Journal of The Mechanics and Physics of Solids最新文献_第2页

Time-dependent constitutive behaviors of a dynamically crosslinked glycerogel governed by bond kinetics and chain diffusion 受键动力学和链扩散影响的动态交联甘油凝胶随时间变化的结构行为

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-12 DOI: 10.1016/j.jmps.2024.105951

Ji Lin , Md. Tariful Islam Mredha , Rumesh Rangana Manimel Wadu , Chuanqian Shi , Rui Xiao , Insu Jeon , Jin Qian

Soft materials featuring dynamic networks represent a burgeoning frontier in materials science, offering multifaceted applications spanning soft robotics, biomaterials, and flexible electronics. Unraveling the time-dependent constitutive behavior of these materials, rooted in dynamic networks, stands as a pivotal pursuit for engineering advancements. Herein, we fabricate a tough and extreme-temperature-tolerant glycerogel with a polymer network crosslinked by metal-coordination crosslinkers and conduct a thorough analysis of its intricate mechanical responses across monotonic loading, relaxation, creep, and cyclic tests. We then develop a physically grounded constitutive model integrating the dynamics of crosslinker association/dissociation and polymer chain diffusion, furnishing a holistic framework to elucidate their interplay. We employ a statistical description, using density functions of chains in terms of end-to-end vectors, to characterize network reconfiguration. The evolution of chain density under external load, mediated by crosslinker kinetics and chain diffusion in a viscous medium, leads to intriguing variations in elastic energy and stress responses. Through meticulous experimental validation and numerical simulations, we demonstrate the efficacy of the model in forecasting the mechanical behavior of dynamic polymer networks under diverse loading scenarios, encompassing strain rate effects, stress relaxation, Mullins effect, and self-recovery phenomena. Our findings provide valuable insights into the design and optimization of dynamic network-based materials for diverse applications in biomedical and engineering fields.

以动态网络为特征的软材料代表了材料科学的一个新兴前沿领域，其应用领域涉及软机器人、生物材料和柔性电子器件等多个方面。揭示这些材料根植于动态网络的随时间变化的构成行为，是工程学进步的关键追求。在本文中，我们制造了一种坚韧且耐极端温度的甘油凝胶，其聚合物网络由金属配位交联剂交联，并对其在单调加载、松弛、蠕变和循环测试中的复杂机械响应进行了深入分析。然后，我们建立了一个以物理为基础的构成模型，该模型整合了交联剂结合/解离和聚合物链扩散的动力学，为阐明它们之间的相互作用提供了一个整体框架。我们采用了一种统计描述方法，利用端到端矢量的链密度函数来描述网络重构的特征。在交联剂动力学和链在粘性介质中的扩散作用下，链密度在外部载荷作用下的演变导致了弹性能量和应力反应的有趣变化。通过细致的实验验证和数值模拟，我们证明了该模型在预测各种加载情况下动态聚合物网络的机械行为方面的功效，包括应变速率效应、应力松弛、穆林斯效应和自我恢复现象。我们的研究结果为设计和优化动态网络材料在生物医学和工程领域的不同应用提供了宝贵的见解。

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引用次数: 0

Double-eigenvalue bifurcation and multistability in serpentine strips with tunable buckling behaviors 具有可调屈曲行为的蛇形带的双特征值分岔和多稳定性

IF 5.3 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-12 DOI: 10.1016/j.jmps.2024.105922

Qiyao Shi, Weicheng Huang, Tian Yu, Mingwu Li

Serpentine structures, composed of straight and circular strips, have garnered significant attention as potential designs for flexible electronics due to their remarkable stretchability. When subjected to stretching, these serpentine strips buckle out of plane, and previous studies have identified two distinct buckling modes whose order of appearance may interchange in serpentine structures with a single cell. In this study, we employ anisotropic rod theory to model serpentine strips as a multi-segment boundary value problem (BVP), with continuity conditions enforced at the interface between the straight and curved strips. We solve the BVP using methods of continuation, and our results reveal that: (1) the exchange of the two buckling modes in a single-cell serpentine strip is induced by a double-eigenvalue and associated secondary bifurcations, which also alter the stability of the two buckling modes; (2) a variety of stable states with reversible symmetry can be manually obtained in tabletop models and are found to be disconnected from the planar branch in numerical continuation. Furthermore, we demonstrate that modulating the strip thickness across different cells leads to the initiation of buckling in the thinnest section, thereby allowing for the tuning of buckling modes in serpentine strips. In structures with two cells, the sequence of the two buckling modes can also be controlled by designing serpentine strips with nonuniform height. This work could enhance the mechanical design of serpentine-interconnect-based flexible structures and could have applications in multistable actuators and mechanical memory devices.

蛇形结构由直条和圆条组成，因其显著的可拉伸性而作为柔性电子器件的潜在设计备受关注。在受到拉伸时，这些蛇形条带会向平面外屈曲，先前的研究已经确定了两种不同的屈曲模式，其出现的顺序可能会在具有单细胞的蛇形结构中互换。在本研究中，我们采用各向异性杆理论，将蛇形条带建模为一个多段边界值问题（BVP），并在直线条带和曲线条带之间的界面上强制执行连续性条件。我们使用延续方法求解了 BVP，结果表明(1) 单细胞蛇形条带中两种屈曲模式的交换是由双特征值和相关的二次分岔引起的，这也改变了两种屈曲模式的稳定性；(2) 在桌面模型中可以手动获得多种具有可逆对称性的稳定状态，并且在数值延续中发现这些状态与平面分支是断开的。此外，我们还证明了在不同单元中调节带材厚度会导致在最薄的部分开始屈曲，从而可以调整蛇形带材的屈曲模式。在具有两个单元的结构中，还可以通过设计高度不均匀的蛇形条来控制两种屈曲模式的顺序。这项研究可提高基于蛇形互连的柔性结构的机械设计水平，并可应用于多稳态致动器和机械存储设备。

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引用次数: 0

Poroelastic fracture of polyacrylamide hydrogels: Enhanced crack tip swelling driven by chain scission 聚丙烯酰胺水凝胶的气弹性断裂：由链裂解驱动的裂缝尖端膨胀增强

IF 5.3 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-12 DOI: 10.1016/j.jmps.2024.105954

Qifang Zhang, Junjie Liu, Gang Zhang, Yuhong Li, Nan Hu, Jinglei Yang, Yan Yang, Shaoxing Qu, Qianhua Kan, Guozheng Kang

The deformation of hydrogels is accompanied by water migration, a process that plays a crucial role in their fracture behaviors. Previous investigations primarily focus on how the water migration between the environment and hydrogel affects the fracture of hydrogels. Herein, a novel mechanism of the rate-dependent fracture of hydrogels induced by interior water migration is uncovered. Notched polyacrylamide (PAAm) hydrogels are stretched at various stretch rates in both oil and deionized (DI) water environments. Notably, the critical stretches to crack propagation are positively correlated with the stretch rates in both the two environments. This rate-dependent fracture is attributed to the crack tip swelling of PAAm hydrogels. Delayed fracture tests conducted in oil further verify the co-existence of delayed fracture and rate-dependent fracture resulted from interior water migration in PAAm hydrogels. The experimental findings are interpreted by considering the imperfection of a real polymer network, in which the scission of short chains in the region neighboring the crack tip reduces the average crosslinking density locally, thereby greatly amplifying the degree of crack tip swelling and its influence on the fracture of hydrogels. A constitutive model coupling the evolution of polymer network and the diffusion of water molecules is proposed, which can predict the crack tip swelling of notched PAAm hydrogels through the finite element method. Assuming that the decrease in fracture toughness is positively related to the swelling along the crack propagation surface, the predicted normalized fracture toughness matches the experimental results of PAAm hydrogels stretched in water well, and satisfies those in oil environment qualitatively. This work highlights the significant influence of interior water migration on the fracture of hydrogels and provides insights that may guide the design of hydrogels with enhanced fracture resistance.

水凝胶的变形伴随着水迁移，这一过程对其断裂行为起着至关重要的作用。以往的研究主要集中于环境与水凝胶之间的水迁移如何影响水凝胶的断裂。本文揭示了内部水迁移诱导水凝胶速率依赖性断裂的新机制。缺口聚丙烯酰胺（PAAm）水凝胶在油和去离子水环境中以不同的拉伸速率拉伸。值得注意的是，在这两种环境中，裂纹扩展的临界拉伸与拉伸速率呈正相关。这种与速率相关的断裂归因于 PAAm 水凝胶的裂纹尖端膨胀。在油中进行的延迟断裂测试进一步验证了 PAAm 水凝胶内部水分迁移导致的延迟断裂和速率依赖性断裂的并存。考虑到真实聚合物网络的不完善性，对实验结果进行了解释，其中裂缝尖端附近区域的短链断裂降低了局部的平均交联密度，从而大大增加了裂缝尖端的膨胀程度及其对水凝胶断裂的影响。本文提出了聚合物网络演化与水分子扩散耦合的构效模型，可通过有限元方法预测缺口 PAAm 水凝胶的裂尖膨胀。假定断裂韧性的降低与沿裂纹扩展面的膨胀呈正相关，预测的归一化断裂韧性与水井中拉伸 PAAm 水凝胶的实验结果相吻合，并在定性上满足石油环境中的实验结果。这项研究强调了内部水迁移对水凝胶断裂的重要影响，并为设计抗断裂性能更强的水凝胶提供了指导。

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引用次数: 0

Fracture of polymer-like networks with hybrid bond strengths 具有混合键强度的类聚合物网络的断裂

IF 5.3 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-10 DOI: 10.1016/j.jmps.2024.105931

Chase M. Hartquist, Shu Wang, Bolei Deng, Haley K. Beech, Stephen L. Craig, Bradley D. Olsen, Michael Rubinstein, Xuanhe Zhao

The design and functionality of polymeric materials hinge on failure resistance. While molecular-level details drive crack evolution in polymer networks, the connection between individual chain scission and bulk failure remains unclear and difficult to probe. In this work, we systematically study the fracture mechanics of polymer-like networks with hybrid bond strengths. We reveal that varying the ratio of strong and weak strands within otherwise identical networks gives a non-monotonic relationship between intrinsic fracture energy and strong strand fraction. Networks with some weak strands can counterintuitively outperform those with exclusively strong strands. Experiments on poly(ethylene glycol) gels and architected polymer-like lattices together with simulations unveil these properties. We show through computational visualization that strand type concentrations impact crack growth patterns and fracture energy trends. Cracks propagate through weak layers at low strong strand fractions. Aggregate clusters deflect or pin cracks at similar concentrations of strong and weak strands. Cracks blunt due to dispersed weak strand failure at high strong strand fractions. The sacrificial weak strands can notably deconcentrate stress near the crack tip, which toughens by delaying crack advancement. The interplay between concentration and clustering of strand types in networks with hybrid bond strengths, combined with crack growth phenomena and nonlocal energy release, provides insights into unusual fracture characteristics. Results shed light on fracture in polymer networks and percolated lattices.

聚合物材料的设计和功能取决于其抗破坏性。虽然分子层面的细节驱动着聚合物网络中裂纹的演化，但单个链的断裂与整体失效之间的联系仍不清楚，也难以探究。在这项工作中，我们系统地研究了具有混合键强度的类聚合物网络的断裂力学。我们发现，在原本相同的网络中，改变强股和弱股的比例会在本征断裂能和强股比例之间产生非单调关系。含有一些弱股的网络会反直觉地优于完全含有强股的网络。对聚（乙二醇）凝胶和结构化聚合物样晶格的实验以及模拟揭示了这些特性。我们通过可视化计算表明，股线类型的集中会影响裂纹生长模式和断裂能量趋势。当强股比例较低时，裂纹会在弱层中传播。在强股和弱股浓度相近的情况下，聚合簇会使裂纹偏转或针刺裂纹。在强股比例较高时，由于分散的弱股失效，裂缝会变钝。牺牲的弱股可显著降低裂纹尖端附近的应力集中度，从而通过延迟裂纹的扩展而增韧。在具有混合粘接强度的网络中，股类型的集中和集群之间的相互作用，再加上裂纹生长现象和非局部能量释放，使人们对不寻常的断裂特性有了更深入的了解。研究结果揭示了聚合物网络和渗滤晶格中的断裂现象。

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引用次数: 0

Micromechanics-based variational phase-field modeling of fatigue fracture 基于微机械学的疲劳断裂变分相场建模

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-10 DOI: 10.1016/j.jmps.2024.105932

Mina Sarem , Nuhamin Eshetu Deresse , Els Verstrynge , Stijn François

In this paper, we extend the micromechanics-based phase-field model to simulate fatigue failure. The coupling of a micromechanics-based framework with the phase-field approach helps to differentiate between failure modes, by distinguishing between open and closed microcracks. This integrated framework links continuum field variables, such as plastic strain and damage variable, to micromechanical mechanisms like frictional sliding and microcrack opening. We first improve the algorithm’s stability during loading–unloading in the tensile regime through a modification of the plasticity evolution equations. Next, we incorporate fatigue damage accumulation and deterioration due to cyclic loading into the micromechanics-based phase-field model. A fatigue degradation function, driven by free energy accumulation, is introduced to degrade the fracture energy upon reaching a specified threshold during cyclic loading. Various cyclic loads are applied to benchmark tests, both with and without imperfections (e.g. holes, inclusions, voids), under plane strain conditions to capture diverse failure modes. The results demonstrate the model’s capability to accurately describe tensile, shear, and mixed-mode fracture under cyclic loading. Furthermore, the model effectively simulates key features of fatigue behavior, including crack nucleation, growth, and coalescence.

在本文中，我们扩展了基于微机械学的相场模型，以模拟疲劳失效。基于微观力学的框架与相场方法的耦合有助于通过区分开放式和封闭式微裂纹来区分失效模式。这种集成框架将塑性应变和损伤变量等连续场变量与摩擦滑动和微裂纹张开等微观机械机制联系起来。我们首先通过修改塑性演变方程，提高了算法在拉伸状态下加载-卸载过程中的稳定性。接下来，我们将循环加载导致的疲劳损伤累积和退化纳入了基于微观力学的相场模型。我们引入了由自由能积累驱动的疲劳退化函数，在循环加载过程中达到指定阈值时降低断裂能。在平面应变条件下，对有缺陷和无缺陷（如孔、夹杂物、空隙）的基准测试施加了各种循环载荷，以捕捉各种失效模式。结果表明，该模型能够准确描述循环载荷下的拉伸、剪切和混合模式断裂。此外，该模型还能有效模拟疲劳行为的关键特征，包括裂纹的成核、生长和凝聚。

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引用次数: 0

Magnetostriction of soft-magnetorheological elastomers 软磁流变弹性体的磁致伸缩性

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-10 DOI: 10.1016/j.jmps.2024.105934

Eric M. Stewart, Lallit Anand

Soft-magnetorheological elastomers (s-MREs) are particulate composites made of a non-magnetic elastomeric matrix dispersed with micron-sized particles of a “soft-magnetic” material. The phenomenon of magnetostriction in specimens made from s-MREs is the change in their shape when they are subjected to an external magnetic field. Experiments in the literature show that for circular cylindrical specimens subjected to an axially applied magnetic field the magnetostriction is strongly dependent on their aspect-ratio, with specimens with a low ratio of the length to the diameter exhibiting a larger tensile magnetostrictive strain than specimens with a large aspect-ratio — the “shape-effect.” This response is also hysteretic because of the underlying viscoelasticity of the matrix material. In this paper we report on a large deformation magneto-viscoelasticity theory for s-MREs and its finite element implementation. Using our theory we show that we can model this non-intuitive geometry-dependent magnetostrictive response of cylindrical s-MRE specimens. We show that the effect of the magnetization

m

of the cylinder is to decrease the magnetic field

h

within the cylinder relative to the applied magnetic field

h^{app}

outside the cylinder, the well-known demagnetization effect, and that this demagnetization is diminished in more slender cylinders due to magnetic fringing at the boundaries of the cylinder. This is the physical reason behind the macroscopically-observed “shape-effect.”

Our magneto-viscoelasticity theory is quite broad, and it has many potential applications beyond modeling the magnetostriction of cylindrical specimens. As an example we apply the theory to study the bending actuation response of beams of s-MREs when they are subjected to magnetic fields at different incidence angles to their longitudinal axis.

软磁流变弹性体（s-MRE）是一种微粒复合材料，由非磁性弹性体基体与微米大小的 "软磁 "材料微粒分散而成。磁性弹性体试样的磁致伸缩现象是指试样在外部磁场作用下的形状变化。文献中的实验表明，对于受到轴向磁场作用的圆柱形试样，磁致伸缩与它们的纵横比密切相关，长度与直径之比小的试样比纵横比大的试样表现出更大的拉伸磁致伸缩应变--这就是 "形状效应"。由于基体材料的基本粘弹性，这种响应也具有滞后性。在本文中，我们报告了针对 s-MRE 的大变形磁-粘弹性理论及其有限元实现。利用我们的理论，我们可以对圆柱形 s-MRE 试样的这种非直观几何依赖性磁致伸缩响应进行建模。我们表明，圆柱体磁化 m 的作用是降低圆柱体内的磁场 h，相对于圆柱体外的外加磁场 happ，这就是众所周知的退磁效应。这就是宏观观察到的 "形状效应 "背后的物理原因。

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引用次数: 0

The topological dynamics of continuum lattice grid structures 连续晶格网格结构的拓扑动力学

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-09 DOI: 10.1016/j.jmps.2024.105935

Yimeng Sun , Jiacheng Xing , Li-Hua Shao , Jianxiang Wang

Continuum lattice grid structures which consist of joined elastic beams subject to flexural deformations are ubiquitous. In this work, we establish a theoretical framework of the topological dynamics of continuum lattice grid structures, and discover the topological edge and corner modes in these structures. We rigorously identify the infinitely many topological edge states within the bandgaps via a theorem, with a clear criterion for the infinite number of topological phase transitions. Then, we obtain analytical expressions for the topological phases of bulk bands, and propose a topological index related to the topological phases that determines the existence of the edge states. The theoretical approach is directly applicable to a broad range of continuum lattice grid structures including bridge-like frames, square frames, kagome frames, continuous beams on elastic springs. The frequencies of the topological modes are precisely obtained, applicable to all the bands from low to high frequencies. Continuum lattice grid structures serve as excellent platforms for exploring various kinds of topological phases and demonstrating the topological modes at multiple frequencies on demand. Their topological dynamics has significant implications in safety assessment, structural health monitoring, and energy harvesting.

由承受弯曲变形的连接弹性梁组成的连续网格结构无处不在。在这项工作中，我们建立了连续晶格网格结构拓扑动力学的理论框架，并发现了这些结构中的拓扑边角模式。我们通过一个定理严格确定了带隙内的无限多拓扑边缘态，并给出了拓扑相变无限多的明确标准。然后，我们得到了体带拓扑相位的分析表达式，并提出了与拓扑相位相关的拓扑指数，以确定边缘态的存在。该理论方法直接适用于广泛的连续晶格网格结构，包括桥式框架、方形框架、卡戈米框架、弹性弹簧上的连续梁。拓扑模态的频率可精确获得，适用于从低频到高频的所有频段。连续晶格网格结构是探索各种拓扑相位和按需展示多频率拓扑模态的绝佳平台。它们的拓扑动力学对安全评估、结构健康监测和能量收集具有重要意义。

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引用次数: 0

Modeling yield stress scaling and cyclic response using a size-dependent theory with two plasticity rate fields 使用具有两个塑性速率场的尺寸相关理论建立屈服应力缩放和循环响应模型

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-08 DOI: 10.1016/j.jmps.2024.105930

Andrea Panteghini , Lorenzo Bardella , M.B. Rubin

This work considers a recently developed finite-deformation elastoplasticity theory that assumes distinct tensorial fields describing macro-plasticity and micro-plasticity, where the latter is determined by a higher-order balance equation with associated boundary conditions. Specifically, micro-plasticity evolves according to a contribution to the Helmholtz free-energy density that depends on a Nye–Kröner-like dislocation density tensor and is referred to as the defect energy. The theory is meant to set the onset of micro-plasticity at a stress level lower than that activating macro-plasticity, such as micro-plasticity aims at explaining and characterizing the increase in yield stress with diminishing size. Additionally, the formulation relies on smooth elastic–plastic transitions for both plasticity fields, even if focusing on rate-independent response. This investigation demonstrates the capability of the proposed theory to predict size-effects of interest in small-scale metal plasticity by focusing on multiple loading cycles and, prominently, on the scaling of the apparent yield stress with sample size, the latter being a crucial open issue in the recent literature on modeling size-dependent plasticity. To this end, this work considers the specialization of the theory to small deformations and proposes a finite element implementation for the constrained simple shear problem. Importantly, it is shown that the simplest treatment of plastic strain gradients, which consists of adopting a quadratic defect energy, can be conveniently used to predict reliable size-effects, although in the literature on strain gradient plasticity quadratic defect energies have always been associated with a relatively poor description of size-effects. In fact, in the present theory the limits of the quadratic defect energy are overcome by leveraging on the complex interplay between micro- and macro-plasticity fields. The capability of the proposed theory is quantitatively demonstrated by predicting results from the literature that are obtained from discrete dislocation dynamics simulations on planar polycrystals of grains with variable size subjected to macroscopic pure shear.

这项研究考虑了最近开发的有限变形弹塑性理论，该理论假定了描述宏观弹塑性和微观弹塑性的不同张量场，其中后者由带有相关边界条件的高阶平衡方程决定。具体来说，微塑性是根据对亥姆霍兹自由能密度的贡献而演变的，该自由能密度取决于类似于 Nye-Kröner 的位错密度张量，被称为缺陷能。该理论旨在将微塑性的起始应力水平设定为低于激活宏观塑性的应力水平，例如微塑性旨在解释和描述屈服应力随尺寸减小而增加的现象。此外，该公式依赖于两个塑性场的平滑弹塑性转换，即使侧重于速率无关响应。这项研究通过关注多次加载循环，特别是关注表观屈服应力与样品尺寸的比例关系，证明了所提出的理论有能力预测小尺寸金属塑性中的尺寸效应。为此，本研究考虑了理论对小变形的特殊化，并提出了受约束简单剪切问题的有限元实现方法。重要的是，尽管在应变梯度塑性的文献中，二次缺陷能总是与对尺寸效应的相对较差描述联系在一起，但研究表明，塑性应变梯度的最简单处理方法（包括采用二次缺陷能）可以方便地用于预测可靠的尺寸效应。事实上，在本理论中，通过利用微观和宏观塑性场之间复杂的相互作用，二次缺陷能的局限性被克服了。通过预测文献中的离散位错动力学模拟结果，对宏观纯剪切作用下尺寸可变的晶粒平面多晶体进行模拟，定量证明了所提理论的能力。

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引用次数: 0

Damage-induced energy dissipation in artificial soft tissues 人造软组织中由损伤引起的能量耗散

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-05 DOI: 10.1016/j.jmps.2024.105933

W.K. Sun , B.B. Yin , K.M. Liew

A systematic understanding of the toughening and self-healing mechanisms of artificial soft tissues is crucial for advancing their robust application in biomedical engineering. However, current models predominantly possess a phenomenological nature, often devoid of micromechanical intricacies and quantitative correlation between microstructure damage and macroscopic energy dissipation. To bridge this gap, we propose a novel energy dissipation mechanism-motivated network model that incorporates three unique physical ingredients with sound theoretical basis for the first time. These innovated features include the bond percolation-mediated network density and stiffness, the damage-induced energy dissipation and stress softening, and the entropic elasticity for the highly stretchable second network. The validity of this model was examined by implementing it within a meshfree peridynamic framework for artificial soft tissues subjected to simple tension and pure shear tests. We quantitatively correlated the dissipation with the network damage to reveal the effects of network density, the breaking stretch dispersion and the stiffness ratio. Our findings highlighted that the inhomogeneity and dispersion of materials properties play significant roles in the controllable progressive damage and dissipation, thereby offering valuable guidance for designing tougher artificial soft tissues. By reactivating the failed network, we further successfully captured the self-healing behaviors of artificial soft tissues. Our work provides an inspiring modeling framework for studying toughening mechanisms of artificial soft tissues.

系统地了解人工软组织的增韧和自愈机制对于推动其在生物医学工程中的稳健应用至关重要。然而，目前的模型主要具有现象学性质，往往缺乏微观机械的复杂性以及微观结构损伤与宏观能量耗散之间的定量相关性。为了弥合这一差距，我们首次提出了一种以能量耗散机制为动机的新型网络模型，该模型包含三个具有坚实理论基础的独特物理成分。这些创新特征包括键渗流介导的网络密度和刚度、损伤诱导的能量耗散和应力软化，以及高伸展性第二网络的熵弹性。通过在无网格周动态框架内对人工软组织进行简单拉伸和纯剪切试验，检验了该模型的有效性。我们对耗散与网络损伤进行了定量关联，以揭示网络密度、断裂拉伸分散性和刚度比的影响。我们的研究结果表明，材料特性的不均匀性和分散性在可控的渐进损伤和耗散中发挥了重要作用，从而为设计更坚韧的人工软组织提供了宝贵的指导。通过重新激活失效网络，我们进一步成功捕捉到了人工软组织的自愈行为。我们的工作为研究人工软组织的增韧机制提供了一个启发性的建模框架。

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引用次数: 0

Regularization of softening plasticity with the cumulative plastic strain-rate gradient 利用累积塑性应变率梯度对软化塑性进行正则化处理

IF 5 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2024-11-04 DOI: 10.1016/j.jmps.2024.105923

G. Bacquaert , J. Bleyer , C. Maurini

We propose a novel variational framework to regularize softening plasticity problems. Specifically, we modify the plastic dissipation potential term by adding a contribution depending on the cumulative plastic strain-rate gradient. We formulate the evolution of the so-obtained strain-rate gradient plasticity model with an incremental variational principle. The time-discretized evolution equations are deduced from the corresponding first-order optimality conditions. To investigate the model, the problem of a bar in traction is studied. Analytical solutions are explicitly derived, and characterized by exponential localization profiles. Contrary to other regularization strategies, no spurious spreading of the plastic localization band is observed. A first numerical implementation in 1D and 2D plane strain conditions is proposed based on conic programming solvers and validated against the analytical predictions. Numerical results on plane strain von Mises plasticity show that the proposed framework leads to mesh-independent results and efficient control of plastic localization bands.

我们提出了一个新颖的变分框架来正则化软化塑性问题。具体来说，我们修改了塑性耗散势项，增加了一个取决于累积塑性应变率梯度的贡献。我们用增量变分原理来计算由此获得的应变率梯度塑性模型的演化。根据相应的一阶最优条件推导出时间细化的演化方程。为了研究该模型，对牵引中的棒材问题进行了研究。明确推导出了解析解，并以指数局部化剖面为特征。与其他正则化策略相反，没有观察到塑性局部化带的虚假扩散。基于圆锥编程求解器，首次提出了一维和二维平面应变条件下的数值实现方法，并与分析预测进行了验证。平面应变冯米塞斯塑性的数值结果表明，所提出的框架能产生与网格无关的结果，并能有效控制塑性局部化带。

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