今日更新:International Journal of Solids and Structures 1 篇,Journal of the Mechanics and Physics of Solids 2 篇,Mechanics of Materials 1 篇,Thin-Walled Structures 2 篇
An accurate and efficient method based on the dynamic stiffness matrix for analyzing wave propagation in defective lattice structures
B.W. Yan, Q. Gao
doi:10.1016/j.ijsolstr.2024.113147
基于动刚度矩阵的缺陷点阵结构波传播分析方法
In this study, we present an efficient and accurate method for analyzing wave propagation in lattice structures with periodic defects, which are composed of three-dimensional (3D) unit cells arranged infinitely in two or three directions, with defects existing periodically along the directions of the arrangement. The unit cell is composed of 3D beams, and the dynamic stiffness formulation of the 3D beam is developed by combining the Timoshenko-Ehrenfest, Rayleigh-Love and torsion theories. Based on the dynamic stiffness matrix, any number or order of natural frequencies of defective lattice structures can be calculated accurately and efficiently using the Wittrick-Williams algorithm. By combining it with the Bloch theorem, the proposed method can be used to calculate the dispersion curves of lattice structures with periodic defects. The accuracy and efficiency of the proposed method are demonstrated through numerical examples. Additionally, the effects of periodic defects in the lattice structures on the bandgap are analyzed.
在这项研究中,我们提出了一种有效而准确的方法来分析具有周期性缺陷的晶格结构中的波传播,这些晶格结构是由在两个或三个方向上无限排列的三维(3D)单元胞组成的,缺陷沿着排列方向周期性地存在。单元格由三维梁组成,结合Timoshenko-Ehrenfest、Rayleigh-Love和扭转理论,建立了三维梁的动刚度公式。基于动态刚度矩阵,利用Wittrick-Williams算法可以准确有效地计算出缺陷晶格结构的任意数量或阶数的固有频率。将该方法与布洛赫定理相结合,可用于计算具有周期性缺陷的晶格结构的色散曲线。通过数值算例验证了该方法的准确性和有效性。此外,还分析了晶格结构中周期性缺陷对带隙的影响。
Strain localization in rate sensitive porous ductile materials
Alok Tripathy, Shyam M. Keralavarma
doi:10.1016/j.jmps.2024.105957
速率敏感多孔延性材料的应变局部化
Ductile failure by the onset of strain localization in rate sensitive porous materials is investigated using a linear perturbation stability analysis. A micromechanics-based constitutive model accounting for inhomogeneous yielding at the micro-scale, due to plastic strain concentration in the inter-void ligaments, is used. Strain and strain rate hardening of the material is accounted for using a phenomenological viscoplastic extension of the model. Unlike in earlier studies employing a rate-dependent model, an analytical closed form expression for the critical value of the hardening modulus at the onset of localization is derived. The predicted shape of the failure locus under proportional loading is shown to be consistent with known results in the literature for the loading path dependence of ductile failure. The model predicted failure loci are validated by comparison with mesoscopic unit cell model simulations of void growth in a viscoplastic power law hardening material. It is shown that the failure strains predicted by the model as a function of the hardening parameters are in good agreement with the strains to the onset of elastic unloading in the cell model simulations, signifying the onset of void coalescence at the micro-scale.
采用线性摄动稳定性分析研究了速率敏感多孔材料中应变局部化的延性破坏。采用了基于微力学的本构模型,考虑了由于空隙间韧带的塑性应变集中而导致的微尺度非均匀屈服。材料的应变和应变率硬化是用模型的现象学粘塑性扩展来解释的。与早期采用速率相关模型的研究不同,本文导出了局部化开始时硬化模量临界值的解析封闭形式表达式。在比例加载下,预测的破坏轨迹形状与文献中已知的延性破坏的加载路径依赖结果一致。通过与粘塑性幂律硬化材料中孔洞生长的介观单胞模型模拟对比,验证了该模型预测的失效位点。结果表明,模型预测的失效应变随硬化参数的变化与胞体模型模拟中弹性卸载开始时的应变吻合较好,表明孔隙聚并在微观尺度上开始发生。
Implicit implementation of a coupled transformation – plasticity crystal mechanics model for shape memory alloys that includes transformation rotations
Rupesh K. Mahendran, Surya R. Kalidindi, Aaron P. Stebner
doi:10.1016/j.jmps.2024.105964
包含变形旋转的形状记忆合金相变-塑性耦合晶体力学模型的隐式实现
A rate-dependent crystal-plasticity (CP) framework that captures the coupled phase transformation - plastic deformation behavior of shape memory alloys (SMAs) is presented. Here, different from previous models, the flow rule for martensitic phase transformation incorporates the entire deformation gradient for transformation, including the rotation. Predictions of transformation strain and variant selection of Nickel-Titanium (NiTi) using this model are directly compared with previous formulations that did not include the rotation. The results show that the rotation is essential to accurately calculate the single crystal and polycrystal micromechanics of variant selection and transformation strains of SMAs. The constitutive law formulation also includes current formulations for both slip and deformation twinning plasticity mechanisms, and the differences in transformation mechanisms are further shown to impact plasticity calculations through transformation-plasticity interactions. In addition to the advancement of the constitutive law, a computationally efficient implicit time integration scheme is given for numerical implementation and demonstrated using a user material subroutine (UMAT) in the commercial finite element code ABAQUS Standard. The proposed framework and the associated numerical protocols achieve stable solutions using strain increments on the order of 0.05 mm/mm in simulating inelastic deformations and strain increments 0.01 mm/mm in the elastic-inelastic transitions. Furthermore, the use of an analytic Jacobian results in stable convergence in fewer than 10 global Newton iterations while calculating solutions for elastic-inelastic transitions, making the computational benefits evident.
提出了一种考虑形状记忆合金(SMA)相变-塑性变形耦合行为的率相关晶体塑性(CP)框架。与以往模型不同,该模型将马氏体相变的流动规则扩展到整个变形梯度,包括旋转。使用该模型对镍钛(NiTi)合金的相变应变和变体选择的预测直接与未考虑旋转的先前公式进行了比较。结果表明,旋转对于准确计算SMA的单晶和多晶微观力学的变体选择和相变应变至关重要。本构方程还包括目前用于描述滑移和塑性孪生机制的现有公式,并进一步显示了变形机制的差异如何通过相变-塑性相互作用影响塑性计算。除了材料本构方程的改进外,还给出了一个高效的隐式时间积分方案用于数值实现,并用商业有限元代码ABAQUS Standard中的用户材料子程序(UMAT)进行了演示。该框架及其相关数值协议在模拟塑性变形时使用0.05 mm/mm的应变增量,在模拟弹塑性过渡时使用0.01 mm/mm的应变增量,实现了稳定的解。此外,使用解析雅可比矩阵在计算弹塑性过渡的解时实现了在不到10次全局牛顿迭代中实现稳定的收敛,使计算优势显而易见。
Buckling instability of graphyne nanosheets under local indentation
Jiazhen Zhang, Peijian Chen, Juan Peng, Hao Liu, Guangjian Peng, Yingying Zhang
doi:10.1016/j.mechmat.2024.105206
石墨烯纳米片在局部压痕下的屈曲不稳定性
As a novel two-dimensional material, a well understanding of mechanical properties of graphyne under various loading conditions is essential for its blooming applications. However, the buckling mechanism of graphyne under local loads is still unclear, which hinders the development of its related nanodevices. In this work, the buckling behavior of graphyne under local indentation is studied by molecular dynamics simulation and theoretical analysis. It is found that the theoretical prediction of the critical indentation depth for buckling of graphyne agrees well with that from molecular dynamics simulation. The buckling morphology lies in the intermediate region between the contact region and the outer boundary. The critical indentation depth and the buckling morphology can be tuned by adopting various geometric and material parameters. The results should be helpful for not only guiding various applications of graphyne, but also improving the development of nanomechanics.
石墨炔作为一种新型的二维材料,深入了解其在各种载荷条件下的力学性能对其广泛应用至关重要。然而,石墨烯在局部载荷作用下的屈曲机理尚不清楚,这阻碍了其相关纳米器件的开发。本文采用分子动力学模拟和理论分析相结合的方法研究了石墨烯在局部压痕作用下的屈曲行为。结果表明,石墨烯屈曲临界压痕深度的理论预测与分子动力学模拟结果吻合较好。屈曲形态位于接触区与外边界之间的中间区域。采用不同的几何参数和材料参数可以调整临界压痕深度和屈曲形态。研究结果不仅有助于指导石墨炔的各种应用,而且有助于促进纳米力学的发展。
Free Vibration and Stability Analyses of Functionally Graded Plates Resting on Elastic Foundations Based on 2D and Quasi-3D Shear Deformation Theories Using the Finite Strip Method
Mohammad Foroughi, Mojtaba Azhari, Saeid Sarrami, Hamid Foroughi
doi:10.1016/j.tws.2024.112715
基于二维和准三维剪切变形理论的弹性基础上功能梯度板自由振动与稳定性分析
This paper explores the elastic buckling and free vibration behavior of thick functionally graded material (FGM) plates placed on elastic foundations, using two-dimensional (2D) and quasi-three-dimensional (quasi-3D) shear deformation theories. The material properties of the FGM plates are assumed to vary continuously through the thickness based on a power-law distribution. By minimizing the total potential energy and solving the associated eigenvalue problem, the classical finite strip method is applied to determine the critical buckling loads and natural frequencies of the FGM plates. A key novelty of this work lies in the development of a quasi-3D shear deformation theory, which incorporates thickness stretching effects, providing a more accurate distribution of transverse shear strains across the plate thickness. Additionally, the FSM is utilized to efficiently discretize the in-plane geometry, offering a computationally cost-effective solution for analyzing free vibration and mechanical buckling characteristics. The elastic foundation is modeled using Winkler and two-parameter Pasternak models. The complexity of the governing equations is reduced by decomposing the transverse displacement into bending, shear, and thickness stretching components. Numerical results for FGM plates with various boundary conditions are validated by comparing them with analytical solutions from existing literature. Additionally, the effects of parameters such as plate thickness-to-length ratio, length-to-width ratio, boundary conditions, and the power-law index are analyzed and discussed.
本文利用二维(2D)和准三维(准3d)剪切变形理论,研究了弹性基础上的功能梯度材料厚板的弹性屈曲和自由振动行为。假设FGM板的材料性能随厚度呈幂律分布而连续变化。通过最小化总势能和求解相关的特征值问题,应用经典有限条法确定了FGM板的临界屈曲载荷和固有频率。这项工作的一个关键新颖之处在于准三维剪切变形理论的发展,该理论结合了厚度拉伸效应,提供了更准确的横向剪切应变在板厚上的分布。此外,利用FSM有效地离散平面内几何结构,为分析自由振动和机械屈曲特性提供了一种计算成本低廉的解决方案。采用温克勒模型和双参数帕斯捷尔纳克模型对弹性地基进行建模。通过将横向位移分解为弯曲、剪切和厚度拉伸分量,降低了控制方程的复杂性。通过与已有文献的解析解的比较,验证了不同边界条件下FGM板的数值结果。此外,还分析和讨论了板的厚长比、长宽比、边界条件和幂律指数等参数的影响。
Vibration behavior of sandwich circular cylindrical shells with auxetic lattice core and CNT-reinforced facesheets
Amit Yadav
doi:10.1016/j.tws.2024.112716
碳纳米管增强面板夹层圆柱壳的振动特性
In this paper, free and forced vibration analyses of sandwich circular cylindrical shells with auxetic lattice core and carnanotubes (CNTs) reinforced facesheets are carried out. Simply supported boundary conditions are considered, and harmonic radial point loading is applied at the mid-length of the cylindrical shell. The equivalent mechanical properties of the proposed core and facesheets are obtained using modified Gibson's formula and rule-of-mixture, respectively. The mathematical model is formulated using the first-order shear deformation theory, incorporating von Kármán-type geometric non-linearity. A set of partial governing differential equations (PDEs) is derived using Hamilton's principle. Further, Galerkin's method is used to convert the PDEs into a set of ordinary differential equations. In order to obtain the frequency-amplitude response of the shells, an incremental harmonic balance method along with the arc length method is adopted. A comprehensive numerical investigation is carried out to examine the influence of geometrical parameters of the auxetic lattice, the volume fraction of CNTs, and the core-to-facesheet thickness ratio on the vibration behavior of sandwich cylindrical shells.
本文对碳纳米管(cnt)增强表面板和带缺陷晶格芯的夹层圆柱壳进行了自由振动和强迫振动分析。考虑简支边界条件,在圆柱壳中长度处施加谐波径向点荷载。采用改进的Gibson公式和混合规则分别获得了所提出的岩心和面板的等效力学性能。数学模型采用一阶剪切变形理论,考虑von Kármán-type几何非线性。利用哈密顿原理导出了一组偏控制微分方程。进一步,利用伽辽金方法将偏微分方程转化为一组常微分方程。为了得到壳的频幅响应,采用了增量谐波平衡法和弧长法。采用数值模拟方法研究了复合晶格几何参数、碳纳米管体积分数和芯面厚度比对夹层圆柱壳振动特性的影响。