【新文速递】2024年3月12日固体力学SCI期刊最新文章

 

今日更新：International Journal of Solids and Structures 2 篇，Journal of the Mechanics and Physics of Solids 1 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 5 篇

International Journal of Solids and Structures

Physically consistent nonlocal macro-meso-scale damage model for quasi-brittle materials: A unified multiscale perspective

Yudong Ren, Guangda Lu, Jianbing Chen

doi:10.1016/j.ijsolstr.2024.112738

准脆性材料物理上一致的非局部宏观-中尺度损伤模型：统一的多尺度视角

Despite great efforts in capturing the damage evolution law in multiscale approaches in damage mechanics, much less attention has been paid to the conversion from geometric damage to energy dissipation. In the present paper, the newly proposed nonlocal macro-meso-scale damage (NMMD) model is physically consolidated and a multiscale point of view is consistently adopted in both the damage evolution and energy dissipation. In this model, for each macroscopic material point a mesoscopic structure is attached such that all the point pairs composed of this point and the points in its influence domain are connected to it when the material is intact. The deformation field under loading will result in deformation of point pairs, and thus mesoscopic damage related to a point pair will occur if the deformation index of this point pair exceeds the prescribed threshold. Such mesoscopic change among point pairs connected to a material point within its influence domain has two-fold consequences: geometrically the accumulation of mesoscopic damage will result in macroscopic discontinuity, and simultaneously the free energy will be dissipated, leading to degradation of mechanical behavior of quasi-brittle materials. In other words, the damage as a metric of the geometric discontinuity will lead to the damage in the sense of energy dissipation and degradation of mechanical behavior for quasi-brittle materials, which can be physically captured by the ratio of summation of all the dissipated mesoscopic free energy in point pairs to the free energy of intact material within the influence domain. This energy-based macroscopic damage could then be inserted into the framework of continuum damage mechanics. Therefore, the conversion from geometric damage to energetic damage is implemented on the mesoscale instead of the macroscale, and thus a macroscopic energetic degradation function is not needed. In addition, the structured strain which is suitable for quasi-brittle materials can be adopted to determine the deformation index of point pairs. Correspondingly, the macroscopic free energy can be split into dissipative and non-dissipative parts. In this way, several inconsistencies in the previous NMMD models are remedied. The influence of mesoscopic model parameters is investigated in depth, and several numerical examples including mode-I, mixed-mode and compressive splitting fracture problems of quasi-brittle materials are carried out. Numerical results indicate that the proposed model can not only well capture the cracking process with or without initial cracks but also quantitatively predict the load-deformation curves without mesh size sensitivity. Moreover, due to the inherent physical consistency, in mixed-mode cracking problems the proposed model performs better than the previous NMMD model. Problems to be further studied are also discussed.

尽管多尺度损伤力学方法在捕捉损伤演化规律方面做出了巨大努力，但对几何损伤到能量耗散的转换却关注较少。本文对新提出的非局部宏观-中尺度损伤（NMMD）模型进行了物理整合，并在损伤演化和能量耗散方面始终采用多尺度观点。在该模型中，每个宏观材料点都附有一个介观结构，当材料完好无损时，由该点及其影响域内的点组成的所有点对都与之相连。加载时的变形场将导致点对变形，因此，如果点对的变形指数超过规定阈值，就会发生与点对相关的介观损伤。在材料的影响域内，与材料点相连的点对之间的这种介观变化会产生两方面的后果：从几何角度看，介观损伤的累积会导致宏观上的不连续性，同时自由能也会耗散，从而导致准脆性材料的力学行为退化。换句话说，作为几何不连续性度量的损伤将导致准脆性材料在能量耗散和力学行为退化意义上的损伤，这可以通过点对中所有耗散的介观自由能之和与影响域内完整材料的自由能之比来物理地捕捉。然后，这种基于能量的宏观损伤可被 插入连续损伤力学的框架中。因此，从几何损伤到能量损伤的转换是在中观尺度而非宏观尺度上实现的，因此不需要宏观能量退化函数。此外，还可以采用适用于准脆性材料的结构应变来确定点对的变形指数。相应地，宏观自由能也可分为耗散和非耗散两部分。这样，以往 NMMD 模型中的一些不一致之处就得到了弥补。我们深入研究了介观模型参数的影响，并进行了几个数值示例，包括准脆性材料的 I 模式、混合模式和压缩劈裂断裂问题。数值结果表明，所提出的模型不仅能很好地捕捉有或无初始裂纹的开裂过程，而且能定量预测载荷-变形曲线，而对网格尺寸不敏感。此外，由于固有的物理一致性，在混合模式开裂问题中，所提出的模型比以前的 NMMD 模型表现更好。此外，还讨论了有待于进一步研究的问题。

Accounting for spatial distribution in mean-field homogenization of particulate composites

O.L. Cruz-González, R. Cornaggia, S. Dartois, R. Brenner

doi:10.1016/j.ijsolstr.2024.112747

颗粒复合材料平均场均质化中的空间分布考虑

Several analytical mean-field homogenization methods, which take into account the particle volume fraction, shape and orientation are readily available to estimate the effective properties of particulate composites. Models have also been proposed to account for the spatial distribution of the particles. The classical Ponte-Castañeda and Willis (PCW) model is based on a parametrization of the statistical distribution law, while the Interaction Direct Derivative (IDD) model associates a matrix cell to each inclusion, representative of close interactions. In the literature, the use of the IDD is commonly reduced to the particular case of the classical Mori and Tanaka (MT) scheme or to the aforementioned PCW model. The present study introduces an original approach to calibrate the IDD model, for 2D linear conductivity, based on representative images of the microstructure. The links between the models and the range of validity of the IDD model are discussed. Besides, an “IDD-based” PCW model and a two-step scheme are proposed for situations where the IDD estimate is inconsistent (lack of major symmetry). Finally, an image analysis method using Voronoï diagrams is implemented to define the cells associated to each inclusion and supply the models. The method is validated by comparisons between the obtained IDD and PCW estimates, the Mori–Tanaka (MT) model and benchmark full-field numerical simulations. Accounting for the inclusion distribution is seen to lead to better estimates, both qualitatively (by capturing anisotropic behaviors due to the sole distribution) and quantitatively. Possible extensions to elastic composites are discussed.

有几种考虑到颗粒体积分数、形状和取向的均场均质化分析方法可用于估算颗粒复合材料的有效特性。此外，还提出了考虑颗粒空间分布的模型。经典的 Ponte-Castañeda and Willis（PCW）模型是基于统计分布规律的参数化，而交互直接衍射（IDD）模型则将代表密切交互作用的矩阵单元与每个包含体联系起来。在文献中，IDD 通常被简化为经典的森和田中（Mori and Tanaka，MT）方案或上述 PCW 模型的特殊情况。本研究基于微观结构的代表性图像，介绍了一种校准二维线性传导性 IDD 模型的独创方法。讨论了模型之间的联系和 IDD 模型的有效范围。此外，针对 IDD 估计值不一致（缺乏主要对称性）的情况，提出了 "基于 IDD 的 "PCW 模型和两步方案。最后，使用 Voronoï 图实施了一种图像分析方法，以定义与每个内含物相关的单元并提供模型。通过比较所获得的 IDD 和 PCW 估计值、Mori-Tanaka（MT）模型和基准全场数值模拟，对该方法进行了验证。结果表明，考虑到夹杂物的分布，可以在定性（通过捕捉唯一分布导致的各向异性行为）和定量两方面获得更好的估算结果。还讨论了向弹性复合材料扩展的可能性。

Journal of the Mechanics and Physics of Solids

Thermal cracking: clarifying the effects of phases, voids and grains through characterisation and crystal plasticity modelling

Wei Wang, Ruiqiang Zhang, Amir A Shirzadi, Daniel S Balint, Lee Aucott, Jun Jiang

doi:10.1016/j.jmps.2024.105600

热裂纹：通过表征和晶体塑性建模澄清相、空隙和晶粒的影响

Thermally-induced cracking typically occurs during the cooling stage of various manufacturing processes, and is commonly seen in multiphase or the joints of dissimilar materials due to mismatch in their thermo-mechanical properties, such as thermal expansion, elastic-plastic deformation and, in some cases, phase transformation. However, the underlying cracking mechanism associated with local microstructure is still elusive. To improve the mechanistic understanding of thermal cracking, this work uses the diffusion-bonded 9Cr-1Mo steel as an example to study the key microstructural variables, such as interfacial phases, voids, grain boundary migration and crystallographic orientations. Meanwhile, a temperature-dependent crystal plasticity model coupled with a cohesive zone model is developed to provide more insights into the thermal-induced stress distribution at the grain scale. It is found that the stress at the void-free boundary of martensite and ferrite is dominated by shear, and its magnitude is insufficient to nucleate cracks. Whereas voids at phase boundaries can induce significant tensile stress, resulting in cracking at the phase boundaries as well as diffusion-bonded interfaces. Also, the occurrence of interfacial grain boundary migration plays an important role in local stress distribution. These microstructure features and their evolution are experimentally observed and used to verify the developed crystal plasticity models. These findings enhance the understanding of the influence of microstructure features on thermal cracking and provide a guide to designing and fabricating the microstructure with improved thermal crack resistance in various manufacturing processes.

热致开裂通常发生在各种制造工艺的冷却阶段，常见于多相材料或异种材料的连接处，其原因是材料的热机械性能不匹配，如热膨胀、弹塑性变形，有时还包括相变。然而，与局部微观结构相关的潜在开裂机制仍然难以捉摸。为了加深对热裂纹机理的理解，本研究以扩散结合的 9Cr-1Mo 钢为例，研究了关键的微观结构变量，如界面相、空隙、晶界迁移和结晶取向。同时，还建立了与温度相关的晶体塑性模型和内聚区模型，以便更深入地了解热诱导应力在晶粒尺度上的分布。研究发现，马氏体和铁素体无空隙边界处的应力主要是剪切力，其大小不足以形成裂纹。而相边界上的空隙会引起很大的拉应力，导致相边界以及扩散结合界面开裂。此外，界面晶界迁移在局部应力分布中也起着重要作用。这些微观结构特征及其演变都是通过实验观察到的，并用于验证所建立的晶体塑性模型。这些发现加深了人们对微观结构特征对热裂纹影响的理解，并为在各种制造工艺中设计和制造具有更好抗热裂纹性能的微观结构提供了指导。

International Journal of Plasticity

Exceptional strength-ductility synergy at room and liquid nitrogen temperatures of Al7.5Co20.5Fe24Ni24Cr24 high-entropy alloy with hierarchical precipitate heterogeneous structure

Chenliang Chu, Weiping Chen, Liran Huang, Hao Wang, Ling Chen, Zhiqiang Fu

doi:10.1016/j.ijplas.2024.103939

具有分层沉淀异质结构的 Al7.5Co20.5Fe24Ni24Cr24 高熵合金在室温和液氮温度下的优异强度-电导率协同作用

The study of alloys exhibiting noteworthy strength-ductility synergy at ambient and cryogenic temperatures has been a persistent area of interest in materials engineering. This interest extends to the recent development of high-entropy alloys (HEAs). The current investigation delves into the impact of diverse thermo-mechanical treatments on the phase and microstructure evolution in a face-centered cubic (FCC) Al7.5Co20.5Fe24Ni24Cr24 HEA. The transition from solid-solution annealing to recrystallization annealing leads to the formation of the desired hierarchical B2+L12+ σ precipitates, accompanied by a heterogeneous FCC matrix. The initiation of the B2 phase originates from nucleation on defect-rich sites, such as deformation bands. However, the coherent L12 phase homogeneously forms in the FCC matrix at intermediate temperature aging, as these sites are scarce or occupied. A heterogeneous structure emerges from the transition in annealing temperatures and the pinning effect of the B2 precipitates. The resulting heterogeneous structure exhibits an exceptional strength-ductility synergy at both room and liquid nitrogen (LN2) temperatures. This is evident in its mechanical properties with a yield strength of ∼717 MPa / ∼1109 MPa, an ultimate tensile strength of ∼1086 MPa / ∼1609 MPa, and an elongation of ∼34.3% / ∼43.2% at room / LN2 temperatures. The formation of deformation twins (DTs) is facilitated by localized stress buildup from hetero-deformation-induced (HDI) hardening stress at room temperature. The exceptional strength and ductility at LN2 temperature are attributed to a combination of factors. These include a high-density of stacking faults (SFs), DTs, and their interactions, including those with precipitates, SFs-based substructures, and Lomer-Cottrell locks. These multiple deformation mechanisms ensure consistent and sustained strain-hardening even under substantial strain. This paper sheds light on the complex interplay of microstructure, deformation mechanisms, and mechanical properties in the Al7.5Co20.5Fe24Ni24Cr24 HEA, potentially guiding the development of ultra-strong yet ductile alloys for cryogenic applications.

研究在常温和低温条件下表现出显著的强度-韧性协同作用的合金一直是材料工程领域的兴趣所在。这种兴趣延伸到最近开发的高熵合金（HEAs）。目前的研究深入探讨了各种热机械处理对面心立方（FCC）Al7.5Co20.5Fe24Ni24Cr24 HEA 的相变和微观结构演变的影响。从固溶退火到再结晶退火的转变导致了所需的分层 B2+L12+ σ 沉淀的形成，并伴随着异质 FCC 基体。B2 相的形成源于富含缺陷部位（如变形带）上的成核。然而，在中温老化时，由于这些位点稀少或被占据，相干的 L12 相会在 FCC 基体中均匀形成。退火温度的变化和 B2 沉淀的钉扎效应产生了一种异质结构。由此产生的异质结构在室温和液氮（LN2）温度下均表现出卓越的强度-电导率协同作用。在室温和液氮温度下，其屈服强度为 ∼717 MPa / ∼1109 MPa，极限拉伸强度为 ∼1086 MPa / ∼1609 MPa，伸长率为 ∼34.3% / ∼43.2% 。变形孪晶（DTs）的形成得益于室温下异种变形诱导（HDI）硬化应力的局部应力积聚。LN2 温度下的超高强度和延展性是由多种因素共同作用的结果。这些因素包括高密度的堆叠断层（SF）、DT 及其相互作用，包括与沉淀物、基于 SF 的子结构和 Lomer-Cottrell 锁的相互作用。这些多重变形机制确保了即使在巨大应变下也能产生一致且持续的应变硬化。本文揭示了 Al7.5Co20.5Fe24Ni24Cr24 HEA 中微观结构、变形机制和机械性能之间复杂的相互作用，为开发低温应用的超强韧性合金提供了潜在的指导。

Thin-Walled Structures

Nonlinear Dynamical Modeling and Free Vibration of Functionally Graded Cylindrical Shell in Air-gap Magnetic and Thermal Fields

Yuda Hu, Jianbo Feng, Tao Yang

doi:10.1016/j.tws.2024.111787

气隙磁场和热场中功能分级圆柱壳的非线性动力学建模和自由振动

Nonlinear dynamical modeling and free vibration of ferromagnetic functionally graded (FG) cylindrical shell in air-gap magnetic and thermal fields are investigated in this work. The shell is surrounded by an armature, and the air-gap layer generated by physical isolation exists between the two structures. The air-gap magnetic field in this space is generated by the armature, which induces the nonlinear magnetization of ferromagnetic materials. The nonlinear heat conduction characteristics along the shell thickness are considered. Under the theory framework for dual-nonlinear magneto-thermal effect, the magneto-thermoelastic dynamical model is established using Hamilton principle. The discrete governing equations and the natural frequency expression separately are derived by Galerkin and Krylov-Bogoliubov-Mitropolski (KBM) methods. Subsequently, the natural frequency characteristics under different parameter conditions are systematically analyzed. The results indicate that magnetic potential, initial air-gap thickness, and volume fraction index have a significant impact on natural frequencies. Temperature has a complex effect on natural frequencies corresponding to different circumferential wave numbers.

本文研究了铁磁功能分级（FG）圆柱形外壳在气隙磁场和热场中的非线性动力学建模和自由振动。外壳周围有电枢，两个结构之间存在由物理隔离产生的气隙层。电枢在此空间产生气隙磁场，诱导铁磁材料非线性磁化。研究还考虑了沿外壳厚度的非线性热传导特性。在双非线性磁热效应理论框架下，利用汉密尔顿原理建立了磁热弹性动力学模型。利用 Galerkin 和 Krylov-Bogoliubov-Mitropolski (KBM) 方法分别推导出离散控制方程和固有频率表达式。随后，系统分析了不同参数条件下的固有频率特性。结果表明，磁势、初始气隙厚度和体积分数指数对固有频率有显著影响。温度对不同圆周波数对应的固有频率有复杂的影响。

Global stability design of double corrugated steel plate shear walls under combined shear and compression loads

Chen-Bao Wen, Bo-Li Zhu, Hao-Jun Sun, Yan-Lin Guo, Wen-Jin Zheng, Li-Lan Deng

doi:10.1016/j.tws.2024.111789

双波纹钢板剪力墙在组合剪力和压缩荷载作用下的整体稳定性设计

As a novel structural component, the Double Corrugated Steel Plate Shear Wall (DCSPSW) is formed by interlocking two corrugated steel plates using high-strength bolts. This paper investigates the global stability design methods for DCSPSWs under combined shear and compression loads. Firstly, this paper examines the elastic buckling performance of DCSPSWs under horizontal shear loads and vertical compression loads separately. A bolt spacing factor (η) is introduced to reflect the influence of bolt spacing on the elastic buckling stress of DCSPSWs. Then, based on extensive finite element analysis (FEA), this paper investigates the elastoplastic buckling behavior of DCSPSWs under shear loads and compression loads and establishes the corresponding stability curves to predict ultimate load-bearing capacity. It is found that the stability coefficients (φs and φc) are closely related to the normalized slenderness ratios (λns and λnc). A smaller bolt spacing allows the DCSPSWs to exhibit improved elastic and elastoplastic stability. Finally, this study investigates the load-bearing performance of DCSPSWs under combined shear and compression loads and proposes the design formulas. The results show that the correlation curve of N/Nu-V/Vu can provide a conservative and accurate design. The research findings of this paper are advantageous for promoting the application of the innovative DCSPSWs.

作为一种新型结构构件，双波纹钢板剪力墙（DCSPSW）是由两块波纹钢板通过高强度螺栓交错连接而成。本文研究了双波纹钢板剪力墙在剪切和压缩联合荷载作用下的整体稳定性设计方法。首先，本文分别研究了 DCSPSW 在水平剪切荷载和垂直压缩荷载作用下的弹性屈曲性能。本文引入了螺栓间距系数 (η)，以反映螺栓间距对 DCSPSW 弹性屈曲应力的影响。然后，本文基于广泛的有限元分析（FEA），研究了 DCSPSW 在剪切载荷和压缩载荷作用下的弹塑性屈曲行为，并建立了相应的稳定曲线来预测最终承载能力。研究发现，稳定系数（φs 和 φc）与归一化纤度比（λns 和 λnc）密切相关。较小的螺栓间距使 DCSPSW 具有更好的弹性和弹塑性稳定性。最后，本研究探讨了 DCSPSW 在剪切和压缩联合载荷下的承载性能，并提出了设计公式。结果表明，N/Nu-V/Vu 的相关曲线可以提供保守而精确的设计。本文的研究成果有利于促进创新型 DCSPSW 的应用。

Experimental behaviour of hybrid carbon steel – stainless steel bolted connections subjected to electrochemical corrosion

Huanxin Yuan, Fengyu Han, Marios Theofanous

doi:10.1016/j.tws.2024.111794

碳钢-不锈钢混合螺栓连接在电化学腐蚀下的实验行为

To minimise cost in practical applications whilst still obtaining a satisfactory performance, stainless steel is often employed in aggressive marine environments to ensure the durability of the structure, whilst parts of the structure less susceptible to corrosion employ conventional carbon steel. When the two materials are in direct contact in the connection region, galvanic corrosion can occur over time thus leading to an increased level of corrosion of the less noble carbon steel parts and an associated degradation in the structural performance. A comprehensive experimental study on the shear behaviour of hybrid carbon steel – stainless steel bolted connections subjected to electrochemical corrosion is presented in this paper. A total of 30 bolted connection specimens were designed and assembled from hot-rolled carbon steel and stainless steel plates. Two bolt grades, the high strength bolts 10.9 and the precipitation hardening stainless steel bolts 10.9 were used to connect the plates. Employing the electrochemical corrosion method, the specimens were subjected to various levels of corrosion by adjusting the duration over which the specimens were sunk in the corrosive medium, which resulted in both different corrosion morphology as well as different levels of mass loss of the carbon steel plates due to corrosion. The corroded connection specimens were thereafter tested to failure under shear exhibiting 4 different failure modes. The load versus deformation curves were recorded and are reported herein, whilst the observed failure modes were also documented. It was revealed that increased level of corrosions led to decreased levels of bolt pretention forces and ultimate resistances of the connections, albeit the severity of the degradation strongly depended on the adopted joint configuration and resulting failure mode.

在实际应用中，为了最大限度地降低成本，同时获得令人满意的性能，通常在腐蚀性较强的海洋环境中使用不锈钢，以确保结构的耐久性，而结构中不易受腐蚀的部分则使用传统的碳钢。当两种材料在连接区域直接接触时，随着时间的推移会发生电化学腐蚀，从而导致惰性较低的碳钢部分腐蚀程度加剧，结构性能随之下降。本文对碳钢-不锈钢混合螺栓连接在电化学腐蚀下的剪切性能进行了全面的实验研究。共设计了 30 个螺栓连接试件，并用热轧碳钢和不锈钢板组装而成。连接板材使用了两种螺栓等级，即高强度螺栓 10.9 和沉淀硬化不锈钢螺栓 10.9。采用电化学腐蚀方法，通过调整试样在腐蚀介质中的下沉时间，使试样受到不同程度的腐蚀，从而产生不同的腐蚀形态以及碳钢板因腐蚀而造成的不同程度的质量损失。随后，对腐蚀连接试样进行了剪切失效测试，测试结果显示了 4 种不同的失效模式。本文记录并报告了载荷与变形的关系曲线，同时还记录了观察到的失效模式。结果表明，腐蚀程度的增加导致螺栓预紧力和连接的极限阻力下降，尽管退化的严重程度主要取决于所采用的连接构造和由此产生的失效模式。

Flexural buckling of cold-formed austenitic stainless steel flat-oval hollow section columns: Testing, modelling and design

Shuai Li, Yating Liang, Man-Tai Chen, Ou Zhao

doi:10.1016/j.tws.2024.111795

冷成形奥氏体不锈钢扁椭圆空心截面柱的挠曲屈曲：测试、建模和设计

The flexural buckling behaviour and resistances of cold-formed austenitic stainless steel flat-oval hollow section columns are studied in this paper, based on experiments and numerical modelling. An experimental investigation was firstly conducted and included tensile coupon tests, initial geometric imperfection measurements and major-axis and minor-axis pin-ended compression tests on ten column specimens. The experimental investigation was followed by a numerical investigation, where the column test results were used to validate finite element models; upon validation, parametric studies were conducted to generate additional numerical data over a wide range of cross-section dimensions and member effective lengths. The obtained test and numerical data were adopted to assess the applicability of the relevant buckling curves for cold-formed austenitic stainless steel circular and elliptical hollow section columns, as specified in the European code, American specification and Australian/New Zealand standard, to cold-formed austenitic stainless steel flat-oval hollow section columns. It was revealed from the assessment results that the buckling curves of the European code and American specification led to overall accurate and consistent flexural buckling resistance predictions, while the flexural buckling resistance predictions from the buckling curve of the Australian/New Zealand standard were slightly conservative.

本文基于实验和数值建模，研究了冷成形奥氏体不锈钢扁椭圆空心截面柱的挠曲屈曲行为和阻力。首先进行了实验研究，包括拉伸试样测试、初始几何缺陷测量以及十个柱试样的主轴和次轴销端压缩测试。实验研究之后进行了数值研究，利用柱子测试结果验证有限元模型；验证之后进行了参数研究，以生成更多横截面尺寸和构件有效长度范围内的数值数据。根据获得的测试和数值数据，评估了欧洲规范、美国规范和澳大利亚/新西兰标准中规定的冷成形奥氏体不锈钢圆形和椭圆形空心截面柱的相关屈曲曲线对冷成形奥氏体不锈钢扁椭圆形空心截面柱的适用性。评估结果表明，欧洲规范和美国规范的屈曲曲线得出的抗弯屈曲性能预测结果总体上准确一致，而澳大利亚/新西兰标准的屈曲曲线得出的抗弯屈曲性能预测结果略显保守。

Nonlinear Dynamic Response of a Temperature-Dependent FGM Spherical Shell under Various Boundary Conditions and Thermal Shocks: Examination of Dynamic Snap-through

Mehran Javani, Yaser Kiani, Mohammad Reza Eslami

doi:10.1016/j.tws.2024.111796

各种边界条件和热冲击下与温度相关的球形 FGM 壳体的非线性动态响应：动态脆穿试验

In this study, a comprehensive exploration of the nonlinear dynamic snap-through phenomenon observed in shallow spherical shells composed of functionally graded materials (FGMs) is examined. The analysis encompasses the interplay of thermomechanical characteristics within metal and ceramic phases, taking into account their temperature-dependent behaviors. To address this problem, the transient heat conduction equation in a nonlinear form, accounting for the temperature dependence factor is derived. To solve this complexity, the Generalized Differential Quadrature (GDQ) method is employed, coupled with the Crank-Nicolson time integrating scheme, leveraging an iterative approach for precision. The formulation of nonlinear dynamic motion equations is based on Hamilton's principle and incorporates the utilization of nonlinear strain-displacement equations and uncoupled thermoelasticity. In the spatial domain, GDQ proves invaluable in solving these nonlinear, coupled equations. In the temporal domain, the Newmark procedure in conjunction with the Newton-Raphson iterative method are utilized to navigate through dynamic equations, yielding insights into shell's behavior over time. In the initial stages of the investigation, we validate our spherical shell formulation and methodologies by comparing shell's response with existing, simpler works. This step ensures the reliability and accuracy of our model. The primary objective is to assess the presence and characteristics of the thermal snap-through phenomenon within the shell under these diverse conditions.

本研究全面探讨了在由功能分级材料（FGM）构成的浅球壳中观察到的非线性动态卡穿现象。分析包括金属相和陶瓷相内部热力学特性的相互作用，并考虑了它们随温度变化的行为。为解决这一问题，推导出了非线性形式的瞬态热传导方程，并考虑了温度依赖性因素。为解决这一复杂问题，采用了广义微分正交（GDQ）方法，并结合 Crank-Nicolson 时间积分方案，利用迭代方法提高精度。非线性动态运动方程的表述基于汉密尔顿原理，并结合使用了非线性应变-位移方程和非耦合热弹性。在空间域，GDQ 被证明在求解这些非线性耦合方程时非常有用。在时间域中，纽马克程序与牛顿-拉斐森迭代法相结合，用于浏览动态方程，从而深入了解壳体随时间变化的行为。在研究的初始阶段，我们通过将外壳的响应与现有的更简单的工作进行比较，来验证我们的球形外壳公式和方法。这一步骤确保了我们模型的可靠性和准确性。主要目标是评估在这些不同条件下，壳体内是否存在热穿透现象及其特征。