Journal of The Mechanics and Physics of Solids最新文献_第10页

Material Fingerprinting for rapid discovery of hyperelastic models: First experimental validation 快速发现超弹性模型的材料指纹：首次实验验证

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-12-05 DOI: 10.1016/j.jmps.2025.106463

Denisa Martonová , Ellen Kuhl , Moritz Flaschel

Material Fingerprinting is an emerging approach for the rapid discovery of mechanical material models directly from experimental data. By interpreting a material’s response in standardized experiments as its fingerprint, Material Fingerprinting employs pattern recognition to match experimental data against a precomputed database, enabling real-time model discovery. This strategy is both fast and robust, as it avoids solving potentially non-convex optimization problems. Unlike traditional calibration methods, Material Fingerprinting simultaneously selects the most suitable material model and identifies its parameters. Since the fingerprint database is fully controllable, the method guarantees interpretable and physically meaningful models. In previous work, we showed the feasibility of this concept for experiments with homogeneous or heterogeneous deformation fields using synthetically generated data. Here we present the first experimental validation of Material Fingerprinting. We carefully design a fingerprint database for uniaxial tension/compression, equibiaxial tension as well as pure and simple shear experiments. Once computed in an offline phase, this database can be reused for rapid model discovery across diverse experimental datasets. We demonstrate that this single database enables the robust and efficient discovery of hyperelastic strain energy functions to accurately characterize the isotropic mechanical responses of rubber, hydrogel, and brain tissue in less than one second on a standard personal computer. To make this approach openly accessible for rapid material model discovery across laboratories, we release the database and the implementation of Material Fingerprinting as a pip-installable Python package alongside this publication.

材料指纹是一种新兴的方法，可以直接从实验数据中快速发现机械材料模型。通过将材料在标准化实验中的反应解释为其指纹，材料指纹技术采用模式识别技术将实验数据与预先计算的数据库进行匹配，从而实现实时模型发现。这种策略既快速又健壮，因为它避免了解决潜在的非凸优化问题。与传统的校准方法不同，材料指纹识别同时选择最合适的材料模型并识别其参数。由于指纹数据库是完全可控的，该方法保证了模型的可解释性和物理意义。在之前的工作中，我们使用合成生成的数据证明了该概念在均匀或非均匀变形场实验中的可行性。在这里，我们提出了材料指纹识别的第一个实验验证。我们精心设计了单轴拉伸/压缩、等双轴拉伸以及纯剪切和简单剪切实验的指纹数据库。一旦在离线阶段计算，该数据库可以被重用，用于跨不同实验数据集的快速模型发现。我们证明，这个单一的数据库能够在不到一秒的时间内，在标准的个人计算机上准确地描述橡胶、水凝胶和脑组织的各向同性力学响应，从而强大而有效地发现超弹性应变能函数。为了使这种方法能够在实验室中快速发现材料模型，我们将数据库和材料指纹的实现作为可安装的Python包与本出版物一起发布。

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引用次数: 0

A neural-network-enhanced micromechanical framework with evolving reference medium for nonlinear heterogeneous materials 具有演化参考介质的非线性非均质材料神经网络增强微力学框架

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-11-15 DOI: 10.1016/j.jmps.2025.106426

Ce Chen , Liujun Wu , Chenyang Xin , Wenbin Liu , Xin Yi , Huiling Duan

The mechanical response of nonlinear heterogeneous materials is strongly influenced by the deformation-dependent spatial variation of properties in the matrix and inclusions. Conventional micromechanical approaches, typically based on linearization techniques and uniform moduli within each material phase, often fail to capture the effective response of such nonlinear systems, where the local tangent modulus acts as a deformation-dependent measure of stiffness rather than an intrinsic material property. Here, we present a neural-network-enhanced micromechanical framework built upon an evolving nonlinear reference medium with spatially non-uniform tangent moduli, for composites comprising an isotropic matrix and isotropic spherical inclusions with nonlinear interfacial effects. Building on a single-inclusion configuration, where an inclusion is embedded in a reference medium, we introduce two physics-guided neural networks that capture the spatial variation with local deformation states. One network models the inclusions with prescribed properties, while the other represents the reference medium, whose material properties evolve with macroscopic deformations. By enforcing the interfacial displacement–traction condition, we identify the varying properties of the reference medium and determine the effective tangent modulus of the composite. Applied to nonlinear particle-reinforced elastomers at high volume fractions, the framework significantly outperforms classical micromechanical approaches. Moreover, the trained model demonstrates remarkable generalization across diverse nonlinear behaviors of inclusions and matrix, interfacial conditions, loading modes, and volume fractions—without retraining. The framework also extends naturally to plasticity problems, yielding accurate predictions for porous plastic solids. This work establishes a new pathway for integrating neural networks into the derivation of micromechanical relations for complex nonlinear composites.

非线性非均质材料的力学响应受基体和夹杂物中变形相关的空间变化的强烈影响。传统的微力学方法，通常基于线性化技术和每个材料阶段的均匀模量，往往无法捕捉到这种非线性系统的有效响应，其中局部切线模量作为变形相关的刚度度量，而不是固有的材料特性。在这里，我们提出了一个神经网络增强的微力学框架，该框架建立在一个不断发展的非线性参考介质上，该介质具有空间非均匀的切模量，用于由各向同性矩阵和各向同性球形夹杂组成的具有非线性界面效应的复合材料。在单内含物配置的基础上，其中包含物嵌入参考介质中，我们引入了两个物理引导的神经网络，以捕获局部变形状态的空间变化。一个网络模拟具有规定性质的夹杂物，而另一个网络代表参考介质，其材料性质随宏观变形而演变。通过施加界面位移-牵引条件，我们确定了参考介质的变化性质，并确定了复合材料的有效切线模量。应用于高体积分数的非线性颗粒增强弹性体，该框架明显优于经典的微力学方法。此外，训练后的模型在不需要再训练的情况下，在包含物和基体、界面条件、加载模式和体积分数的各种非线性行为中表现出显著的泛化。该框架也自然地扩展到塑性问题，对多孔塑性固体产生准确的预测。本工作为将神经网络集成到复杂非线性复合材料微力学关系的推导中建立了一条新的途径。

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引用次数: 0

Coupled time and space homogenization of viscoelastic–viscoplastic composite materials under large numbers of loading cycles 大次数加载循环下粘弹粘塑性复合材料的时空耦合均匀化

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-11-12 DOI: 10.1016/j.jmps.2025.106423

I. Doghri , M. Haddad , G. Tsilimidos , S. Haouala

A coupled time and space homogenization formulation is proposed for heterogeneous micro-structures with viscoelastic–viscoplastic (VE–VP) constituents and subjected to large numbers of cycles. A time homogenization theory is presented in a general setting, based on two time scales and asymptotic time expansion of the fields. It leads to a macro-time VE–VP problem being fed with stress fluctuations computed from a micro-time VE problem. New theoretical results are discussed. Coupling with space homogenization is detailed for the incremental-secant mean-field homogenization (MFH) formulation. The latter takes into account per phase residual strains and stresses upon virtual VE unloading and leads to an incremental stiffness operator which is naturally isotropic for an isotropic VE–VP constituent. Coupling with time homogenization brings new terms which are not present in the original MFH method. Computational algorithms are proposed based on implicit time integration schemes, and numerical simulations illustrate the remarkable performance of the proposed formulation and algorithms.

提出了具有粘弹粘塑性（VE-VP）成分的非均质微结构的时间和空间耦合均匀化公式。在一般情况下，基于两个时间尺度和场的渐近时间展开式，提出了时间均匀化理论。这将导致宏观VE - vp问题被注入由微观VE问题计算得到的应力波动。讨论了新的理论结果。详细讨论了增量-割线平均场均质化（MFH）公式与空间均质化的耦合。后者考虑了虚拟VE卸载时的每相残余应变和应力，并导致对各向同性VE - vp成分自然各向同性的增量刚度算子。与时间均匀化的耦合带来了原始MFH方法中不存在的新项。提出了基于隐式时间积分格式的计算算法，数值模拟表明了所提出的公式和算法的显著性能。

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引用次数: 0

Stress boundedness and existence of radial minimizers in constrained nonlinear elasticity 约束非线性弹性中应力有界性及径向最小值的存在性

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-11-30 DOI: 10.1016/j.jmps.2025.106449

Paolo Maria Mariano , Domenico Mucci

For simple elastic bodies in small strain regime, the convexity of the energy allows one to discuss equilibrium problems under stress constraints (the specification of an admissible convex region in the stress space) in terms of the complementary energy. In the presence of large strains, the necessary lack of energy convexity does not allow one to retrace the same path. A significant concept of complementary energy in large strain regime rests on the Legendre transform of the energy with respect to the deformation gradient, its cofactor and determinant. The related minimum problem necessarily requires that constraints be assigned to the derivatives of the energy density with respect to the variables already listed (these derivatives are required to be in a convex subset of an appropriate linear space). A problem is to characterize the related stresses in terms of a constrained energy. We tackle this problem for radially symmetric simple bodies under radial deformations and show how the resulting stress is bounded. We also prove the existence of radially symmetric minimizers for the constrained elastic energy under Dirichlet boundary conditions.

对于小应变状态下的简单弹性体，能量的凸性允许用互补能量讨论应力约束下的平衡问题（应力空间中可容许凸区域的规定）。在存在大应变的情况下，必要的能量凹凸性的缺乏不允许人们回溯相同的路径。在大应变状态下，互补能量的一个重要概念取决于能量相对于变形梯度的勒让德变换，它的协因式和行列式。相关的最小问题必然要求对已经列出的变量的能量密度导数指定约束（这些导数要求在适当线性空间的凸子集中）。一个问题是用受限能量来描述相关应力。我们解决了径向变形下径向对称简单体的这个问题，并展示了产生的应力是如何有界的。我们还证明了在Dirichlet边界条件下约束弹性能的径向对称极小值的存在性。

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引用次数: 0

Bounds on the uniaxial effective complex permittivity tensor of two-phase composites and optimal or near optimal microstructures 两相复合材料单轴有效复介电常数张量的界与最优或接近最优微结构

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-11-20 DOI: 10.1016/j.jmps.2025.106429

Kshiteej J. Deshmukh , Graeme W. Milton

Electromagnetic metamaterials with a uniaxial effective permittivity tensor, characterized by its transverse (

ϵ_{⊥}

) and axial (ϵ_∥) components, play a central role in the design of advanced photonic and electromagnetic materials including hyperbolic metamaterials, and biological imaging platforms. Tight bounds on the complex effective permittivity of such metamaterials are critical for predicting and optimizing their macroscopic electromagnetic response. While rigorous tight bounds exist for isotropic two-phase composites, corresponding results for uniaxial composites remain relatively unexplored. In this work, we systematically investigate the attainable range of

ϵ_{⊥}

and ϵ_∥ in the quasistatic regime for two-phase metamaterials with isotropic homogeneous phases. By analyzing known microgeometries and constructing hierarchical laminates (HLs), we demonstrate that the classical bounds on

ϵ_{⊥}

are not optimal. We conjecture improved bounds based on numerically fitted circular arcs derived from convex hulls of

ϵ_{⊥}

values obtained from HLs, and we identify optimal rank-4 HL structures that achieve all points on the conjectured bounds. Additionally, we quantify the correlation between

ϵ_{⊥}

and ϵ_∥ for fixed volume fractions, and propose a design algorithm to construct HL microstructures achieving prescribed values of

ϵ_{⊥}

. Leveraging the Cherkaev-Gibiansky transformation and the translation method, we extend recent techniques developed for isotropic composites by Kern-Miller-Milton to derive translation bounds on the uniaxial complex effective permittivity tensor. Using the trace bounds we also numerically obtain the correlated bounds on

ϵ_{⊥}

when

ϵ_{⊥}

and ϵ_∥ differ by a fixed proportionality constant. Finally, bounds on the sensitivity of the effective permittivity tensor of low-loss composites are obtained and their optimality is shown in two-dimensions. Our results advance the theoretical understanding of uniaxial metamaterials and provide practical tools for the design of tailored anisotropic metamaterials.

具有单轴有效介电常数张量的电磁超材料，其特征是其横向（⊥）和轴向（∥）分量，在设计先进的光子和电磁材料（包括双曲超材料和生物成像平台）中发挥着核心作用。这类超材料复杂有效介电常数的严格界限对于预测和优化其宏观电磁响应至关重要。虽然各向同性两相复合材料存在严格的紧密边界，但单轴复合材料的相应结果仍然相对未被探索。在这项工作中，我们系统地研究了具有各向同性均相的两相超材料在准静态状态下的⊥和∥的可达到范围。通过分析已知的微观几何和构造分层层板（HLs），我们证明了⊥上的经典界不是最优的。我们基于从HLs获得的⊥值的凸壳导出的数值拟合圆弧来推测改进的界，并且我们确定了在推测界上实现所有点的最优秩-4 HL结构。此外，我们量化了固定体积分数的⊥与λ∥之间的相关性，并提出了一种设计算法来构建实现⊥规定值的HL微结构。利用Cherkaev-Gibiansky变换和平移方法，我们扩展了Kern-Miller-Milton为各向同性复合材料开发的最新技术，以推导单轴复有效介电常数张量的平移界。使用迹界，我们也在数值上获得了当⊥和∥相差一个固定比例常数时，⊥的相关界。最后，给出了低损耗复合材料有效介电常数张量的灵敏度界，并给出了其二维最优性。我们的研究结果促进了对单轴超材料的理论认识，并为定制各向异性超材料的设计提供了实用工具。

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引用次数: 0

Reduced-order representations of crystallographic texture for application to surrogate modelling of austenitic stainless steel 用于奥氏体不锈钢替代模型的晶体织构的降阶表示

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-11-25 DOI: 10.1016/j.jmps.2025.106444

Hugh Dorward , Mahmoud Mostafavi , David M. Knowles , Matthew J. Peel

Surrogate models are a useful tool in enabling efficient modelling and propagation of uncertainty through material process-structure-property linkages. One promising application is in the modelling the dependence of macroscopic material properties on the microstructure of polycrystalline materials. However, this requires parameterisation of complex microstructural features such as crystallographic texture.

This study compares two methods for parameterising texture for use in reduced-order models: a principal component analysis reduction of generalised spherical harmonics (GSH-PCA), and a simpler, scalar parameterisation using the Taylor factor. The effectiveness of each method is demonstrated by applying each to a Gaussian process (GP) regression surrogate of material deformation, trained on data from crystal plasticity simulation.

The GSH-PCA parameterisation reduces the number of variables required to capture texture to between 5–10 for cubic-orthorhombic symmetry and has the advantage of allowing reconstruction of the original texture from the GSH-PCA coefficients. In comparison, the Taylor factor offers a simpler surrogate model with a single input parameter, however this model has less overall predictive accuracy with more uncertainty in the input variable space. Despite this, the use of GP regression as the surrogate model with functional outputs allows the uncertainties from both texture parameterisations to be propagated through to the prediction of macroscopic mechanical behaviour.

代理模型是一种有用的工具，可以通过材料-过程-结构-属性联系实现不确定性的有效建模和传播。一个有前景的应用是在模拟宏观材料性能对多晶材料微观结构的依赖。然而，这需要参数化复杂的微观结构特征，如晶体结构。本研究比较了用于降阶模型的参数化纹理的两种方法：广义球面谐波（GSH-PCA）的主成分分析减少，以及使用泰勒因子的更简单的标量参数化。通过将每种方法应用于基于晶体塑性模拟数据训练的材料变形高斯过程（GP）回归代理，证明了每种方法的有效性。GSH-PCA参数化将捕获纹理所需的变量数量减少到5-10个立方正交对称，并且具有允许从GSH-PCA系数重建原始纹理的优点。相比之下，泰勒因子提供了一个具有单个输入参数的更简单的代理模型，但是该模型在输入变量空间中具有更大的不确定性，整体预测精度较低。尽管如此，使用GP回归作为具有功能输出的代理模型允许两个纹理参数化的不确定性传播到宏观力学行为的预测。

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引用次数: 0

The broad wrinkling landscape of hyperelastic parallelogram-shaped membranes: From wrinkle migration to restabilization and their subsequent reappearance elsewhere 超弹性平行四边形膜的广泛起皱景观：从皱纹迁移到再稳定及其随后在其他地方的再现

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-12-04 DOI: 10.1016/j.jmps.2025.106461

Mohammad Hosein Nejabatmeimandi , Francesco Dal Corso

Wrinkling is a commonly observed out-of-plane instability in membrane structures due to their extremely low bending-to-stretching stiffness ratio. It has been extensively investigated for symmetric membrane geometries and boundary conditions that induce planar non-uniform stress states by preventing the lateral contraction at the edges, and is also known to potentially display self-restabilization. This study investigates an initially flat, parallelogram-shaped hyperelastic membrane, focusing on the effect of the inclination angle that defines its deviation from rectangular geometry. It is shown that wrinkling can occur either centrally or at the two opposite obtuse-angled corners–even for small inclination angles–during stretching with unconstrained lateral contraction, a condition under which the flat configuration for the rectangular counterpart remains always stable. Three distinct evolutions of the wrinkling pattern are numerically identified, all ultimately leading to corner-localized wrinkles. This final state may arise (i) directly, without a prior bifurcation, or after the appearance of central wrinkling that either (ii) restabilizes or (iii) separates and migrates toward the corners. A closed-form expression for the critical wrinkling condition is derived by combining a perturbation approach with an energy-based method in the framework of linear elasticity. This provides an accurate estimate of the onset and pattern of central wrinkling. The present findings reveal new pathways in wrinkling pattern evolution and introduce a novel approach to unconventional boundary-value problems, with potential applications ranging from lightweight structural systems to flexible electronics.

由于薄膜结构的弯曲-拉伸刚度比极低，起皱是一种常见的面外失稳现象。人们对对称膜的几何形状和边界条件进行了广泛的研究，这些条件通过防止边缘的侧向收缩来诱导平面非均匀应力状态，并且也知道可能显示自再稳定。本研究研究了一个最初平坦的平行四边形超弹性膜，重点研究了倾角对其偏离矩形几何形状的影响。结果表明，在无约束横向收缩拉伸过程中，褶皱既可以发生在中心，也可以发生在两个相对的钝角处，即使倾角很小，在这种条件下，矩形对应的平面构型始终保持稳定。三个不同的演变的皱纹模式被数字识别，所有最终导致角落局部皱纹。这种最终状态可能出现在(i)没有事先分叉的情况下直接出现，也可能出现在（ii）重新稳定或（iii）分离并向角落迁移的中心褶皱出现之后。在线性弹性的框架下，将微扰法与能量法相结合，导出了临界起皱条件的封闭表达式。这提供了中心起皱的开始和模式的准确估计。目前的研究结果揭示了皱纹模式演变的新途径，并引入了一种解决非常规边值问题的新方法，其潜在应用范围从轻型结构系统到柔性电子产品。

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引用次数: 0

Micromechanical insights into the uniaxial stress-strain behaviour of glassy amorphous polymers through molecular dynamics simulations 通过分子动力学模拟对非晶态聚合物单轴应力-应变行为的微观力学见解

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-12-28 DOI: 10.1016/j.jmps.2025.106496

Pramod Kumar Patel, Sumit Basu

The intrinsic uniaxial stress-strain response of a glassy amorphous polymer exhibits a set of generic features that determine its toughness under monotonic or cyclic loads. Phenomenological constitutive models successfully mimic these generic features and often insightfully allude to their micromechanical origins. On the other hand, atomistic simulations, notwithstanding their well-known limitations, are also successful in capturing these features using a variety of force fields. This motivates us to delve deeper into these simulations and attempt to identify the micromechanical events that synergistically give rise to these very distinctive features. Especially, we study the roles of the evolution of the free volume and the entanglement network formed by the macromolecules. We show that the small-strain response is largely governed by how free volume proliferates in the material. At larger strains, entanglement slips and disentanglement events decide the extent of plastic strain that will accumulate and the reversibility of the material on unloading. The cohesive strength of the non-bonded interactions between monomers and the energy barrier between torsional flips are the most important underlying features of the force field that affect both evolution of free volume and behaviour of the entanglement network. By perturbing these parameters, we can, control the extent of strain softening, hardening, accumulation of plastic strains and reversibility on unloading. The parameters of the force field, which are determined by the macromolecular architecture, can be used to ‘sculpt’ a targeted stress-strain response.

非晶玻璃聚合物固有的单轴应力-应变响应表现出一组通用特征，这些特征决定了其在单调或循环载荷下的韧性。现象学本构模型成功地模仿了这些一般特征，并经常深刻地暗示了它们的微观力学起源。另一方面，原子模拟尽管有众所周知的局限性，但也成功地利用各种力场捕获了这些特征。这促使我们更深入地研究这些模拟，并试图识别协同产生这些非常独特特征的微力学事件。特别地，我们研究了自由体积的演化和大分子形成的纠缠网络的作用。我们表明，小应变响应在很大程度上取决于材料中自由体积的增殖方式。在较大应变下，缠结滑移和解缠事件决定了塑性应变的累积程度和材料卸载时的可逆性。单体间非键相互作用的内聚强度和扭转翻转之间的能量势垒是影响自由体积演化和纠缠网络行为的力场最重要的潜在特征。通过扰动这些参数，可以控制应变软化、硬化程度、塑性应变积累程度和卸荷可逆性。由大分子结构决定的力场参数可用于“雕刻”目标应力-应变响应。

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引用次数: 0

TPMS sheet structures with orthorhombic symmetry: Anisotropic elasticity and energy absorption 正交对称TPMS片材结构：各向异性弹性和能量吸收

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-12-20 DOI: 10.1016/j.jmps.2025.106489

Stephen Daynes

Triply periodic minimal surface (TPMS) architectures have gained prominence as high-performance cellular structures due to their smooth geometry, load-bearing efficiency, and suitability for additive manufacturing. While prior work has explored TPMS lattices with cubic symmetry, this is the first study to systematically evaluate orthorhombic TPMS lattices using a combined experimental, finite element analysis (FEA), and orientation tensor approach to derive predictive structure–property scaling laws. This study investigates the anisotropic elastic and energy absorption characteristics of four orthorhombic TPMS topologies (CLP, I-6, I-8, and I-9) through a combination of FEA, geometric orientation tensor analysis, and experimental compression testing. Thin-walled TPMS specimens (0.3 mm thickness) were additively manufactured and tested along three orthogonal directions. A novel, interpretable method is proposed to relate directional stiffness and energy absorption to the eigenvalues of orientation tensors derived from surface geometry. The results reveal topology-dependent scaling laws that capture the influence of anisotropy and relative density on mechanical response. Experimental and simulated outcomes show strong agreement, validating the predictive capability of the geometric scaling models. These findings provide new insights into the structure-property relationships of anisotropic shell-based cellular solids, enabling more efficient and targeted design of multifunctional architected cellular materials.

三周期最小表面（TPMS）结构由于其光滑的几何形状、承载效率和增材制造的适用性而成为高性能的细胞结构。虽然之前的工作已经探索了具有立方对称性的TPMS晶格，但这是第一次使用结合实验、有限元分析（FEA）和取向张量方法来系统地评估正交TPMS晶格，以得出预测的结构-性质标度定律。本研究通过有限元分析、几何取向张量分析和实验压缩测试相结合的方法，研究了四种正交TPMS拓扑（CLP、I-6、I-8和I-9）的各向异性弹性和能量吸收特性。制备厚度为0.3 mm的TPMS薄壁试样，沿三个正交方向进行试验。提出了一种新的、可解释的方法，将方向刚度和能量吸收与由表面几何导出的方向张量的特征值联系起来。结果揭示了拓扑相关的标度定律，该定律捕捉了各向异性和相对密度对力学响应的影响。实验结果与模拟结果吻合较好，验证了几何尺度模型的预测能力。这些发现为各向异性壳基细胞固体的结构-性能关系提供了新的见解，使多功能结构细胞材料的设计更加有效和有针对性。

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引用次数: 0

A continuum mechanics approach for the deformation of non-Euclidean origami generated by piecewise constant nematic director fields 非欧几里得折纸由分段常向列方向场产生的变形的连续介质力学方法

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

Journal of The Mechanics and Physics of Solids

Pub Date : 2026-02-01 Epub Date: 2025-12-02 DOI: 10.1016/j.jmps.2025.106460

Linjuan Wang , Fan Feng

We merge classical origami concepts with active actuation by designing origami patterns whose panels undergo prescribed metric changes. These metric changes render the system non-Euclidean, inducing non-zero Gaussian curvature at the vertices after actuation. Such patterns can be realized by programming piecewise constant director fields in liquid crystal elastomer (LCE) sheets. In this work, we address the geometric design of both compatible reference director patterns and their corresponding actuated configurations. On the reference configuration, we systematically construct director patterns that satisfy metric compatibility across interfaces. We prove the existence and uniqueness of compatible director fields at a vertex for the generic case, up to orthogonal duals. The Gaussian curvature of the actuated vertex is computed based on the compatible director fields. On the actuated configuration, we develop a continuum mechanics framework to analyze the kinematics of non-Euclidean origami. In particular, we fully characterize the deformation spaces of three-fold and four-fold vertices and establish analytical relationships between their deformations and the director patterns. Building on these kinematic insights, we propose rational designs of large director patterns: one based on a quadrilateral tiling with alternating positive and negative actuated Gaussian curvature, and the other combining three-fold and four-fold vertices governed by a folding angle theorem. Remarkably, both designs achieve compatibility in both the reference and actuated states. We also propose a design strategy for active metamaterials based on the periodic non-Euclidean origami. The active metamaterials can have two modes of motions by folding or stimulating. We anticipate that our geometric framework will facilitate the design of non-Euclidean/active origami structures and broaden their application in active metamaterials, soft actuators, and robotic systems.

我们通过设计折纸图案，其面板经过规定的度量变化，将经典折纸概念与主动驱动相结合。这些度量变化使系统非欧几里得，在驱动后在顶点处诱导非零高斯曲率。这种模式可以通过在液晶弹性体（LCE）片上分段编程来实现。在这项工作中，我们讨论了兼容的参考指示器模式及其相应的驱动配置的几何设计。在参考配置上，我们系统地构建了满足跨接口度量兼容性的指令模式。我们证明了在一般情况下，直至正交对偶，在一个顶点处相容方向域的存在唯一性。基于兼容的方向域计算被驱动顶点的高斯曲率。在驱动构型上，我们建立了一个连续力学框架来分析非欧几里得折纸的运动学。特别是，我们充分表征了三重和四重顶点的变形空间，并建立了它们的变形与指向图案之间的解析关系。在这些运动学见解的基础上，我们提出了大型定向模式的合理设计：一个基于四边形平铺，具有交替的正负驱动高斯曲率，另一个结合由折叠角定理控制的三重和四重顶点。值得注意的是，两种设计在参考和驱动状态下都实现了兼容性。我们还提出了一种基于周期性非欧几里得折纸的活性超材料设计策略。活性超材料有两种运动模式：折叠运动模式和刺激运动模式。我们预计我们的几何框架将促进非欧几里得/活性折纸结构的设计，并扩大其在活性超材料，软致动器和机器人系统中的应用。

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