矩阵不同，张拉整体结构由于其固有的力学特性，其弹性刚度矩阵包含一个零空间。刚度组件在这个零空间完全是由预应力引起的几何刚度贡献;这构成了张拉整体在刚度调整方面的优势。本文揭示了相对于预应力，结构刚度组件的敏感性，以抵御一个特定的外部载荷取决于在零空间的弹性刚度矩阵上的荷载的投影。因此，定义“零空间比例”来量化该投影，并作为调整刚度-预应力灵敏度的指标。弹性刚度矩阵的零空间在理论上对应于机构位移模态的空间，并且仅由张拉整体的几何形状决定。根据建立的零空间特征向量与构件休息长度向量之间的增量关系，提出了一种调整刚度-预应力灵敏度的策略。该策略可以通过构件长度驱动的张拉整体主动变形来增加或抑制这种敏感性。给出了两个示例，包括6杆24索张拉整体和4层模块化张拉整体机械臂，以验证所提出策略的有效性。可调刚度-预应力敏感性突出了张拉整体自适应的一个重要方面。

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引用次数: 0

Postbuckling analysis of multi-segment interconnects for stretchable electronics 可拉伸电子元件多段互连的后屈曲分析

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-02-05 DOI: 10.1016/j.ijsolstr.2026.113884

Feiyu Xie , Shu Guo , Lijuan Sun , Yang Zhao , Yewang Su

The advent of stretchable electronics marks a revolutionary departure from brittle silicon-based technology, enabling devices to adapt, flex, and operate in previously inaccessible ways. Multi-segment interconnects, such as zigzag, serpentine and fractal designs, substantially enhance the stretchability compared with the single-segment straight/curved interconnects for the island-bridge, mesh structures of stretchable electronics. However, the absence of rigorous mechanical continuity conditions at segment junctions hinders the application of well-established single-segment interconnect postbuckling theories to multi-segment systems. In this paper, mechanical continuity conditions at segment junctions are formulated and integrated with our developed single-segment straight interconnect postbuckling theory, enabling a systematic method for accurate postbuckling analysis of multi-segment interconnects. Crucially, to ensure the accuracy of the postbuckling analysis, it is demonstrated that these mechanical continuity conditions must account for displacement terms up to the 3rd order. A zigzag interconnect under stretch is analyzed as a representative example using the proposed method, revealing the presence of both symmetric and anti-symmetric buckling modes. For both buckling modes, the analysis establishes the relationships between the apparent applied strain and maximum deformation quantities, namely the maximum twist angle for the symmetric mode and the maximum lateral displacement for the anti-symmetric mode, and evaluates the impact of inter-segment angles on postbuckling load increments. This analytical framework provides an efficient theoretical basis for the design of stretchable electronics.

可伸缩电子设备的出现标志着脆性硅基技术的革命性转变，使设备能够以以前无法实现的方式适应、弯曲和操作。多段互连，如之字形、蛇形和分形设计，与单段直/弯互连相比，大大提高了可拉伸电子器件的岛桥、网格结构的可拉伸性。然而，在节段连接处缺乏严格的力学连续性条件，阻碍了成熟的单节段互连后屈曲理论在多节段系统中的应用。本文建立了管片连接点的力学连续性条件，并将其与我们开发的单管片直线型互连后屈曲理论相结合，为多管片互连后屈曲的精确分析提供了系统的方法。至关重要的是，为了确保后屈曲分析的准确性，证明了这些力学连续性条件必须考虑到三阶位移项。以拉伸下的锯齿形互连为例进行了分析，揭示了对称和反对称屈曲模式的存在。对于两种屈曲模式，分析建立了视外加应变与最大变形量之间的关系，即对称模态的最大扭转角和反对称模态的最大侧向位移，并评估了段间角对屈曲后载荷增量的影响。该分析框架为可拉伸电子器件的设计提供了有效的理论依据。

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引用次数: 0

A framework for finite-strain viscoelasticity based on rheological representations 基于流变学表征的有限应变粘弹性框架

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-02-09 DOI: 10.1016/j.ijsolstr.2026.113893

Chongran Zhao, Hongyan Yuan, Ju Liu

This work presents a new constitutive and computational framework based on strain-like internal variables belonging to Sym(3) and two representative rheological configurations. The generalized Maxwell and generalized Kelvin–Voigt models are considered as prototypes for parallelly and serially connected rheological devices, respectively. For each configuration, distinct kinematic assumptions are introduced. The constitutive theory is derived based on thermomechanical principles, where the free energies capture recoverable elastic responses and dissipation potentials govern irreversible mechanisms. The evolution equations for the internal variables arise from the principle of maximum dissipation. A key insight is the structural distinction in the constitutive laws resulted from the two rheological architectures. In particular, the Kelvin–Voigt model leads to evolution equations with non-equilibrium processes coupled, which pose computational challenges for the constitutive integration. To address this, we exploit the Sherman–Morrison–Woodbury formula and extend it to tensorial equations to design an efficient strategy during constitutive integration. With that strategy, the integration can be performed based on an explicit update formula, and the algorithmic complexity scales linearly with the number of non-equilibrium processes. This framework offers both modeling flexibility and computational feasibility for simulating materials with multiple non-equilibrium processes and complex rheological architectures under finite strain.

这项工作提出了一个新的本构和计算框架，该框架基于属于Sym(3)和两个代表性流变构型的类应变内部变量。将广义Maxwell模型和广义Kelvin-Voigt模型分别视为并联和串联流变装置的原型。对于每种构型，引入了不同的运动学假设。本构理论是基于热力学原理推导的，其中自由能捕获可恢复的弹性响应，耗散势控制不可逆机制。内部变量的演化方程来源于最大耗散原理。一个关键的洞察力是本构律的结构区别，这是由两种流变结构造成的。特别是，Kelvin-Voigt模型导致非平衡过程耦合的演化方程，这给本构积分的计算带来了挑战。为了解决这个问题，我们利用Sherman-Morrison-Woodbury公式并将其扩展到张量方程，以设计本构积分期间的有效策略。使用该策略，可以基于显式更新公式执行集成，并且算法复杂度随非平衡过程的数量线性扩展。该框架为模拟有限应变下具有多种非平衡过程和复杂流变结构的材料提供了建模灵活性和计算可行性。

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引用次数: 0

Scattering of cylindrical waves by a finite crack in 2D: dynamic stress intensity factors governed by wavefront curvature 二维有限裂纹对圆柱波的散射：由波前曲率控制的动应力强度因子

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-31 DOI: 10.1016/j.ijsolstr.2026.113879

Shangqi Yuan , Fuqing Chu , Hui Qi , Haikun Chen , Jing Guo

The scattering of elastic waves by cracks is a fundamental mechanism governing dynamic fracture and structural integrity assessment. While solutions for plane wave incidence are well-established, the more practically relevant scenario of scattering by cylindrical wavefronts has remained a significant analytical challenge due to the complex, spatially non-uniform loading it induces along finite crack faces. This work presents the comprehensive semi-analytical solution for the scattering of time-harmonic cylindrical SH-waves by a finite Griffith crack in an infinite, homogeneous, isotropic elastic medium. The solution is achieved via a rigorous regional matching method that systematically decomposes the domain into near-tip regions, capturing the asymptotic singularity, and a far-field region accommodating wave propagation. This framework enables the direct and computationally efficient extraction of frequency-dependent dynamic stress intensity factors (DSIFs). Our results reveal a pronounced and persistent crack-tip asymmetry in the DSIFs under oblique incidence. A detailed parametric study demonstrates that wavefront curvature alters the dynamic fracture response, significantly expanding the critical azimuthal range for crack activation in the near-field and inducing complex, tip-dependent oscillatory behavior. The model has been rigorously verified against the classical plane-wave solutions and provides a definitive benchmark and a powerful analytical framework that advances the fundamental understanding of wave-scattering by defects in elastic media, with primary implications for the core theories of dynamic fracture.

弹性波在裂纹中的散射是动态断裂和结构完整性评价的基本机制。虽然平面波入射的解决方案已经建立，但圆柱波前散射的实际情况仍然是一个重大的分析挑战，因为它沿有限裂纹面引起了复杂的空间非均匀载荷。本文给出了有限Griffith裂纹在无限均匀各向同性弹性介质中散射时谐圆柱形sh波的综合半解析解。该解决方案是通过严格的区域匹配方法实现的，该方法系统地将域分解为近尖端区域，捕获渐近奇点，以及容纳波传播的远场区域。该框架能够直接和计算高效地提取频率相关的动态应力强度因子（DSIFs）。我们的结果揭示了明显和持久的裂纹尖端不对称在斜入射下的DSIFs。一项详细的参数研究表明，波前曲率改变了动态断裂响应，显著扩大了近场裂纹激活的临界方位范围，并诱发了复杂的、依赖于尖端的振荡行为。该模型已与经典平面波解进行了严格验证，并提供了一个明确的基准和强大的分析框架，促进了对弹性介质中缺陷波散射的基本理解，并对动态断裂的核心理论产生了初步影响。

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引用次数: 0

Exact analysis of bending of a heterogeneous plate with irregularly-shaped inclusions 含不规则形状夹杂物的非均质板弯曲的精确分析

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-04-15 Epub Date: 2026-01-02 DOI: 10.1016/j.ijsolstr.2025.113828

Emad Hasrati, Ankur Jain

Composite and functionally graded materials are used commonly in a broad variety of engineering systems. This work presents theoretical bending analysis of a simply supported heterogeneous rectangular plate containing discrete inclusions of irregular shapes. The commonly used governing equation for a homogeneous plate is generalized by accounting for inclusions of irregular shapes and different mechanical properties embedded within the plate. The heterogeneous plate problem is then solved by representing the spatial distributions of elastic moduli and Poisson’s ratios using Heaviside functions, thereby enabling an exact and efficient modeling of sharp discontinuities in these properties at the plate-inclusion interfaces. A series solution for the displacement field is derived using the integral and differential properties of the Heaviside function. The derivation is an exact generalized approach to handle multi-inclusion configurations with nonuniform properties, in contrast with previously presented approximate techniques such as homogenization and laminate approximation. Results are shown to reduce to the well-known Navier solution under special conditions. Good agreement with independent finite element simulations is also shown. A key finding of this work is that the location and shape of discrete inclusions, particularly their intersection with the high-bending regions of the plate, significantly influence the magnitude and spatial distribution of transverse deflection. Notably, stiff inclusions tend to displace the deflection peak away from themselves, while soft inclusions attract it, and in both cases, proximity to the plate boundaries can reverse these trends due to geometric and support-induced constraints. The technique developed here enables analysis of a number of practical problems comprising heterogeneous composites, as demonstrated through several examples. In addition to extending the state-of-the-art in theoretical analysis of composite structures, this work may also find practical applications in a number of engineering systems where such materials are used commonly.

复合材料和功能梯度材料广泛应用于各种工程系统中。这项工作提出了包含不规则形状离散夹杂物的简支非均质矩形板的理论弯曲分析。通过考虑嵌在板内的不规则形状和不同力学性能的夹杂物，推广了常用的均匀板控制方程。然后通过使用Heaviside函数表示弹性模量和泊松比的空间分布来解决非均质板问题，从而能够精确有效地模拟板-包裹体界面上这些属性的尖锐不连续。利用Heaviside函数的积分和微分性质，导出了位移场的级数解。与先前提出的近似技术（如均匀化和层压近似）相比，该推导是一种精确的广义方法来处理具有非均匀性质的多包含配置。结果表明，在特殊条件下，其解可约化为众所周知的纳维耶解。与独立有限元模拟结果吻合较好。这项工作的一个关键发现是，离散夹杂物的位置和形状，特别是它们与板块高弯曲区域的相交，显著影响横向挠度的大小和空间分布。值得注意的是，硬包裹体倾向于将偏转峰从自身移开，而软包裹体则吸引它，在这两种情况下，由于几何和支撑诱导的约束，靠近板块边界可以扭转这些趋势。本文开发的技术可以分析包含异质复合材料的许多实际问题，如通过几个示例所演示的那样。除了扩展复合材料结构理论分析的最新技术外，这项工作还可以在许多通常使用这种材料的工程系统中找到实际应用。

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引用次数: 0