Journal of The Mechanics and Physics of Solids最新文献_第3页

Dynamic crushing of metal lattice metamaterials: Shock mode diagrams and transition to topology-independent compaction regime 金属晶格超材料的动态破碎：激波模式图和向拓扑无关压实状态的过渡

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jmps.2026.106515

Brandon K. Zimmerman, Eric B. Herbold, Mukul Kumar, Jonathan Lind

Additively manufactured lattice metamaterials offer design versatility in strength and energy absorption and provide an additional degree of freedom through the selection of the lattice topology. Under quasistatic loading, the unit cell structure can strongly affect the stiffness, yield, and post-yield behavior, but whether and to what degree the effect of lattice topology persists into dynamic loading scenarios, up to the compaction shock regime, has not been established. LLNL’ s ALE3D hydrocode was used to perform a computational investigation of dynamic loading in multiple lattice types, including the gyroid, octet, Schwarz D, and rhombic dodecahedron, under impact velocities from 0.25 to 2.25 km/s. Shock Hugoniots for each lattice topology are generated and compared, suggesting that above a critical velocity, distinctions between architectures may not persevere and compacted lattices behave similarly. To investigate the transition between topology-dependent quasistatic compression and the topology-independent regime above the critical velocity, a one-dimensional elastic-linear hardening plasticity-densified solid (E-LHP-DS) shock model for lattice materials was developed that relies upon confined compression to link the quasistatic and shock mechanics. Unlike similar works, the model does not assume rigid behavior prior to yield or locking behavior at densification, allowing a richer exploration of lattice mechanics. With only six parameters, the analytical model simultaneously fit quasistatic confined compression simulations for relative densities

0.1 \leq \bar{ρ} \leq 0.9

and predicted dynamic compaction behavior to traverse several distinct shock modes, each defined by a critical impact speed (equivalently, critical stresses). Comparing the numerical results to the one-dimensional E-LHP-DS shock model predictions suggests that the topology-independence under strong shocks is linked to the onset of densification, which can be predicted based on quasistatic confined compression results.

增材制造的晶格超材料在强度和能量吸收方面提供了设计上的通用性，并通过选择晶格拓扑提供了额外的自由度。在准静态加载下，单胞结构可以强烈地影响刚度、屈服和后屈服行为，但晶格拓扑的影响是否以及在多大程度上持续到动态加载场景，直到压实冲击状态，还没有确定。利用LLNL的ALE3D氢代码对冲击速度为0.25 ~ 2.25 km/s的多种晶格类型（包括回转体、八面体、Schwarz D和菱形十二面体）的动载荷进行了计算研究。我们生成并比较了每个晶格拓扑的震荡Hugoniots，这表明在临界速度以上，结构之间的区别可能不会持久，而压缩晶格的行为相似。为了研究临界速度以上拓扑相关准静态压缩和拓扑无关压缩之间的转变，建立了晶格材料的一维弹性线性硬化塑性致密固体（E-LHP-DS）冲击模型，该模型依赖于受限压缩将准静态力学和冲击力学联系起来。与类似的工作不同，该模型不假设在屈服之前的刚性行为或致密化时的锁定行为，允许对晶格力学进行更丰富的探索。该分析模型只有6个参数，同时适合相对密度0.1≤ρ¯≤0.9的准静态受限压缩模拟，并预测了动态压缩行为，以穿越几种不同的冲击模式，每种冲击模式都由临界冲击速度（相当于临界应力）定义。将数值结果与一维E-LHP-DS冲击模型预测结果进行比较表明，强冲击下的拓扑独立性与致密化的发生有关，致密化可以基于准静态受限压缩结果进行预测。

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引用次数: 0

Contact in strain gradient elasticity: The rigid flat punch problem 应变梯度弹性中的接触：刚性平冲问题

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jmps.2026.106527

P.A. Gourgiotis , Th. Zisis , A.E. Giannakopoulos , H.G. Georgiadis

This work revisits the classical flat-punch indentation problem within the framework of Mindlin’s form-II strain-gradient elasticity, uncovering new phenomena driven by the interplay between contact geometry and material length scale. The analysis is carried out under plane strain conditions, and the corresponding mixed boundary value problem is solved using integral equation techniques. Two distinct contact regimes are examined. In the first, assuming full contact beneath the rigid indenter, the pressure distribution exhibits hypersingular behavior with tensile (adhesive-like) tractions near the contact edges. These arise purely from kinematic constraints, without invoking any cohesive law or surface energy. The second regime emerges by relaxing the flatness assumption, allowing for partial separation beneath the punch. In this case, contact is sustained only within a central region, flanked by separation gaps near the edges and balanced by concentrated edge reactions. The resulting pressure is entirely positive and exhibits a classical square-root singularity. Both the contact width and edge forces are shown to depend sensitively on Poisson’s ratio and the material length scale. Beyond a critical length, the contact region collapses, and the problem reduces to the superposition of two Flamant-type concentrated contact solutions. These findings reveal a rich class of indentation responses naturally captured by strain gradient elasticity-phenomena inaccessible to classical continuum models. They may have important implications for nano/micro-indentation experiments on materials with pronounced internal length scales, such as polymers, ceramics, composites, cellular solids, masonry, and biological tissues.

这项工作在Mindlin的ii型应变梯度弹性框架内重新审视了经典的平冲压痕问题，揭示了接触几何形状和材料长度尺度之间相互作用驱动的新现象。在平面应变条件下进行了分析，采用积分方程技术求解了相应的混合边值问题。研究了两种不同的接触机制。在第一种情况下，假设刚性压头下方完全接触，压力分布表现出超奇异行为，在接触边缘附近具有拉伸（类似粘合剂）牵引力。这些纯粹是由运动学约束产生的，而不调用任何内聚定律或表面能。第二种机制是通过放松平面假设，允许冲孔下方部分分离而出现的。在这种情况下，接触仅在中心区域内维持，两侧是靠近边缘的分离间隙，并通过集中的边缘反应来平衡。由此产生的压力完全是正的，并表现出经典的平方根奇点。两者的接触宽度和边缘力显示敏感地依赖于泊松比和材料长度尺度。超过临界长度后，接触区域坍塌，问题就变成了两种flamant型浓缩接触溶液的叠加。这些发现揭示了一种丰富的压痕响应类别，自然地被应变梯度弹性捕获-经典连续体模型无法获得的现象。它们可能对具有明显内部长度尺度的材料（如聚合物、陶瓷、复合材料、细胞固体、砌体和生物组织）的纳米/微压痕实验具有重要意义。

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引用次数: 0

Generalized configurational force for thermoelasticity with application to isogeometric analysis of thermoelastic crack propagation 热弹性广义构形力及其在热弹性裂纹扩展等几何分析中的应用

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jmps.2026.106541

Chung-Shuo Lee, Pei-En Chou, Ganesh Subbarayan

Accurately predicting the forces driving crack propagation is critical for engineering applications where fracture is an important failure criterion. An easy to apply configurational force theory for estimating crack driving force in thermoelastic solids is derived in this study. The derivation relies on the notion of a configurational optimization problem for heterogeneities inserted into a homogeneous domain. The configurational optimization allows arbitrary objectives subject to constraints of variational principles governing the solid behavior. The optimality criteria obtained by solving an adjoint problem naturally yields a generalized Eshelby Energy-Momentum tensor, which leads to the classical

J -

,

L -

and

M -

integrals of fracture mechanics when Helmholtz free energy is chosen as the objective and the problem is constrained to be isothermal. We calculate the configurational force using an isogeometric computational framework that relies on a recently developed enrichment procedure for multi-material corner singularities, of which cracks are a special case. Enriched displacement and temperature functions applied at crack tips are illustrated and demonstrated through several numerical examples on thermoelastic solids. Examples include (a) crack driving force estimation under adiabatic/isothermal conditions, (b) edge crack propagation simulation and (c) bimaterial wedge under varying mechanical and thermal loadings.

在断裂是重要破坏准则的工程应用中，准确预测驱动裂纹扩展的力至关重要。本文推导了一种易于应用的热弹性固体裂纹驱动力计算的构形力理论。推导依赖于插入到齐次域中的异构的构型优化问题的概念。结构优化允许任意目标服从于控制固体行为的变分原则的约束。通过求解伴随问题得到的最优性准则自然产生广义的Eshelby能量-动量张量，当选择Helmholtz自由能作为目标并将问题限制为等温时，可得到经典的断裂力学J−，L−和M−积分。我们使用一个等几何计算框架来计算构型力，该框架依赖于最近开发的多材料角点奇点的浓缩程序，其中裂纹是一个特殊情况。通过几个热弹性固体的数值例子，说明了裂纹尖端的丰富位移和温度函数。例子包括(a)绝热/等温条件下的裂纹驱动力估计，(b)边缘裂纹扩展模拟和(c)不同机械和热载荷下的双材料楔。

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引用次数: 0

Coupled grain-pore fabric evolutions in sheared granular materials: Anisotropy lagging and geometric emergence 剪切颗粒材料中耦合颗粒-孔隙结构演化：各向异性滞后和几何涌现

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-01-29 DOI: 10.1016/j.jmps.2026.106530

Amiya Prakash Das , Jidong Zhao , Thomas Sweijen

The morphological evolution of pore spaces is a critical yet poorly quantified microstructural determinant of the macroscopic mechanical and hydraulic behavior of granular materials. While the anisotropy of the grain contact network (F_c) is known to dictate material response, the concurrent evolution of pore space anisotropy (F_p) and its coupling with F_c remains inadequately understood. This study employs Minkowski moment tensor analysis within a Discrete Element Method (DEM) framework to bridge this gap. We systematically investigate dense and loose, monodisperse and polydisperse assemblies under cyclic triaxial loading to quantify the dynamic coupling between F_c and F_p. We demonstrate a moderate to strong correlation between F_c and F_p, with a systematic lag in the response of F_p attributed to hierarchical geometric emergence across scales. This lag is constrained by particle-scale free-volume reorganization and its kinematic compatibility with particle motion. Additionally, key pore-scale metrics, including inverse Voronoi cell fractions

(ϕ_{v}^{- 1})

, pore-scale porosity (ϕ_p), and pore shape anisotropy

\hat{β}

, are well described by gamma distributions across all packing densities and strain levels. Notably, the scaled

ϕ_{v}^{- 1}

follows a k-gamma distribution, providing a statistically consistent descriptor for volume fluctuations. A strong correlation is also observed between the average pore shape factor (|β|_avg) and global porosity, suggesting that |β|_avg serves as a geometry-based descriptor linking collective pore deformation to packing density. These findings underscore the utility of the Minkowski tensor approach in capturing 3D fabric evolution and explicitly linking pore- and grain-scale interactions. The quantitative relationships and statistical descriptors presented here provide a new foundation for enhancing constitutive models in geotechnics and powder technology, offering insights relevant to future investigations into permeability evolution and shear band formation.

孔隙空间的形态演化是颗粒材料宏观力学和水力行为的一个关键但量化不足的微观结构决定因素。虽然已知颗粒接触网络（Fc）的各向异性决定了材料的响应，但孔隙空间各向异性（Fp）的同步演化及其与Fc的耦合仍然没有得到充分的了解。本研究采用离散元法（DEM）框架内的闵可夫斯基矩张量分析来弥补这一差距。我们系统地研究了密集和松散、单分散和多分散组件在循环三轴载荷下的动态耦合。我们证明了Fc和Fp之间存在中度到强烈的相关性，而Fp的响应存在系统性滞后，这归因于不同尺度的分层几何涌现。这种滞后受到粒子尺度自由体积重组及其与粒子运动的运动学相容性的限制。此外，关键的孔隙尺度指标，包括逆Voronoi细胞分数（ϕv−1），孔隙尺度孔隙率（ϕp）和孔隙形状各向异性β^，都可以通过所有充填密度和应变水平的伽马分布来很好地描述。值得注意的是，缩放后的ϕv−1遵循k-gamma分布，为体积波动提供了统计上一致的描述符。平均孔隙形状因子（|β|avg）与整体孔隙度之间也存在很强的相关性，表明|β|avg可以作为一个基于几何的描述符，将孔隙集体变形与充填密度联系起来。这些发现强调了闵可夫斯基张量方法在捕捉三维织物演化和明确连接孔隙和颗粒尺度相互作用方面的实用性。本文提出的定量关系和统计描述符为增强岩土工程和粉末技术中的本构模型提供了新的基础，为未来研究渗透率演化和剪切带形成提供了相关见解。

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引用次数: 0

Toggling energy landscape to enable commutative and non-commutative responses in multistable structures 在多稳定结构中切换能量格局以启用交换和非交换响应

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-02-03 DOI: 10.1016/j.jmps.2026.106544

Lei Wu, Damiano Pasini

The deformation of a structure may be either insensitive or sensitive to the sequence of the applied forces: the former corresponds to a commutative response, whereas the latter indicates a non-commutative response. Among diverse physical systems, an elastic multistable structure tessellated from bistable units or bits can display commutative or non-commutative responses, each dictated by the manner of interaction between the units. In this work, we elucidate the underlying physics of commutative and non-commutative responses through the lens of the energy landscape of a multistable structure, and demonstrate that initially non-commutative units can be toggled to become commutative by altering the number and distribution of local energy minima in their state space, thus enabling reprogrammable sensitivity to the loading sequence. The concept is realized and demonstrated as a multistable switch in an electrical circuit capable of offering in situ adjustable levels of information protection through reprogrammable sequence sensitivity.

结构的变形可能对施加力的顺序不敏感或敏感：前者对应于交换响应，而后者则表示非交换响应。在不同的物理系统中，由双稳态单元或位镶嵌而成的弹性多稳态结构可以显示交换或非交换响应，每个响应都由单元之间的相互作用方式决定。在这项工作中，我们通过多稳定结构的能量景观镜头阐明了交换和非交换响应的基本物理，并证明了最初的非交换单元可以通过改变其状态空间中局部能量最小值的数量和分布来切换为交换单元，从而实现对加载序列的可重新编程灵敏度。该概念被实现并演示为电路中的多稳态开关，能够通过可重新编程的序列灵敏度提供现场可调的信息保护水平。

引用次数: 0

3D phase-field modeling of H2→H3 phase transition induced intragranular cracking in single-crystal Ni-rich layered cathodes 富镍单晶层状阴极H2→H3相变致晶内裂纹的三维相场模拟

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-01-23 DOI: 10.1016/j.jmps.2026.106528

Zhengtao Liao , Xiangbiao Liao , Yuyang Lu , Chengcheng Cao , Linghui He , Yong Ni

Understanding the intragranular cracking mechanisms of single-crystal Ni-rich layered cathodes (SCNCM) during electrochemical cycling is essential for next-generation high-energy-density and long-life Li-ion batteries. However, the complex interplay among the factors driving crack initiation and propagation remains unclear. Herein, we present a fully coupled three-dimensional phase-field model that integrates anisotropic lithium diffusion, the H2-H3 structural phase transition, stress evolution, and fracture mechanics to elucidate intragranular fracture in SCNCM during deep delithiation. Simulations on representative particle geometries reveal that anisotropic diffusion and fracture energy alone can not initiate layer-parallel cracks, instead, layered delithiation pathways govern shape-dependent phase transition dynamics, while lattice mismatch from spatially heterogeneous phase transitions nucleates cracks preferentially at particle surfaces and drives their propagation along layered planes, in good agreement with experimental observations. Cubic particles with uniform layers form cracks prematurely, whereas spherical and octahedral particles—with shorter surface layers—delay crack initiation by 5.3% state of charge (SoC) due to retarded phase transition in central layers, thereby expanding the safe-charging window. Elevated charging rates accelerate central-layer phase transition, amplifying misfit and triggering earlier cracking, while reduced phase-transition eigenstrain or flatter aspect ratios mitigate stress concentrations and suppress damage. These results establish a predictive link between phase transition dynamics and intragranular fracture, providing design strategies for mechanically robust high-energy-density cathodes.

了解电化学循环过程中单晶富镍层状阴极（SCNCM）的晶内开裂机制对下一代高能量密度和长寿命锂离子电池至关重要。然而，驱动裂纹萌生和扩展的因素之间复杂的相互作用仍不清楚。在此，我们提出了一个全耦合的三维相场模型，该模型集成了各向异性锂扩散、H2-H3结构相变、应力演化和断裂力学，以阐明SCNCM在深度剥蚀过程中的晶内断裂。对典型颗粒几何形状的模拟表明，各向异性扩散和断裂能本身不能引发层平行裂纹，相反，层状衰减路径控制着形状相关的相变动力学，而空间非均质相变导致的晶格失配优先在颗粒表面形成裂纹，并驱动裂纹沿层状面扩展，这与实验观察结果吻合良好。具有均匀层的立方粒子过早形成裂纹，而具有较短表面层的球形和八面体粒子由于中心层的相变延迟，延迟了5.3%的荷电状态（SoC），从而扩大了安全充电窗口。升高的充注速率加速了中间层的相变，放大了错配，引发了早期的开裂，而降低的相变特征应变或平坦的长径比则缓解了应力集中，抑制了损伤。这些结果建立了相变动力学与晶内断裂之间的预测联系，为机械坚固的高能量密度阴极的设计提供了策略。

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引用次数: 0

A generalized higher-order phase-field model for brittle fracture in anisotropic rocks 各向异性岩石脆性断裂的广义高阶相场模型

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-04-01 Epub Date: 2026-01-27 DOI: 10.1016/j.jmps.2026.106526

Sijia Liu , Yunteng Wang , Xueyu Geng , Wei Wu

In this work, we formulate a generalized higher-order phase-field model within the rotated anisotropic framework for simulating brittle phenomena in anisotropic rocks. Our phase-field model accounts for both the anisotropic critical fracture energy release rate and the anisotropic degradation in stiffness. The innovative aspects of this model include (i) a fourth-order structural tensor enabling simulations of strongly anisotropic fractures with arbitrary, non-orthogonal symmetry axes for capturing the complexity of natural geological media; (ii) a volumetric–deviatoric coupling energy density for transitions from anisotropic responses in the undamaged state to isotropic responses in the damaged state; (iii) a patch-based Hessian recovery algorithm ensuring stable solutions of the higher-order PDEs to reduce the computational cost; and (iv) stochastic perturbations integrated into the anisotropic crack surface density function to capture microstructural heterogeneity. Several numerical benchmark examples are provided. The numerical results are compared with some laboratory experiments on brittle fracture in anisotropic rocks.

在这项工作中，我们建立了一个在旋转各向异性框架内的广义高阶相场模型来模拟各向异性岩石中的脆性现象。我们的相场模型考虑了各向异性临界断裂能量释放率和刚度的各向异性退化。该模型的创新之处包括(i)一个四阶结构张量，可以模拟具有任意非正交对称轴的强各向异性裂缝，以捕捉自然地质介质的复杂性；（ii）从未损伤状态的各向异性响应到损伤状态的各向同性响应的体积-偏差耦合能量密度；（iii）基于patch的Hessian恢复算法，保证高阶偏微分方程解稳定，降低计算成本；（iv）将随机扰动集成到各向异性裂纹表面密度函数中，以捕获微观结构的非均质性。给出了几个数值基准算例。数值结果与一些各向异性岩石脆性断裂的室内实验结果进行了比较。

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引用次数: 0

In search of constitutive conditions in isotropic hyperelasticity: polyconvexity versus true-stress-true-strain monotonicity 寻找各向同性超弹性的本构条件：多凸性与真应力-真应变单调性

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-03-01 Epub Date: 2025-12-04 DOI: 10.1016/j.jmps.2025.106465

Maximilian P. Wollner , Gerhard A. Holzapfel , Patrizio Neff

The polyconvexity of a strain-energy function is nowadays increasingly presented as the ultimate material stability condition for an idealized elastic response. While the mathematical merits of polyconvexity are clearly understood, its mechanical consequences have received less attention. In this contribution we contrast polyconvexity with the recently rediscovered true-stress-true-strain monotonicity (TSTS-M⁺⁺) condition. By way of explicit examples, we show that neither condition by itself is strong enough to guarantee physically reasonable behavior for ideal isotropic elasticity. In particular, polyconvexity does not imply a monotone trajectory of the Cauchy stress in unconstrained uniaxial extension which TSTS-M⁺⁺ ensures. On the other hand, TSTS-M⁺⁺ does not impose a monotone Cauchy shear stress response in simple shear which is enforced by Legendre-Hadamard ellipticity and in turn polyconvexity. Both scenarios are proven through the construction of appropriate strain-energy functions. Consequently, a combination of polyconvexity, ensuring Legendre-Hadamard ellipticity, and TSTS-M⁺⁺ seems to be a viable solution to Truesdell’s Hauptproblem. However, so far no isotropic strain-energy function has been identified that satisfies both constraints globally at the same time. Although we are unable to deliver a valid solution here, we provide several results that could prove helpful in the construction of such an exceptional strain-energy function. In memory of Miroslav Šilhavý (1949–2025)

应变-能量函数的多凸性现在越来越多地被认为是理想弹性响应的最终材料稳定性条件。虽然多凸性的数学优点已被清楚地理解，但它的力学后果却很少受到关注。在这篇贡献中，我们将多凸性与最近重新发现的真应力-真应变单调性（tsts - m++）条件进行了比较。通过明确的例子，我们表明，这两个条件本身都不足以保证理想各向同性弹性的物理合理行为。特别是，多凸性并不意味着柯西应力在无约束单轴拉伸中的单调轨迹，而tsts - m++保证了这一点。另一方面，tsts - m++在简单剪切中不施加单调的柯西剪应力响应，而单调的柯西剪应力响应是由legende - hadamard椭圆性和多凸性所施加的。通过构造适当的应变-能函数来证明这两种情况。因此，确保legende - hadamard椭圆性的多凸性与tsts - m++的组合似乎是解决Truesdell Hauptproblem的可行方案。然而，到目前为止，还没有发现同时满足这两个约束的各向同性应变能函数。虽然我们无法在这里提供一个有效的解决方案，但我们提供了几个结果，可以证明有助于构建这样一个特殊的应变-能量函数。纪念米罗斯拉夫Šilhavý （1949-2025）

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引用次数: 0

Homogenization framework for rigid and non-rigid foldable origami metamaterials 刚性和非刚性可折叠折纸超材料的均匀化框架

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-03-01 Epub Date: 2026-01-16 DOI: 10.1016/j.jmps.2026.106519

Xuwen Li, Amin Jamalimehr, Mathias Legrand, Damiano Pasini

Origami metamaterials typically consist of folded sheets with periodic patterns, conferring them with remarkable mechanical properties. In the context of Continuum Mechanics, the majority of existing predictive methods are mechanism analogs which favor rigid folding and panel bending. While effective in predicting primary deformation modes, existing methods fall short in capturing the full spectrum of deformation of non-rigid foldable origami, such as the emergence of curvature along straight creases, local strain at vertices and warpage in panels. To fully capture the entire deformation spectrum and enhance the accuracy of existing methods, this paper introduces a homogenization framework for origami metamaterials where the faces are modeled as plate elements. Both asymptotic and energy-based homogenization methods are formulated and implemented. As a representative crease pattern, we examine the Miura origami sheet homogenized as an equivalent Kirchhoff-Love plate. The results reveal that certain effective elastic properties are nonlinearly related to both the initial fold angle and the crease stiffness. When benchmarked with results from fully resolved simulations, our framework yields errors up to 12.9%, while existing models, including the bar-and-hinge model and the rigid-panel model, show up to 161% error. The differences in errors are associated with the complex modes of crease and panel deformation in non-rigid origami, unexplored by the existing models. This work demonstrates a precise and efficient continuum framework for origami metamaterials as an effective strategy for predicting their elastic properties, understanding their mechanics, and designing their functionalities.

折纸超材料通常由具有周期性图案的折叠片组成，赋予它们非凡的机械性能。在连续介质力学的背景下，大多数现有的预测方法是机制类比，有利于刚性折叠和板弯曲。虽然现有的方法可以有效地预测原始变形模式，但在捕捉非刚性可折叠折纸的全变形谱方面存在不足，例如沿直折痕出现的曲率、顶点处的局部应变和面板中的翘曲。为了充分捕获整个变形谱，提高现有方法的精度，本文引入了一种折纸超材料的均匀化框架，其中面建模为板单元。提出并实现了渐近均匀化方法和基于能量的均匀化方法。作为一个代表性的折痕图案，我们研究了三浦折纸片均质为等效的基希霍夫-洛夫板。结果表明，某些有效弹性性能与初始折叠角和折痕刚度均呈非线性关系。当与完全解析的模拟结果进行基准测试时，我们的框架产生的误差高达12.9%，而现有模型，包括杆铰模型和刚性面板模型，显示的误差高达161%。误差的差异与非刚性折纸中折痕和面板变形的复杂模式有关，这是现有模型未探索的。这项工作为折纸超材料提供了一个精确而高效的连续体框架，作为预测其弹性特性、理解其力学和设计其功能的有效策略。

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引用次数: 0

The effect of fiber plasticity on domain formation in soft biological composites—Part I: A bifurcation analysis 纤维塑性对软生物复合材料结构域形成的影响——第一部分：分岔分析

IF 6 2区工程技术 Q2 MATERIALS SCIENCE, MULTIDISCIPLINARY

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-03-01 Epub Date: 2025-12-25 DOI: 10.1016/j.jmps.2025.106482

Michalis Agoras , Fernanda F. Fontenele , Nikolaos Bouklas

The main objective of this work is to shed light on the effect of fiber plasticity on the macroscopic response and domain formation in soft biological composites. This goal is pursued by analyzing the plane-strain response of two-phase laminates. In the context of this problem, the effect of fiber plasticity is accounted for by allowing the elastically stiffer layers (“fiber” phase) to also yield plastically and by taking the soft layers (“matrix” phase) to be purely elastic solids. The analysis is carried out at finite elastic and plastic strains, but it is restricted to unidirectional, non-monotonic loading paths, applied by initially increasing the macroscopic stretch along the direction of the layers up to a prescribed maximum value and then decreasing the same stretch down to a minimum value. A simple expression is derived for the critical conditions at which the homogenized behavior of the laminate loses strong ellipticity for the first time along the loading path. The relevance of this result stems from the fact that the loss of macroscopic ellipticity of these composites is known to coincide with the onset of bifurcations of the long-wavelength type. It follows from this result that, just like hyperelastic laminates, elastoplastic laminates may lose macroscopic ellipticity whenever their incremental strength in shear perpendicular to the layers vanishes for the first time. It is shown by means of specific numerical calculations that fiber plasticity has a softening effect on the critical shear strength of the laminate under monotonically increasing loading and a hardening effect under monotonically decreasing loading, whereas local elasticity has the opposite effects. Thus, the effects of local elasticity and fiber plasticity compete with each other at every stage of the deformation where both mechanisms are active and whether or not a specific laminate will lose its macroscopic ellipticity along a given loading path depends crucially on the relative strengths of these effects. In this regard, the influence of the relevant loading and material parameters is investigated in detail. For situations in which loss of macroscopic ellipticity does take place, a corresponding post-bifurcation solution for the homogenized behavior of the laminate is computed. The deformed state of the material described by this solution is characterized by twin lamellar domains that are formed at a length scale much larger than the width of the original, microscopic layers, but still much smaller than the overall dimensions of the macroscopic specimen under consideration. The macroscopic response of these composites is found to be much softer along the bifurcated equilibrium path than along the corresponding principal path. Nevertheless, no macroscopic unloading has been observed in the post-bifurcation regime, indicating accordingly that the macroscopic, post-bifurcation behavior of these materials is stable.

本研究的主要目的是揭示纤维塑性对软质生物复合材料宏观响应和结构域形成的影响。通过分析两相层合板的平面应变响应来实现这一目标。在这个问题的背景下，纤维塑性的影响是通过允许弹性较硬的层（“纤维”相）也具有塑性屈服，并通过将软层（“基体”相）作为纯弹性固体来解释的。该分析是在有限的弹塑性应变下进行的，但它仅限于单向、非单调的加载路径，通过首先沿层向增加宏观拉伸到规定的最大值，然后减少相同的拉伸到最小值来施加。导出了层合板沿加载路径均匀性首次失去强椭圆性临界条件的简单表达式。这一结果的相关性源于这样一个事实，即已知这些复合材料的宏观椭圆性的损失与长波长型分岔的开始相吻合。由此可知，弹塑性层合板与超弹性层合板一样，在垂直于层合板的剪切强度增量首次消失时，也会失去宏观椭圆性。通过具体的数值计算表明，在单调递增加载条件下，纤维塑性对层合板的临界抗剪强度有软化作用，在单调递减加载条件下，纤维塑性对层合板的临界抗剪强度有硬化作用，而局部弹性则相反。因此，局部弹性和纤维塑性的影响在变形的每个阶段都是相互竞争的，在这两个机制都是活跃的，一个特定的层合板是否会沿着给定的加载路径失去宏观椭圆性，关键取决于这些影响的相对强度。为此，详细研究了相关载荷和材料参数的影响。对于确实发生宏观椭圆度损失的情况，计算了相应的层合板均匀化行为的分岔后解。该溶液描述的材料变形状态的特征是双片层畴，其形成的长度尺度远大于原始微观层的宽度，但仍远小于所考虑的宏观试样的总体尺寸。这些复合材料的宏观响应沿分岔平衡路径比沿相应的主路径要软得多。然而，在分岔后没有观察到宏观卸载，这表明这些材料的宏观分岔后行为是稳定的。

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