今日更新:International Journal of Solids and Structures 3 篇,Mechanics of Materials 1 篇,Thin-Walled Structures 2 篇
Analysis of Frictionless Contact between a Spherical Indenter and a Poroviscoelastic Medium with a Constant Contact Radius
Yu-Yun Lin
doi:10.1016/j.ijsolstr.2023.112643
球形压头与接触半径恒定的多孔弹性介质之间的无摩擦接触分析
The research aims to understand the force relaxation that occurs when a spherical indenter is pressed into poroviscoelastic materials, which exhibit viscoelastic properties of solid network and drainage behavior of infiltrated fluid. To achieve this, an analytical approach is proposed to model spherical indentation on a poroviscoelastic medium under the condition of a constant contact radius. This analysis is conducted in the Laplace-transformed domain, and provides closed-form expressions in the transformed domain for both the normal approach and the contact force of the indenter while maintaining a fixed contact radius. These expressions are then numerically inverse-transformed to the time domain for practical analysis. To account for different scenarios, we consider various combinations of drainage conditions at the top and smoothness conditions at the bottom of the medium. We examine three categories of viscoelastic solid behavior, as understanding how they respond under indentation is crucial for characterizing their mechanical behavior. Additionally, we conduct finite element simulations of spherical indentation on poroviscoelastic media, serving as a comparison to the semi-analytic results obtained. Notably, the thickness of the medium relative to the contact radius and the Poisson's ratio play significant roles in the evolution of both the normal approach and contact force of the spherical indenter over time.
该研究旨在了解球形压头压入多孔弹性材料时发生的力松弛,多孔弹性材料表现出固体网络的粘弹性和渗透流体的排水行为。为此,我们提出了一种分析方法,在接触半径恒定的条件下对多孔弹性介质上的球形压头进行建模。该分析在拉普拉斯变换域中进行,并在变换域中提供了保持固定接触半径的压头法向和接触力的闭式表达式。然后将这些表达式数值反变换到时域,进行实际分析。为了考虑不同的情况,我们考虑了介质顶部排水条件和底部光滑条件的各种组合。我们对三类粘弹性固体行为进行了研究,因为了解它们在压痕作用下的反应对于描述其机械行为至关重要。此外,我们还对多孔粘弹性介质上的球形压痕进行了有限元模拟,以与半解析结果进行比较。值得注意的是,介质相对于接触半径的厚度和泊松比对球形压头的法向接近和接触力随时间的演变起着重要作用。
Plane strain problem of flexoelectric cylindrical inhomogeneities
Jinchen Xie, Christian Linder
doi:10.1016/j.ijsolstr.2024.112649
柔电圆柱不均匀体的平面应变问题
In nanotechnology, flexoelectric solids exhibit notable electrical polarization induced by internal strain gradients, rendering them promising for various applications. However, inherent material imperfections are inevitable. Particularly within flexoelectric solids, substantial strain gradients exist in proximity to internal defects, resulting in localized concentration of electrical polarization and potential structural failure. Among the various defect types, circular-shaped inhomogeneity is prevalent. This paper comprehensively investigates the plane strain problem on cylindrical inhomogeneities within flexoelectric solids. The full-field analytical solution is derived for this problem for the first time. Given that flexoelectric theory encompasses pure strain gradient elasticity theory, the strain gradient elasticity solution for plane strain cylindrical inhomogeneities is also established for the first time. This study reveals that the stiffness and size of the inhomogeneity, along with the loading ratio in two directions, exert a noteworthy influence on the local electromechanical coupling behavior near the inhomogeneity. Finally, the mixed finite element method is utilized to approximate the solution numerically, and the close agreement between the finite element results and the analytical solution demonstrates this study’s reliability and rigor. Therefore, this investigation imparts valuable insights into examining defects in flexoelectric solids and serves as a foundation for studying more intricate defect typologies.
在纳米技术中,挠电固体在内部应变梯度的诱导下表现出显著的电极化,使其在各种应用中大有可为。然而,材料固有的缺陷是不可避免的。特别是在挠电固体内部,大量应变梯度存在于内部缺陷附近,从而导致局部电极化集中和潜在的结构失效。在各种缺陷类型中,圆弧形不均匀性最为普遍。本文全面研究了挠电固体内部圆柱形不均匀体的平面应变问题。首次推导出该问题的全场解析解。鉴于挠电理论包含纯应变梯度弹性理论,本文还首次建立了平面应变圆柱不均匀体的应变梯度弹性解。研究发现,非均质体的刚度和尺寸以及两个方向的加载比对非均质体附近的局部机电耦合行为有显著影响。最后,利用混合有限元法对解法进行了数值逼近,有限元结果与分析解法之间的密切吻合证明了本研究的可靠性和严谨性。因此,这项研究为研究挠性固体中的缺陷提供了宝贵的见解,并为研究更复杂的缺陷类型奠定了基础。
Incompatible-mode geometrically non-linear finite element for micropolar elasticity
Sara Grbčić Erdelj, Adnan Ibrahimbegović, Gordan Jelenić
doi:10.1016/j.ijsolstr.2024.112647
微弹性的不相容模式几何非线性有限元
In this work a new three-dimensional geometrically non-linear hexahedral micropolar finite element enhanced with incompatible modes is presented. The analytical model is expressed in terms of Biot-like stress and couple-stress tensors and corresponding Biot-like strain and curvature tensors, with a linear, elastic and isotropic constitutive law. The numerical model is derived based on the principle of virtual work, and the residual derivation together with the linearisation and static condensation procedure is given in detail. The newly developed finite element is tested against the analytical solution of the geometrically non-linear micropolar pure bending problem and the element accuracy and robustness is compared against hexahedral Lagrangian finite elements of first and second order on several numerical examples. It is shown that the newly presented element is fast convergent, more robust and more accurate than the available Lagrangian elements. Moreover, the operator split and static condensation provide for a significantly lower computational cost than standard elements.
本研究提出了一种新的三维几何非线性六面体微波有限元增强不相容模式。分析模型由类毕奥应力和耦合应力张量以及相应的类毕奥应变和曲率张量表示,并采用线性、弹性和各向同性的构成定律。数值模型是根据虚功原理推导出来的,并详细介绍了残差推导、线性化和静态压缩过程。新开发的有限元根据几何非线性微波纯弯曲问题的分析解法进行了测试,并在几个数值示例中与一阶和二阶六面体拉格朗日有限元进行了精确性和鲁棒性比较。结果表明,与现有的拉格朗日有限元相比,新提出的有限元收敛速度更快、鲁棒性更强、精度更高。此外,算子拆分和静态凝缩使计算成本大大低于标准元素。
Elastic foundation-introduced defective phononic crystals for tunable energy harvesting
Gongye Zhang, Zhuangzhuang He, Shaopeng Wang, Jun Hong, Yu Cong, Shuitao Gu
doi:10.1016/j.mechmat.2024.104909
用于可调能量采集的弹性基础引入缺陷声子晶体
Defective phononic crystals offer the advantage of concentrating elastic waves, thereby enhancing the potential for piezoelectric energy harvesting (PEH). However, a key limitation is their reliance on a fixed operating frequency, rendering them susceptible to the prevailing vibration environment. To surmount this constraint, this study introduces a novel approach involving a tunable elastic foundation system for defective phononic crystal structures. The newly developed phononic crystal is fashioned by integrating a periodically elastic foundation beneath a uniform beam. A defect is induced by selectively removing specific elastic foundations and integrating piezoelectric components. Explicit analytical solutions are established through the transfer matrix method and the spectral element method, which are subsequently corroborated via comparison with finite element results. The findings underscore that the periodic elastic foundations impart bandgaps in the elastic wave band structure. The absence of specific elastic foundations results in the emergence of distinct defect modes. Additionally, frequency response analysis exposes the potential for energy enhancement, albeit with inherent variations. Noteworthy is the revelation that manipulating the stiffness of the elastic foundation triggers shifts in the resonant frequency of the output voltage. Therefore, the proposed tunable elastic foundation system exhibits promising potential to engender versatile and adaptive phononic crystal configurations, thereby advancing the domain of PEH.
有缺陷声子晶体具有集中弹性波的优势,从而提高了压电能量收集(PEH)的潜力。然而,它们的一个主要局限是依赖于固定的工作频率,因此容易受到普遍振动环境的影响。为了克服这一限制,本研究引入了一种新方法,涉及一种用于缺陷声波晶体结构的可调弹性基础系统。新开发的声波晶体是通过在均匀梁下集成一个周期性弹性基础而形成的。通过有选择性地移除特定弹性基础并集成压电元件,可诱发缺陷。通过传递矩阵法和谱元法建立了显式解析解,并随后通过与有限元结果的比较加以证实。研究结果表明,周期性弹性地基在弹性波段结构中产生了带隙。缺乏特定的弹性基础会导致出现不同的缺陷模式。此外,频率响应分析揭示了能量增强的潜力,尽管存在固有的差异。值得注意的是,操纵弹性地基的刚度会引发输出电压谐振频率的变化。因此,所提出的可调弹性地基系统具有产生多功能、自适应声波晶体配置的巨大潜力,从而推动了 PEH 领域的发展。
Instabilities of an inflated and extended doubly fiber-reinforced cylindrical membrane under damage processes and different natural configurations of its constituents with application to abnormal artery dilation
Heiko Topol, Hojjat Nazari, Marcus Stoffel, Bernd Markert, Jesús Lacalle, José Merodio
doi:10.1016/j.tws.2024.111562
充气和伸展的双纤维增强圆柱膜在损伤过程中的不稳定性及其成分的不同自然构型在异常动脉扩张中的应用
This article studies extended and inflated tubes made of doubly fiber-reinforced hyperelastic material in which the constituents undergo damage processes at large deformations. Damage processes are initiated by a combination of external loads and material characteristics including volume changes in the ground substance matrix and constituents with different natural configurations. The inflation of such a cylinder is stable at relatively small deformations. Under higher inflation pressures the cylinder is likely to develop various types of instabilities that are shown to be related to loading, geometry, and (current) mechanical properties of the solid. Analyses focus on the role of material volume changes, fiber pre-stretch, and damage processes in the initiation of bulging and inflation-jump instabilities.
本文研究了由双纤维增强超弹性材料制成的延伸管和充气管,其中的成分在大变形时会发生损坏过程。破坏过程由外部载荷和材料特性(包括地层物质基体的体积变化和具有不同自然构型的成分)共同引发。在变形相对较小的情况下,这种圆柱体的充气是稳定的。在较高的充气压力下,圆柱体可能会出现各种类型的不稳定性,这些不稳定性与加载、几何形状和固体的(当前)机械特性有关。分析的重点是材料体积变化、纤维预拉伸和损伤过程在引发隆起和充气跳跃不稳定性中的作用。
Nonlinear topology optimization on thin shells using a reduced-order elastic shell model
Fan Feng, Shiying Xiong, Hiroki Kobayashi, Yuqing Zhou, Masato Tanaka, Atsushi Kawamoto, Tsuyoshi Nomura, Bo Zhu
doi:10.1016/j.tws.2024.111566
利用减阶弹性壳模型对薄壳进行非线性拓扑优化
We present a novel numerical algorithm to perform nonlinear topology optimization on elastic thin shells. The main component of our method is a differentiable thin-shell simulator based on discrete differential geometry (DDG) discretization and the projected Newton method to solve geometrically nonlinear elasticity and its derivatives on a triangle mesh. We build a density-based topology optimization algorithm, enhanced by a density filter and a Heaviside projection scheme, to emerge and optimize topologically complex shell structures on curved surfaces. We validate our approach using standard test cases for nonlinear topology optimization and demonstrate the efficacy of our method by tackling highly nonlinear topology optimization problems by producing complex and high-resolution shell structural designs under various load conditions.
我们提出了一种对弹性薄壳进行非线性拓扑优化的新型数值算法。我们方法的主要组成部分是基于离散微分几何(DDG)离散化和投影牛顿法的可微分薄壳模拟器,用于求解三角形网格上的几何非线性弹性及其导数。我们建立了一种基于密度的拓扑优化算法,并通过密度滤波器和海维塞德投影方案进行了增强,以在曲面上出现并优化拓扑复杂的壳结构。我们使用非线性拓扑优化的标准测试案例验证了我们的方法,并通过在各种载荷条件下生成复杂的高分辨率壳结构设计来解决高度非线性拓扑优化问题,从而证明了我们方法的有效性。