今日更新:International Journal of Solids and Structures 1 篇,Journal of the Mechanics and Physics of Solids 1 篇,Mechanics of Materials 2 篇,International Journal of Plasticity 2 篇,Thin-Walled Structures 2 篇
Hamiltonian/Stroh formalism for reversible poroelasticity (and thermoelasticity)
Andrea Nobili
doi:10.1016/j.ijsolstr.2024.112935
可逆孔弹性(和热弹性)的哈密顿/斯特罗形式主义
Stroh’s sextic formalism represents the equilibrium equations of anisotropic elasticity in a particularly attractive form, that is most suitable for studying interface-dominated multilayered solids, composite materials and time-harmonic problems. Taking advantage of the fact that the Stroh formalism really amounts to the canonical form of the equations in the Hamiltonian sense, the case of Biot’s reversible (i.e. no fluid dissipation) poroelasticity is here addressed, in the absence of a fluid pressure gradient. This framework is the same as thermoelasticity of perfect conductors. Two Hamiltonian formulations are developed: the first describes both the solid and the fluid phases and it exhibits, besides energy conservation, momentum conservation, as a result of pressure uniformity (perfectly drained conditions). The second is restricted to the solid skeleton and perfectly parallels anisotropic elasticity, where the Stroh matrices refer to the effective stress tensor. The case of weak fluid-solid coupling is also considered and it produces a perturbation from anisotropic elasticity with the same structure as incompressibility, although in an “opposing” manner. This comparison suggests that the incompressibility limit introduced by Biot should be revised. The energy conservation integral and the edge impedance matrix are also illustrated.
斯特罗的六元形式主义以一种特别有吸引力的形式表示各向异性弹性的平衡方程,最适合研究界面主导的多层固体、复合材料和时谐问题。利用 Stroh 公式实际上等同于哈密顿方程的典型形式这一事实,在没有流体压力梯度的情况下,本文讨论了 Biot 可逆(即无流体耗散)孔弹性的情况。这一框架与完美导体的热弹性相同。提出了两种哈密顿公式:第一种同时描述了固体和流体相,由于压力均匀性(完全排水条件),除了能量守恒外,还表现出动量守恒。第二种仅限于固体骨架,完全平行于各向异性弹性,其中 Stroh 矩阵指的是有效应力张量。我们还考虑了流固弱耦合的情况,它产生了各向异性弹性的扰动,其结构与不可压缩性相同,但方式 "相反"。这种比较表明,应修改 Biot 引入的不可压缩性限制。此外,还说明了能量守恒积分和边缘阻抗矩阵。
A unified discontinuous Galerkin formulation for interfacial multiphysics modeling of thermo-chemically driven fracture
Daniel Pickard, Raúl Radovitzky
doi:10.1016/j.jmps.2024.105748
用于热化学驱动断裂界面多物理场建模的统一非连续伽勒金公式
Many engineering and natural materials exhibit coupled thermo-chemo-mechanical phenomena, which can result in embrittlement and fracture. These fractures, in turn, can alter the subsequent thermal, chemical, and mechanical response. We present a theoretical formulation and computational framework for the analysis of thermo-chemically fractured solids, with emphasis on the post-fracture thermal and chemical interfacial behavior. The theoretical model is based on the thermodynamically-consistent formulation of Loeffel and Anand (IJP, 2011). The computational method extends the scalable discontinuous Galerkin/Cohesive Zone Model (DG/CZM) of Radovitzky et al. (CMAME, 2011) to thermo-chemo-mechanics, which facilitates coupled, large-scale simulations of materials and structures containing failed interfaces. In the proposed framework, all balance laws are enforced weakly via the DG formalism, resulting in a unified formulation for multiphysics problems in solids. This naturally enables the incorporation of general interface models, e.g. to account for effects such as the aeolotropic reduction in thermochemical transport due to the presence of fractures, or the acceleration of chemical reactions along crack flanks. The approach is verified against two analytical solutions of boundary value problems drawn from thermo-poro-elasticity and thermally-driven delamination. A scalable, three-dimensional simulation of thermochemically-driven concrete cracking illustrates the complete capabilities of the interfacial multiphysics modeling framework.
许多工程材料和天然材料都会出现热-化学-机械耦合现象,从而导致脆化和断裂。这些断裂反过来又会改变后续的热、化学和机械响应。我们提出了热化学断裂固体分析的理论公式和计算框架,重点关注断裂后的热界面和化学界面行为。理论模型基于 Loeffel 和 Anand 的热力学一致性公式(IJP,2011 年)。该计算方法将 Radovitzky 等人(CMAME,2011 年)的可扩展非连续伽勒金/粘合区模型(DG/CZM)扩展到了热-化学-力学领域,有助于对包含断裂界面的材料和结构进行大规模耦合模拟。在提议的框架中,所有平衡定律都是通过 DG 形式主义弱化执行的,从而为固体中的多物理场问题提供了统一的表述方式。这就自然而然地使一般界面模型成为可能,例如,考虑到由于裂缝的存在而导致热化学传输的各向异性降低,或沿裂缝侧面的化学反应加速等效应。该方法根据热孔弹性和热驱动分层的两个边界值问题的分析解决方案进行了验证。对热化学驱动的混凝土开裂进行了可扩展的三维模拟,展示了界面多物理场建模框架的全部能力。
Probabilistic analysis of homogenized elastic property for resin products fabricated by additive manufacturing based on three-dimensional random field modeling of microstructure
Sei-ichiro Sakata, George Stefanou, Takayoshi Kikkawa, Yuki Aikawa
doi:10.1016/j.mechmat.2024.105071
基于微观结构三维随机场建模的增材制造树脂产品均质弹性性能概率分析
Additive manufacturing (AM) techniques have been used in several fields of science and industry, and fabrication techniques are being updated. For this fact, especially, for industrial use, mechanical property evaluation methodologies for AM products and standards for product quality assessment should also be well established. In this paper, a probabilistic evaluation of the homogenized elastic properties of a resin product fabricated by a material extrusion-based AM technique is attempted by considering the randomness of both material and microscopic geometrical quantities. This AM method fabricates a resin structure by piling up melted resin, and to decrease consumed material and influence of thermal deformation, the inner structure of the fabricated products will include many pores and its geometry is difficult to be well controlled. From this fact, the products will be regarded as a heterogeneous material with complex random microstructure. This will cause difficulty in the evaluation of its apparent material properties and therefore a probabilistic homogenization analysis is attempted for quantitative estimation of the apparent material property in this study. In particular, to investigate probabilistic properties of microscopic geometry, a random field modeling technique is employed for the evaluation of autocorrelation of the microscopic geometrical parameter, and the results of the autocorrelation identified by experimental observation are introduced to the probabilistic homogenization analysis. The two-dimensional or three-dimensional random field modeling is attempted, and the effectiveness of this approach is investigated by comparing it with the experimental result.
快速成型制造(AM)技术已在多个科学和工业领域得到应用,其制造技术也在不断更新。因此,特别是在工业应用中,应建立完善的 AM 产品机械性能评估方法和产品质量评估标准。本文通过考虑材料和微观几何量的随机性,尝试对基于材料挤压的 AM 技术制造的树脂产品的均质弹性特性进行概率评估。这种 AM 方法通过堆积熔化的树脂来制造树脂结构,为了减少材料消耗和热变形的影响,制造产品的内部结构将包括许多孔隙,其几何形状难以很好地控制。因此,产品将被视为具有复杂随机微观结构的异质材料。这将给表观材料特性的评估带来困难,因此本研究尝试采用概率均质化分析方法对表观材料特性进行定量评估。其中,为了研究微观几何的概率特性,采用了随机场建模技术来评估微观几何参数的自相关性,并将实验观察所确定的自相关性结果引入概率均质化分析。尝试了二维或三维随机场建模,并通过与实验结果的比较研究了这种方法的有效性。
The extended scaling laws of the mechanical properties of additively manufactured body-centered cubic lattice structures under large compressive strains
Zhi Chen, Souvik Sahoo, María Teresa Pérez-Prado, Dan Mordehai
doi:10.1016/j.mechmat.2024.105075
增材制造体心立方晶格结构在大压应变下力学性能的扩展缩放规律
Additively manufactured lattice structures are porous light-weight structures with mechanical properties that are dictated both from the topology and the parent material properties. When printed from metals, these structures can withstand large continuous plastic deformation. In this paper, we focus on body-centered cubic (BCC) lattice structures under compression up to large deformation strains, and we propose relations between the slenderness ratio of struts and the following mechanical properties: Young’s modulus, yield strength, hardening rate of the structure and the densification strain. We perform a systematic study using finite element modelling (FEM) to find how both material properties and lattice structures are affecting the effective mechanical properties of BCC lattice structures under compression. Based on this analysis we propose the scaling laws of the mechanical properties. The scaling laws can be explained as an extension of the Gibson-Ashby power law relations for bend-dominated structures with non-slender beams. We also discuss how rounding the connections between the struts using fillets affects the scaling laws. We demonstrate the scaling laws in the analysis of experimental results, showing the accuracy and limitations of the scaling laws in predicting the mechanical properties, with an emphasis on large deformations. In the analysis, we use experimental values published in literature, and we also present here experimental results of lattice structures printed from Inconel 718.
叠加制造的晶格结构是一种多孔轻质结构,其机械特性由拓扑结构和母体材料特性共同决定。当用金属打印时,这些结构可以承受较大的连续塑性变形。在本文中,我们重点讨论了体心立方(BCC)晶格结构在压缩至大变形应变时的力学性能,并提出了支杆细长比与以下力学性能之间的关系:我们提出了细长比与下列力学性能之间的关系:杨氏模量、屈服强度、结构硬化率和致密化应变。我们使用有限元建模(FEM)进行了系统研究,以了解材料特性和晶格结构如何影响 BCC 晶格结构在压缩条件下的有效机械特性。在此分析基础上,我们提出了机械性能的缩放规律。这些缩放定律可以解释为吉布森-阿什比幂律关系的扩展,适用于以弯曲为主的非细长梁结构。我们还讨论了使用圆角对支柱之间的连接进行圆角处理如何影响缩放定律。我们在实验结果分析中演示了缩放定律,显示了缩放定律在预测力学性能方面的准确性和局限性,重点是大变形。在分析过程中,我们使用了文献中公布的实验值,并在此介绍了由 Inconel 718 印刷而成的晶格结构的实验结果。
On the anisotropic coalescence of elliptic cylindrical voids considering the geometric and distributive properties
Jiawei Chen, Tsuyoshi Furushima
doi:10.1016/j.ijplas.2024.104036
考虑几何和分布特性的椭圆柱形空洞各向异性凝聚问题
The geometric and distributive properties of voids significantly influence anisotropic coalescence behavior. However, this problem has received little attention owing to the complexity of considering all the properties in the current analytical framework of limit analysis. To address this issue, this study proposes an analytical framework based on an elliptic coordinate system, including the determination of the ligament zone, characterization of plastic flow, and derivation of the void coalescence criterion, for porous materials with various geometric and distributive properties, including size, shape, spacing, and orientation. This framework is motivated by our observations that the evolution of the void geometry and surrounding plastic flow can be well characterized by the grid of the elliptic coordinate system. Subsequently, an analytical function is proposed to determine the ligament zone and coalescence direction with various void properties. A hollow nonaxisymmetric cylindrical unit cell is proposed to describe this ligament zone, and the corresponding trial velocity field is derived by extending the previous Gurson-like velocity field into the elliptic cylindrical coordinate system. The rationality of the field is validated by comparing its equivalent strain rate field with numerical simulations. Finally, a coalescence criterion is derived via the limit analysis of the proposed unit cell undergoing internal necking. Two heuristic adjustments are formulated for the overflow phenomenon in the rigid zone and outer ligament zones. Numerical assessments with various void properties confirm the accuracy of the analytical model. The coalescence criterion can predict the independent and coupling effects of geometric and distributive properties on anisotropic void coalescence. This study provides possible solutions to future plasticity problems of ellipsoidal inclusions.
空隙的几何特性和分布特性对各向异性凝聚行为有重大影响。然而,由于在当前的极限分析框架中考虑所有属性的复杂性,这一问题很少受到关注。为了解决这个问题,本研究提出了一个基于椭圆坐标系的分析框架,包括韧带区的确定、塑性流动的表征以及空隙凝聚准则的推导,适用于具有各种几何和分布特性(包括尺寸、形状、间距和取向)的多孔材料。我们观察到,椭圆坐标系的网格可以很好地描述空隙几何形状和周围塑性流动的演变过程,因此我们提出了这一框架。随后,我们提出了一个分析函数,用于确定具有各种空隙属性的韧带区和凝聚方向。提出了一个空心非轴对称圆柱单元来描述该韧带区,并通过将之前的古尔森速度场扩展到椭圆圆柱坐标系得出了相应的试验速度场。通过将其等效应变率场与数值模拟进行比较,验证了该场的合理性。最后,通过对发生内部缩颈的拟议单元尺寸进行极限分析,得出了凝聚准则。针对刚性区和外韧带区的溢出现象,提出了两种启发式调整方法。利用各种空隙特性进行的数值评估证实了分析模型的准确性。凝聚准则可以预测几何特性和分布特性对各向异性空隙凝聚的独立和耦合效应。这项研究为未来椭圆形夹杂物的塑性问题提供了可能的解决方案。
Double-peak Strain Hardening Behavior of Mg–1.2 wt.%Y Alloy
Bo Guan, Li Wang, Yunchang Xin, Peidong Wu, Jing Xu, Xiaoxu Huang, Qing Liu
doi:10.1016/j.ijplas.2024.104041
Mg-1.2 wt.%Y 合金的双峰应变硬化行为
In this study, the mechanical behavior and deformation mechanism of an extruded Mg–1.2 wt.%Y rod under tension and compression along the extrusion direction (ED) were systematically investigated through experiments and crystal plasticity simulations. A double-peak strain hardening behavior comprising five distinct stages was observed under compression along the ED. The five stages are as follows: a fast drop in the strain hardening rate (stage I), steady increase in the strain hardening rate (stage II), gradual decrease in the hardening rate (stage III), second increase in the strain hardening rate (stage IV), and rapid decrease in the strain hardening rate (stage V). This unique strain hardening behavior led to an ultimate compressive strength of up to 539 MPa at a high strain of 0.4. Crystal plastic simulations using an elastic viscoplastic self-consistent model revealed a high activity and a long process of {101¯2} twinning in a strain range of 0–0.35 under compression along the ED. The twinning behavior examined via electron backscattering diffraction indicated that the {101¯2} twinning was activated in both grains with relatively high and very low Schmid factors. Subsequently, the mechanism for the presence of this double-peak strain hardening was established and, finally, the significance of this double-peak strain hardening for strengthening Mg alloys was discussed.
本研究通过实验和晶体塑性模拟,系统地研究了挤压 Mg-1.2 wt.%Y 棒在沿挤压方向(ED)拉伸和压缩条件下的力学行为和变形机制。在沿 ED 方向压缩时,观察到了由五个不同阶段组成的双峰应变硬化行为。这五个阶段如下:应变硬化率快速下降(第一阶段)、应变硬化率稳定上升(第二阶段)、硬化率逐渐下降(第三阶段)、应变硬化率第二次上升(第四阶段)和应变硬化率快速下降(第五阶段)。这种独特的应变硬化行为使其在 0.4 高应变下的极限抗压强度高达 539 兆帕。使用弹性粘塑性自洽模型进行的晶体塑性模拟显示,在沿 ED 压缩的 0-0.35 应变范围内,{101¯2}孪晶的活性很高,过程很长。通过电子反向散射衍射检查的孪生行为表明,{101¯2}孪生在施密德因子相对较高和非常低的两种晶粒中都被激活。随后,确定了这种双峰应变硬化的存在机制,最后讨论了这种双峰应变硬化对强化镁合金的意义。
Transient behavior of a plate partially immersed in the fluid subjected to impact loadings: Theoretical analysis and experimental measurements
Chan-Yi Liao, Guan-Wei Chen, Chien-Ching Ma
doi:10.1016/j.tws.2024.112134
部分浸入流体中的板材在受到冲击载荷时的瞬态行为:理论分析和实验测量
This study aimed to investigate the transient behavior of a rectangular plate partially in contact with fluid subjected to a dynamic external force. To this purpose, a theoretical model was developed to analyze vibration characteristics and transient wave propagation. Based on superposition method, the dry mode shapes and natural frequencies of the plate under vacuum could be obtained. The dry mode shapes were treated as the fundamental function to construct the wet mode that describes the vibration behavior of the fluid-plate coupled system. The velocity potential and fluid pressure within a finite tank due to the plate deflection were derived using an equation governing the incompressible fluid. Based on the relationship between dry mode shape and wet mode shape, the fluid-plate coupled system's wet mode shape and resonant frequency could be determined from the frequency response function. Applying the normal mode method, the transient displacement of plate and fluid pressure can be obtained by solving a system of non-homogeneous differential equations. The theoretical predictions were verified by finite element method (FEM) and experimental measurements. Experiments were conducted using piezoelectric film sensors (polyvinylidene fluoride, PVDF) to measure the force history induced by a steel ball impact to quantitatively analyze the transient response. The comparison results proved that the theoretical predictions and experiments were in good agreement, including the transient responses of the displacement and in-plane strain of a plate partially submerged in the fluid. The results indicate that changes in water depth can induce resonance frequency shifts and wet mode shape distortions, which also illustrate that the vibrational properties of wet modes affect transient behavior. The proposed transient solution demonstrates an analytical approach that connects the physical significance of the dynamic behavior of the fluid-plate coupled system in time and frequency domains; it provides a connection between the transient behaviors and vibration characteristics.
本研究旨在探讨部分与流体接触的矩形板在动态外力作用下的瞬态行为。为此,建立了一个理论模型来分析振动特性和瞬态波传播。基于叠加法,可以得到真空条件下板的干模态振型和固有频率。干模态形状被视为基本函数,用于构建描述流体-板耦合系统振动行为的湿模态。利用不可压缩流体方程推导出了板挠度导致的有限槽内速度势能和流体压力。根据干模态振型和湿模态振型之间的关系,可以从频率响应函数中确定流体-板耦合系统的湿模态振型和共振频率。应用法向模态方法,通过求解非均质微分方程系统,可以得到板的瞬态位移和流体压力。有限元法(FEM)和实验测量验证了理论预测。实验使用压电薄膜传感器(聚偏氟乙烯,PVDF)测量钢球撞击引起的受力历史,以定量分析瞬态响应。对比结果证明,理论预测与实验结果非常吻合,包括部分浸没在流体中的平板的位移和平面应变的瞬态响应。结果表明,水深变化会引起共振频率偏移和湿模态形状扭曲,这也说明了湿模态的振动特性会影响瞬态行为。所提出的瞬态解决方案展示了一种在时域和频域上连接流体-板耦合系统动态行为的物理意义的分析方法;它提供了瞬态行为和振动特性之间的联系。
User friendly FE Formulation for anisotropic distortional hardening model based on non-associated flow plasticity and its application to springback prediction
Qi Hu, Lorenz Maier, Takeshi Nishiwaki, Christoph Hartmann, Wolfram Volk, Jeong Whan Yoon
doi:10.1016/j.tws.2024.112142
基于非关联流塑性的各向异性变形硬化模型的用户友好型 FE 公式及其在回弹预测中的应用
Based on non-associated flow plasticity, a newly developed anisotropic distortional hardening model developed by Hu and Yoon [15] is implemented in finite element analysis in a user-friendly manner. The derivatives of complex hardening models are calculated using the Finite Difference Method (FDM), which is much more convenient than using the analytical derivatives. To further improve the accuracy of the proposed method, the step size analysis in FDM is performed by analyzing the derivative formation. To evaluate the accuracy and computational efficiency of a proposed step size for FDM, single element simulations are performed under different loading paths. It has been found that the maximum absolute error of the flow curves between the simulation and the theoretical result is less than 0.3 %. The U-bending tests for DP600 and TRIP1180 are used to verify the ability of the distortional hardening model for springback prediction. The simulation result of the strain hardening model is in good agreement with the experiment. The computational efficiency is also increased by 24 % due to the improved convergence rate.
基于非关联流塑性,Hu 和 Yoon [15] 新开发的各向异性变形硬化模型以用户友好的方式在有限元分析中实现。复杂硬化模型的导数采用有限差分法(FDM)计算,这比使用解析导数要方便得多。为了进一步提高所提方法的精度,通过分析导数的形成,对 FDM 中的步长进行了分析。为了评估所提出的 FDM 步长的精度和计算效率,我们在不同的加载路径下进行了单元素模拟。结果发现,模拟结果与理论结果之间流动曲线的最大绝对误差小于 0.3%。DP600 和 TRIP1180 的 U 形弯曲试验用于验证变形硬化模型预测回弹的能力。应变硬化模型的模拟结果与实验结果非常吻合。由于收敛速度提高,计算效率也提高了 24%。