【新文速递】2024年6月16日固体力学SCI期刊最新文章

 

今日更新：International Journal of Solids and Structures 4 篇，Journal of the Mechanics and Physics of Solids 1 篇，Mechanics of Materials 1 篇，International Journal of Plasticity 1 篇，Thin-Walled Structures 2 篇

International Journal of Solids and Structures

Homogenization of non-rigid origami metamaterials as Kirchhoff–Love plates

Siva P. Vasudevan, Phanisri P. Pratapa

doi:10.1016/j.ijsolstr.2024.112929

作为基尔霍夫-洛夫板的非刚性折纸超材料的均质化

Origami metamaterials have gained considerable attention for their ability to control mechanical properties through folding. Consequently, there is a need to develop systematic methods for determining their effective elastic properties. This study presents an energy-based homogenization framework for non-rigid origami metamaterials, effectively linking their mechanical treatment with that of traditional materials. To account for the unique mechanics of origami systems, our framework incorporates out-of-plane curvature fields alongside the usual in-plane strain fields used for homogenizing planar lattice structures. This approach leads to a couple-stress continuum, resembling a Kirchhoff–Love plate model, to represent the homogeneous response of these lattices. We use the bar-and-hinge method to assess lattice stiffness, and validate our framework through analytical results and numerical simulations of finite lattices. Initially, we apply the framework to homogenize the well-known Miura-ori pattern. The results demonstrate the framework’s ability to capture the unconventional relationship between stretching and bending Poisson’s ratios in origami metamaterials. Subsequently, we extend the framework to origami lattices lacking centrosymmetry, revealing two distinct neutral surfaces corresponding to bending along two lattice directions, unlike in the Miura-ori pattern. Our framework enables the inverse design of metamaterials that can mimic the unique mechanics of origami tessellations using techniques like topology optimization.

折纸超材料因其通过折叠控制机械特性的能力而备受关注。因此，有必要开发确定其有效弹性特性的系统方法。本研究针对非刚性折纸超材料提出了一种基于能量的均质化框架，有效地将其力学处理与传统材料的力学处理联系起来。为了考虑到折纸系统的独特力学特性，我们的框架将平面外曲率场与用于均质化平面晶格结构的常用平面内应变场结合起来。这种方法产生了一种耦合应力连续体，类似于基尔霍夫-洛夫板模型，用于表示这些晶格的均匀响应。我们使用条铰法评估晶格刚度，并通过有限晶格的分析结果和数值模拟验证我们的框架。首先，我们应用该框架对著名的 Miura-ori 图案进行均质化。结果表明，该框架能够捕捉折纸超材料中拉伸和弯曲泊松比之间的非常规关系。随后，我们将该框架扩展到了缺乏中心对称性的折纸晶格，揭示了与 Miura-ori 图案不同的、与沿两个晶格方向的弯曲相对应的两个截然不同的中性面。通过我们的框架，可以利用拓扑优化等技术反向设计超材料，从而模仿折纸方格的独特力学原理。

Research on the low-frequency fatigue behavior of NEPE solid composite propellant based on fractional derivative constitutive model

Wenqin Zhang, Dapeng Zhang, Yongjun Lei, Zhibin Shen

doi:10.1016/j.ijsolstr.2024.112931

基于分数导数构成模型的 NEPE 固体复合推进剂低频疲劳行为研究

The long-term fatigue loading history from offshore vibration environment will cause microdamage and affect the mechanical properties of NEPE solid propellant grains. The paper investigates the evolution law of microdamage through constant-strain-amplitude fatigue tests, and proposes an improved fractional derivative constitutive model for effectively predicting the low-frequency fatigue behavior of NEPE solid propellant based on the experimental phenomena. The evolution law of microdamage is negative power functional with the loading time and exponential with the maximum loading strain during the fatigue loading process. The stress-softening behavior, the Mullins effect, and the accumulation of residual strain are observed, as characteristics of low-frequency fatigue behavior. The theoretical modeling of the stress-softening behavior and the Mullins effect is proven to be significant for effectively predicting the low-frequency fatigue behavior by the improved fractional derivative constitutive model, while strain-modfication is also necessary for eliminating the influence of residual strain. The fatigue damage in solid propellant grains cannot be neglected when assessing the structural integrity of a solid propellant grain which has experienced long-term transportation or offshore storage.

海上振动环境的长期疲劳加载历史会造成微损伤，影响 NEPE 固体推进剂晶粒的力学性能。本文通过恒应变-振幅疲劳试验研究了微损伤的演变规律，并根据试验现象提出了改进的分数导数构成模型，以有效预测 NEPE 固体推进剂的低频疲劳行为。在疲劳加载过程中，微损伤的演变规律与加载时间呈负幂函数关系，与最大加载应变呈指数关系。观察到了应力软化行为、穆林斯效应和残余应变累积，这是低频疲劳行为的特征。事实证明，应力软化行为和 Mullins 效应的理论建模对于利用改进的分数导数构成模型有效预测低频疲劳行为具有重要意义，而应变修正对于消除残余应变的影响也是必要的。在评估经过长期运输或海上储存的固体推进剂晶粒的结构完整性时，不能忽视固体推进剂晶粒的疲劳损伤。

Crystal plasticity finite element simulations of nanoindentation and simple compression for yielding of Ta crystals

Sajjad Izadpanah Najmabad, Olajesu F. Olanrewaju, Siddhartha Pathak, Curt A. Bronkhorst, Marko Knezevic

doi:10.1016/j.ijsolstr.2024.112928

针对 Ta 晶体屈服的纳米压痕和简单压缩的晶体塑性有限元模拟

Experiments and corresponding crystal plasticity finite element (CPFE) simulations of spherical nanoindentation were performed to determine yield stress under indentation of fifteen Ta single crystals randomly distributed in the orientation space. Agreement between the measured and simulated indentation yield stresses and initial hardening slopes demonstrated accuracy of the model. Moreover, simple compression simulations were performed for the same crystals to study the differences in compressive versus indentation yielding. Ratios of the indentation to compressive yield stress were found to vary with crystal orientation in the range from 2.6 to 3.6. The simulations allowed us to reveal underlying deformation mechanisms accommodating the yielding in indentation and simple compression. It is found that more crystallographic glid mechanisms activate under indentation than simple compression owing to the more complex state of stress and strain in indentation than in compression. Owing to the activation of more glide systems in indentation than in simple compression, the indentation yield stress is less anisotropic than the simple compression yield stress. The modeling framework, simulation setups, results, and insights from the results are presented and discussed in this paper.

通过球形纳米压痕实验和相应的晶体塑性有限元（CPFE）模拟，确定了在取向空间中随机分布的 15 个 Ta 单晶体在压痕作用下的屈服应力。测量和模拟的压痕屈服应力与初始硬化斜率之间的一致性证明了模型的准确性。此外，还对相同晶体进行了简单的压缩模拟，以研究压缩屈服与压痕屈服的差异。结果发现，压痕屈服应力与压缩屈服应力的比率随晶体取向而变化，范围在 2.6 到 3.6 之间。通过模拟，我们揭示了压痕屈服和简单压缩屈服的基本变形机制。我们发现，由于压入时的应力和应变状态比压缩时更为复杂，因此与简单压缩相比，压入时会激活更多的晶体滑动机制。由于压入比简单压缩激活了更多的滑动系统，压入屈服应力的各向异性小于简单压缩屈服应力。本文介绍并讨论了建模框架、模拟设置、结果以及从结果中得到的启示。

A rate-dependent cohesive zone model for dynamic crack growth in carbon nanotube reinforced polymers

Reza Yazdanparast, Roham Rafiee

doi:10.1016/j.ijsolstr.2024.112932

碳纳米管增强聚合物动态裂纹增长的速率依赖性内聚区模型

Carbon nanotubes (CNTs) enhance the fracture toughness of polymer-based matrix composites by dissipating the fracture energy through the pull-out deformation damage mechanism. The rate-dependent behavior of the matrix phase and the CNT/matrix interface affects the contribution of CNTs in enhancing the fracture toughness under dynamic loading and rapid crack growth. A continuum-based finite element (FE) model is utilized in this research to analyze the CNT pull-out damage mechanism. The influence of CNTs on the dynamic fracture behavior of polymer-based composites is studied taking into account the crack opening speed and loading rate effects. The matrix phase is treated as a viscoelastic-viscoplastic material and a new rate-dependent cohesive zone model (CZM) is proposed for modeling the behavior of interface between the CNTs and matrix. The rate-dependent traction-separation laws for the cohesive zone elements are established at different pull-out or crack opening speeds. The proposed rate-dependent FE model of pull-out mechanism facilitates the investigation of the effective factors of CNTs, including length, orientation, and waviness, on fracture energy dissipation at different pull-out speeds. Developed model is very suitable for very long CNTs where atomistic-based molecular dynamics and molecular mechanics methods are associated with difficulties and are more costly and time-consuming.

碳纳米管（CNT）通过拉出变形破坏机制耗散断裂能量，从而增强聚合物基复合材料的断裂韧性。基体相和 CNT/基体界面的速率依赖行为会影响 CNT 在动态加载和快速裂纹生长条件下对提高断裂韧性的贡献。本研究采用基于连续体的有限元（FE）模型来分析 CNT 拔出破坏机制。在研究 CNT 对聚合物基复合材料动态断裂行为的影响时，考虑了裂纹张开速度和加载速率的影响。基体相被视为粘弹性-粘塑性材料，并提出了一种新的速率依赖性内聚区模型（CZM），用于模拟 CNT 与基体之间的界面行为。在不同的拉出或裂纹打开速度下，建立了内聚区元素的速率相关牵引分离定律。所提出的依赖速率的拉出机制 FE 模型有助于研究 CNT 在不同拉出速度下对断裂能量耗散的有效因素，包括长度、取向和波形。所开发的模型非常适合超长 CNT，因为基于原子的分子动力学和分子力学方法存在困难，而且成本高、耗时长。

Journal of the Mechanics and Physics of Solids

Mineral Asperities Reinforce Nacre through Interlocking and Friction-like Sliding

Hao LI, Kun GENG, Bingzhan ZHU, Qiang ZHANG, Yi WEN, Zuoqi ZHANG, Yanan YUAN, Huajian GAO

doi:10.1016/j.jmps.2024.105712

矿物微孔通过交错和摩擦滑动加固珍珠质

While the surface asperities of mineral platelets are widely believed to play important roles in stiffening, strengthening, and toughening nacre, their effects have not been thoroughly investigated. Here, a computationally efficient bar-spring model is adopted to simulate, as platelets with multiple interfacial asperities slide over each other, the tensile force versus elongation behaviors as well as the effective mechanical properties such as modulus, strength, and work-to-fracture in nacre or nacre-like composites. The model employs an effective cohesive law derived from a micromechanical model based on the kinematic and deformation analysis of a single pair of contacting asperities to characterize the traction-separation relationship during the asperity inter-climbing. Strikingly, we find that the mineral asperities and resulting interfacial roughness can elevate the composites’ strength and toughness by up to 2-3 orders of magnitude through a combination of mechanical interlocking and multimodal friction-like mechanisms. Of particular interest is that the asperity-induced strengthening and toughening mechanisms are insensitive to the asperity shapes such as ellipse, hyperbolic cosine, cosine, and parabola. These findings may provide useful guidelines for developing advanced engineering composites with nacre-inspired interface designs.

虽然人们普遍认为矿物小板的表面凸起在珍珠质的硬化、强化和韧化方面发挥着重要作用，但对它们的影响尚未进行深入研究。在此，我们采用了一种计算效率高的条形弹簧模型，来模拟具有多个界面微孔的板块相互滑动时，珍珠质或类似珍珠质复合材料的拉力与伸长行为，以及模量、强度和加工至断裂等有效力学性能。该模型采用了一种有效的内聚法则，该法则源自基于单对接触尖晶石运动学和变形分析的微机械模型，用于描述尖晶石相互攀爬过程中的牵引-分离关系。令人惊讶的是，我们发现矿物尖晶和由此产生的界面粗糙度可以通过机械互锁和多模态摩擦样机制的组合，将复合材料的强度和韧性提高 2-3 个数量级。尤其令人感兴趣的是，表面粗糙度诱导的强化和增韧机制对椭圆形、双曲余弦形、余弦形和抛物线形等表面粗糙度形状并不敏感。这些发现可为开发具有珍珠质灵感界面设计的先进工程复合材料提供有用的指导。

Mechanics of Materials

Yield behavior of aluminum foam under multi-axial loading

Yue Zhang, Tao Jin, Shiqiang Li, Zhihua Wang, Guoxing Lu

doi:10.1016/j.mechmat.2024.105069

多轴向加载下泡沫铝的屈服行为

In the current work, the initial yield behavior of closed-cell aluminum foams with three different relative densities under complex stress states have been investigated. A total of 16*3 (three different relative densities of closed-cell aluminum foam) experiments were conducted, which included uniaxial compression, uniaxial tension, combined tension-shear, and triaxial compression tests. Experimental results show that the initial yield behavior of closed-cell aluminum foam is isotropic and is associated with the first invariant of stress tensor, the second and third invariants of deviatoric stress tensor. A constitutive model to describe yield behavior of closed-cell aluminum foam was proposed and the relationship between the first invariant of stress tensor and the second invariant of deviatoric stress tensor was analyzed. Furthermore, tension-compression strength asymmetry of foams was introduced in the proposed model.

本研究对三种不同相对密度的闭孔铝泡沫在复杂应力状态下的初始屈服行为进行了研究。共进行了 16*3（三种不同相对密度的闭孔铝泡沫）实验，包括单轴压缩、单轴拉伸、拉伸-剪切组合和三轴压缩试验。实验结果表明，闭孔铝泡沫的初始屈服行为是各向同性的，与应力张量的第一不变式、偏差应力张量的第二和第三不变式有关。提出了描述闭孔铝泡沫屈服行为的构成模型，并分析了应力张量第一不变量与偏差应力张量第二不变量之间的关系。此外，模型还引入了泡沫的拉伸-压缩强度不对称。

International Journal of Plasticity

Rediscovering the Mullins effect with deep symbolic regression

Rasul Abdusalamov, Jendrik Weise, Mikhail Itskov

doi:10.1016/j.ijplas.2024.104037

通过深度符号回归重新发现穆林斯效应

The Mullins effect represents a softening phenomenon observed in rubber-like materials and soft biological tissues. It is usually accompanied by many other inelastic effects like for example residual strain and induced anisotropy. In spite of the long term research and many material models proposed in literature, accurate modeling and prediction of this complex phenomenon still remain a challenging task. In this work, we present a novel approach using deep symbolic regression (DSR) to generate material models describing the Mullins effect in the context of nearly incompressible hyperelastic materials. The two step framework first identifies a strain energy function describing the primary loading. Subsequently, a damage function characterizing the softening behavior under cyclic loading is identified. The efficiency of the proposed approach is demonstrated through benchmark tests using the generalized the Mooney–Rivlin and the Ogden-Roxburgh model. The generalizability and robustness of the presented framework are thoroughly studied. In addition, the proposed methodology is extensively validated on a temperature-dependent data set, which demonstrates its versatile and reliable performance.

穆林斯效应是在类橡胶材料和软生物组织中观察到的一种软化现象。它通常伴随着许多其他非弹性效应，例如残余应变和诱导各向异性。尽管经过长期研究并在文献中提出了许多材料模型，但对这一复杂现象进行精确建模和预测仍是一项具有挑战性的任务。在这项工作中，我们提出了一种新方法，利用深度符号回归（DSR）生成材料模型，在几乎不可压缩的超弹性材料中描述穆林斯效应。该框架分为两步，首先确定描述主要加载的应变能函数。随后，确定描述循环加载下软化行为的损伤函数。通过使用广义穆尼-里夫林模型和奥格登-罗克斯堡模型进行基准测试，证明了所提方法的效率。对所提出框架的通用性和稳健性进行了深入研究。此外，所提出的方法还在与温度相关的数据集上进行了广泛验证，证明了其通用性和可靠性能。

Thin-Walled Structures

Strength degradation and damage mechanism of TA1 titanium alloy clinched joints under fatigue loading

Lei Lei, Zhiqiang Zhao, Ming Yan, Heting Qiao, Ye Shi, Chunyu Song

doi:10.1016/j.tws.2024.112125

疲劳载荷下 TA1 钛合金咬合接头的强度退化和损伤机理

A digital model for the strength degradation of titanium alloy clinched joints was established using strength degradation tests and a fatigue cumulative damage model. This model aims to investigate the strength degradation law and fatigue damage failure mechanism of titanium alloy clinched joints under fatigue loading. Fractured test specimens were scanned to analyse the fatigue damage failure mechanism by examining the evolution of fracture morphology under varying fatigue cyclic loading times. The results demonstrate that the power index degradation model accurately predicts the strength degradation of titanium alloy clinched joints. As the number of fatigue loading cycles increases, cleavage features emerge alongside fatigue cracks, leading to a gradual reduction in joint strength. Ultimately, the strength degradation power index model for titanium alloy clinched joints is verified by the test to have high accuracy in predicting residual strength.

利用强度退化试验和疲劳累积损伤模型，建立了钛合金咬合接头强度退化的数字模型。该模型旨在研究疲劳载荷下钛合金咬合接头的强度退化规律和疲劳损伤失效机理。对断裂试样进行扫描，通过研究不同疲劳循环加载时间下断口形态的演变来分析疲劳损伤失效机制。结果表明，幂指数降解模型能准确预测钛合金咬合接头的强度降解。随着疲劳加载循环次数的增加，劈裂特征与疲劳裂纹同时出现，导致接头强度逐渐降低。最终，试验验证了钛合金夹紧接头强度退化功率指数模型在预测残余强度方面具有很高的准确性。

A flexible design framework for lattice-based chiral mechanical metamaterials considering dynamic energy absorption

Weiyun Xu, Chang Zhou, Hanyu Zhang, Zhao Liu, Ping Zhu

doi:10.1016/j.tws.2024.112108

考虑动态能量吸收的基于晶格的手性机械超材料的灵活设计框架

While chiral mechanical metamaterials (CMMs) are reported promising in energy absorption due to the unique chiral effect, the energy-absorbing CMMs lack effective and generalized design methodologies and corresponding structure-property relationship studies. To this end, a design framework for lattice-based CMMs was proposed, and the dynamic compressive behaviors of CMMs were systematically investigated. Firstly, based on a predefined design baseline that considered a support-free metal additive manufacturing process, a screw-theory-based assembly rule was presented, which enabled the scalable twist effects and the characterization of chiral features. Secondly, an aperiodic design process that sequentially defines joints, strut connections, and geometrical features was proposed. This framework via parameterization enables the rapid generation of geometric and finite element models that contain a large number of unit cells. It also enables the integration of joint enhancement design, bio-inspired helical design, and gradient design. Finally, by finite element analysis and experiments of uniaxial medium-strain-rate (50 s−1) compression, the effects of chirality on mechanical properties (compressive strength, yield plateau, energy absorption, etc.) during the nonlinear large-deformation responses were elucidated. Results show that a comprehensive and flexible method is presented by independently defining each rod component or joint of the lattice type metamaterials, which enables the design from chiral to achiral, from rectangular to helical, and from uniform to gradient. The bidirectional gradient CMMs design along the axial and radial directions achieves a 52.0 % specific energy absorption enhancement compared with achiral lattices, demonstrating the energy absorption advantage of CMMs, and laying the foundation for further optimization, inverse design, and engineering applications.

据报道，由于独特的手性效应，手性机械超材料（CMMs）在能量吸收方面大有可为，但吸能 CMMs 缺乏有效的通用设计方法和相应的结构-性能关系研究。为此，我们提出了基于晶格的 CMM 设计框架，并对 CMM 的动态压缩行为进行了系统研究。首先，基于无支撑金属增材制造工艺的预定义设计基线，提出了基于螺旋理论的装配规则，从而实现了可扩展的扭曲效应和手性特征的表征。其次，还提出了一种非周期性设计流程，可按顺序定义接头、支柱连接和几何特征。通过参数化框架，可以快速生成包含大量单元格的几何和有限元模型。它还能整合关节增强设计、生物螺旋设计和梯度设计。最后，通过有限元分析和单轴中等应变速率（50 s-1）压缩实验，阐明了手性在非线性大变形响应期间对机械性能（抗压强度、屈服高原、能量吸收等）的影响。结果表明，通过独立定义晶格型超材料的每个杆组件或接头，提出了一种全面而灵活的方法，从而实现了从手性到非手性、从矩形到螺旋、从均匀到梯度的设计。与非手性晶格相比，沿轴向和径向的双向梯度 CMMs 设计实现了 52.0% 的比能量吸收增强，证明了 CMMs 的能量吸收优势，并为进一步优化、反向设计和工程应用奠定了基础。