International Journal of Solids and Structures最新文献

Multiscale modeling and analysis of coupled thermo-electro-structural behavior in heterogeneous materials and structures with direct FE2 method 非均质材料和结构中热-电-结构耦合行为的多尺度建模与直接FE2分析

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-02-10 DOI: 10.1016/j.ijsolstr.2026.113895

Lu Meng , Ji Qiu , Pei Li , Heng Zhang , Zhe Liu

The coupled thermo-electro-structural effect is a key factor affecting the performance and reliability of electrical devices. As the number of coupled physical fields increases, the computational complexity grows nonlinearly, rendering existing methods inadequate for achieving concurrent multiscale modeling of tri-field coupling, which severely constrains the optimal design for multiscale electrical devices under complex operating conditions. To this end, a coupled thermal-electro-structural direct finite element square (D-FE²) method is developed to perform full coupled multiphysics concurrent multiscale computation in heterogeneous materials and structures. Numerical results show that the proposed method not only accurately captures the Joule heating-induced thermal expansion phenomena in three-dimensional heterogeneous materials and structures under various temperature fields (i.e., steady-state and transient) and electrical excitations (i.e., direct current and alternating current), but also achieves over 91% reduction in intrinsic computational workload and above 95% savings in practical resource consumption compared to conventional direct numerical simulation (DNS) methods. This study provides a breakthrough solution for concurrent multiscale modeling and optimization of complex coupled multiphysics systems in large-scale electrical devices.

热-电-结构耦合效应是影响电气器件性能和可靠性的关键因素。随着耦合物理场数量的增加，计算复杂度呈非线性增长，现有方法无法实现三场耦合的多尺度并行建模，严重制约了复杂工况下多尺度电气器件的优化设计。为此，开发了一种热-电-结构耦合直接有限元平方法（D-FE2），用于非均质材料和结构的全耦合多物理场并行多尺度计算。数值结果表明，该方法不仅能准确捕捉三维非均质材料和结构在不同温度场（即稳态和瞬态）和电激励（即直流和交流）下的焦耳热致热膨胀现象，与传统的直接数值模拟（DNS）方法相比，还可以减少91%以上的内在计算工作量，节省95%以上的实际资源消耗。该研究为大型电气设备中复杂耦合多物理场系统的并行多尺度建模和优化提供了突破性的解决方案。

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引用次数: 0

Theoretical modeling of out-of-plane crashworthiness of a wavy tri-chiral honeycomb 波浪状三手性蜂窝的面外耐撞性理论建模

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-25 DOI: 10.1016/j.ijsolstr.2026.113873

Yilin Zhu , Miao Zhou , Xue Rui , Chao Yu , Yifeng Zhong , Chuanzeng Zhang

Chiral honeycombs are demonstrated to exhibit exceptional out–of–plane mechanical properties owing to their distinctive chirality. However, systematic investigations, particularly theoretical studies, remain limited. In this work, a comprehensive study is conducted on the out‑of‑plane crashworthiness of a prototypical chiral topology, namely the wavy tri‑chiral honeycomb (WTCH). The configuration of the WTCH can be interpreted as a transformation of the conventional hexagonal honeycomb (CHH), achieved by substituting its straight cell walls with curved segments. Finite element (FE) simulations are first performed to elucidate the out-of-plane crashworthiness and underlying deformation mechanism of the WTCH. Under quasi-static loading condition, three distinct collapse modes, i.e., progressive folding, concertina-like buckling, and global bending, are identified, governed by a trade-off between wave slope and cell wall slenderness ratio. The latter two modes are characterized by significantly elevated peak stresses, rendering them unfavorable for energy-absorbing applications. In contrast, under dynamic loading conditions, all WTCH configurations exhibit a progressive folding collapse mode. Based on the identified deformation mechanism, theoretical models for predicting the plateau stresses of the WTCH undergoing progressive folding collapse are developed using the Simplified Super Folding Element (SSFE) theory and validated against numerical simulations, showing strong agreement. Finally, a quantitative comparison with the CHH demonstrates that the WTCH achieves at least a 47 % improvement in specific energy absorption under identical cell size and relative density, along with consistently higher crush force efficiency. These findings provide valuable insights for the structural optimization and engineering applications of wavy chiral honeycombs in crash protection and safety contexts.

手性蜂窝由于其独特的手性而表现出特殊的面外机械性能。然而，系统的研究，特别是理论研究仍然有限。在这项工作中，对一种典型的手性拓扑结构，即波浪状三手性蜂窝（WTCH）的面外耐撞性进行了全面的研究。WTCH的结构可以解释为传统六角形蜂窝（CHH）的转变，通过用弯曲的部分代替其直细胞壁来实现。首先进行了有限元模拟，阐明了WTCH的面外耐撞性和潜在的变形机理。在准静态加载条件下，在波浪斜率和胞壁长细比的权衡作用下，确定了三种不同的坍塌模式，即渐进式折叠、锥形屈曲和整体弯曲。后两种模式的特点是峰值应力显著升高，使得它们不利于吸能应用。而在动态加载条件下，所有WTCH结构均表现为渐进式折叠坍缩模式。在确定变形机制的基础上，利用简化超级折叠单元（SSFE）理论建立了预测WTCH渐进式折叠崩塌过程中高原应力的理论模型，并通过数值模拟进行了验证，结果吻合较好。最后，与CHH的定量比较表明，在相同的电池尺寸和相对密度下，WTCH在比能吸收方面至少提高了47%，同时具有更高的压碎力效率。这些发现为波浪状手性蜂窝在碰撞保护和安全方面的结构优化和工程应用提供了有价值的见解。

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引用次数: 0

Boundary element method for normal contacts of poroelastic layers 孔弹性层法向接触的边界元法

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-23 DOI: 10.1016/j.ijsolstr.2026.113866

Jean-Emmanuel Leroy, Valentin L. Popov

The paper builds upon a method previously developed and introduced by the authors for the normal contact of a rigid smooth indenter with a poroelastic half-space extending it to a single layer. Fundamental solutions in the Fourier and Laplace space for two types of the layer support, bonded and unbonded, are presented. It is shown how using these solutions discrete kernels can be constructed, enabling FFT-accelerated computation of the layer response to applied pressure distributions in both space and time, and therefore efficient solution of contact problems with indenters of arbitrary shape.

本文建立在一种方法以前开发和介绍的作者为刚性光滑压头的法向接触与孔弹性半空间延伸到一个单层。给出了有键和无键两种类型的层支撑的傅里叶和拉普拉斯空间的基本解。它显示了如何使用这些解决方案离散核可以构造，使fft加速层响应的计算施加压力分布在空间和时间，从而有效地解决与任意形状的压头接触问题。

引用次数: 0

Design, fabrication, and characterization of solid–liquid dual-state mechanical metamaterials 固液双态机械超材料的设计、制造与表征

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-23 DOI: 10.1016/j.ijsolstr.2026.113865

Xiaojun Tan , Jian Ma , Shaohua Liu , Bo Cao , Xueyan Chen , Bing Wang , Muamer Kadic

High-performance and reusable energy-absorbing materials have tremendous potential in industrial applications. Achieving both high performance and reusability has long been a challenge due to their apparent incompatibility. To address this, we proposed a solid–liquid dual-state mechanical metamaterial. This metamaterial exhibits robust mechanical properties when the liquid metal is solid and achieves high energy absorption through its plastic deformation. Upon heating-induced solid–liquid state transition, its deformed state fully recovers its initial state, ensuring reusability. The metamaterials can be fabricated by injecting liquid metal into an hollow elastic lattice structure manufactured through additive manufacturing processes. The mechanical properties of solid–liquid dual-state mechanical metamaterials prepared from different liquid metal, such as gallium, Field’s metal, and Wood’s metal, are analyzed in this paper through a combined approach of experiments, theoretical analysis, and numerical simulations. The results reveal that the proposed metamaterial significantly outperforms all previously reported reusable energy-absorbing materials in specific energy absorption (SEA). This breakthrough driven by the solid–liquid state transition redefines the limits of reusable energy absorption and opens the path to develop a complete family of robust, reusable materials.

高性能、可重复使用的吸能材料具有巨大的工业应用潜力。由于它们明显的不兼容性，实现高性能和可重用性长期以来一直是一个挑战。为了解决这个问题，我们提出了一种固液双态机械超材料。当液态金属为固体时，该材料表现出坚固的力学性能，并通过塑性变形实现高能量吸收。加热诱导固液态转变后，其变形状态完全恢复到初始状态，保证了可重复使用。超材料可以通过将液态金属注入通过增材制造工艺制造的空心弹性晶格结构中来制造。本文采用实验、理论分析和数值模拟相结合的方法，对不同液态金属镓、Field金属和Wood金属制备的固液双态机械超材料的力学性能进行了分析。结果表明，所提出的超材料在比能吸收（SEA）方面明显优于所有先前报道的可重复使用吸能材料。这一由固液状态转变驱动的突破重新定义了可重复使用能量吸收的极限，并为开发一整套坚固耐用的可重复使用材料开辟了道路。

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引用次数: 0

Enhancing elastic energy focusing in multimode strain regions via Bayesian optimization of gradient-index phononic crystals for energy harvesting 利用梯度折射率声子晶体的贝叶斯优化增强多模应变区的弹性能量聚焦

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-22 DOI: 10.1016/j.ijsolstr.2026.113871

Wabi Demeke , Sangryun Lee , Wonju Jeon , Seunghwa Ryu

Metamaterials composed of gradient-index (GRIN) phononic crystals (PnCs), which contain unit cells whose sizes vary perpendicular to the direction of wave propagation, serve as a means of focusing elastic waves for energy harvesting. Owing to the finite wavelength of the propagating wave, GRIN PnCs localize the wave within a finite-sized region, which experiences multimodal strains instead of focusing on a single focal point with a single mode of strain. Consequently, the energy harvesting of elastic waves across a localized, finite region has recently gained research interest. This is due to the advantage of harvesting more energy through a properly designed piezoelectric energy harvester (PEH) that is larger than the wavelength of the elastic wave. However, the design of unit cells in GRIN PnC has been predominantly limited to simple shapes. This study introduces random hole shapes in GRIN PnC to enhance the intensity of elastic energy localization across targeted finite-sized region, utilizing a data-efficient surrogate model through Bayesian optimization (BO). Additionally, the developed BO method identifies a unit cell design that offers wave focusing intensity comparable to that of benchmark deep neural network (DNN)-based optimization, while requiring only 5.9% of the dataset. This advancement in wave localization significantly enhances the wave localization intensity in the target region by 36% and improves power generation by up to 1.5 times compared to GRIN PnC design with simple circular hole.

由梯度指数（GRIN）声子晶体（pnc）组成的超材料，其包含大小垂直于波传播方向变化的单元胞，可作为聚焦弹性波的能量收集手段。由于传播波的波长有限，GRIN pnc将波定位在有限尺寸的区域内，该区域经历多模态应变，而不是聚焦在单一焦点上，具有单一应变模态。因此，弹性波在局部有限区域的能量收集最近引起了人们的研究兴趣。这是由于通过适当设计的比弹性波波长更大的压电能量收集器（PEH）收集更多能量的优势。然而，GRIN PnC中单元胞的设计主要局限于简单的形状。本研究通过贝叶斯优化（BO），利用数据高效的替代模型，在GRIN PnC中引入随机空穴形状，以增强目标有限尺寸区域的弹性能量局部化强度。此外，开发的BO方法确定了一种单元格设计，提供与基准深度神经网络（DNN）优化相当的波聚焦强度，而只需要5.9%的数据集。与具有简单圆孔的GRIN PnC设计相比，这一波定位技术的进步将目标区域的波定位强度显著提高了36%，发电量提高了1.5倍。

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引用次数: 0

Research on the repeated folding mechanism of membrane antennas based on crease endurance degradation 基于折痕耐久性退化的膜天线重复折叠机理研究

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-20 DOI: 10.1016/j.ijsolstr.2026.113856

Zhiyuan Li, Yuang Zhang, Wang Zhong, Yiqun Zhang, Zihan Sun, Naigang Hu

Deployable membrane antennas are extensively utilized in space exploration due to their high packing efficiency and lightweight properties. Prior to orbital deployment, these antennas must undergo repeated ground-based deployment tests to verify their reliability and performance during deployment. However, repeated deployment aggravates damage at the membrane creases, compromising structural integrity and deployment accuracy. To address this issue, this paper establishes an endurance degradation model for membrane creases under repeated folding based on experimental data, and derives a quantitative relationship between the crease characteristic dimension (i.e., crease angle) and the number of folding cycles. A deployment analysis model for the membrane structure is then developed based on the Flasher folding method, incorporating the effects of both repeated folding and initial bending stress at the creases on deployment behavior. Through the stress-bending moment relationship, it is demonstrated that an increasing number of folding cycles leads to higher initial bending stress at the creases, resulting in a significant reduction in deployment accuracy. Concurrently, the energy required for the deployment process, i.e., the driving force, increases substantially. Finally, repeated folding-deployment experiments were conducted on a prototype planar membrane antenna. The experimental results validate the crease endurance degradation model and confirm the mechanistic influence of repetitive folding on the unfolding process.

可展开膜天线以其封装效率高、重量轻的特点在空间探索中得到了广泛的应用。在轨道部署之前，这些天线必须经过反复的地面部署测试，以验证其在部署期间的可靠性和性能。然而，重复部署会加剧膜折痕处的损坏，影响结构完整性和部署精度。针对这一问题，本文基于实验数据建立了重复折叠条件下膜折痕的耐久性退化模型，推导出折痕特征维数（即折痕角）与折叠循环次数的定量关系。基于Flasher折叠方法，建立了膜结构的展开分析模型，考虑了折痕处的重复折叠和初始弯曲应力对展开行为的影响。通过应力-弯矩关系，证明了增加折叠循环次数会导致折痕处的初始弯曲应力升高，从而导致部署精度显著降低。同时，部署过程所需的能量，即驱动力，大大增加。最后，在原型平面膜天线上进行了多次折叠展开实验。实验结果验证了折痕耐久性退化模型，证实了重复折叠对展开过程的机理影响。

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引用次数: 0

Mathematical modelling and dynamic analysis of visco-elastic woven fabric composite shafts 粘弹性机织复合材料轴的数学建模与动力学分析

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-20 DOI: 10.1016/j.ijsolstr.2026.113855

Aditya Sharma , Krishanu Ganguly , Rajan Prasad , Jayanta Kumar Dutt

The present work investigates the dynamic behaviour of viscoelastic composite shafts by developing a detailed mathematical model for woven fabric composites. Frequency-dependent properties of the epoxy resin are obtained using a Dynamic Mechanical Analyzer (DMA) and subsequently curve-fitted to derive a viscoelastic operator through a Genetic Algorithm–based optimization scheme. The key novelty of this study lies in proposing an operator-based composite modulus formulation, wherein elastic fibers are integrated into the viscoelastic matrix at the constitutive level, enabling a frequency-dependent representation of woven composites. This integration yields a theoretical operator modulus for the composite based on the rule of mixture concept that naturally introduces higher-order terms into the governing equations of motion. The proposed theoretical operator modulus is further experimentally validated by fabricating and testing a woven fabric composite in DMA. The validated model is then employed to analyze the dynamic behaviour of a viscoelastic shaft–rotor system. The influence of fiber orientation on system stability is examined, revealing a symmetric stability pattern, with minimum stability at 45° and maximum stability at 0° and 90° orientations relative to the spin axis. This behaviour is attributed to the alignment of fibers along principal stiffness directions. The findings underscore the critical importance of fiber orientation and provide a robust, experimentally supported modelling framework for designing dynamically stable composite shafts.

本文通过建立机织复合材料的详细数学模型来研究粘弹性复合材料轴的动力特性。使用动态力学分析仪（DMA）获得环氧树脂的频率相关特性，随后通过基于遗传算法的优化方案进行曲线拟合，推导粘弹性算子。这项研究的关键新颖之处在于提出了一种基于算子的复合模量公式，其中弹性纤维在本构水平上集成到粘弹性矩阵中，从而实现了编织复合材料的频率相关表示。这种整合产生了基于混合规则概念的复合材料的理论算子模量，该混合规则自然地将高阶项引入运动控制方程。通过在DMA中制造和测试机织复合材料，进一步验证了所提出的理论算子模量。然后将验证的模型应用于粘弹性轴-转子系统的动力学特性分析。研究了光纤取向对系统稳定性的影响，揭示了一个对称的稳定性模式，相对于自转轴的45°方向具有最小稳定性，0°和90°方向具有最大稳定性。这种行为是由于纤维沿主刚度方向排列。研究结果强调了纤维取向的重要性，并为设计动态稳定的复合材料轴提供了一个强大的、实验支持的建模框架。

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引用次数: 0

Computational study of nanoindentation on an elastoplastic solid with an interface parallel to the indentation direction 界面平行于压痕方向的弹塑性固体上纳米压痕的计算研究

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-20 DOI: 10.1016/j.ijsolstr.2026.113857

Takashi Akatsu , Wataru Kubota , Yutaka Shinoda , Fumihiro Wakai

Nanoindentation has been developed to map the local mechanical properties of heterogeneous solids. Although the local properties at the indentation site are required for mapping, the map resolution worsens because of the deformation of other components surrounding the indentation, such as the grains encompassing an indentation in heterogeneous polycrystals. To quantify the transitional change in a P-h curve with an increase in h, where P is the indentation load and h is the indentation penetration depth, this study proposes weight functions. These functions aim to quantify point-sharp nanoindentations on a circular column embedded in a matrix, which has an interface parallel to the indentation direction. The mechanical properties of the column can be accurately evaluated by extrapolating the weight functions to an indentation depth of zero, which improves the map resolution. When comparing the effects of the parallel and vertical interfaces, the impact of the vertical interface on the P-h curve is more significant than that of the parallel interface. This suggests that the correlation between the heterogeneity of local mechanical properties and the microstructure observed at the surface is controversial.

纳米压痕已被用于绘制非均质固体的局部力学特性。虽然在压痕位置的局部性质是测绘所必需的，但由于压痕周围的其他成分的变形，例如在非均质多晶中包围压痕的晶粒，地图分辨率会下降。为了量化P-h曲线随h增加的过渡变化，其中P为压痕载荷，h为压痕穿透深度，本研究提出了权函数。这些函数旨在量化嵌入在矩阵中的圆形柱上的尖锐纳米压痕，该矩阵具有平行于压痕方向的界面。通过将权重函数外推到压痕深度为零，可以准确地评估柱的力学性能，从而提高了地图分辨率。在比较平行界面和垂直界面的影响时，垂直界面对P-h曲线的影响比平行界面的影响更显著。这表明，局部力学性能的异质性与表面观察到的微观结构之间的关系是有争议的。

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引用次数: 0

Phase-field fracture modeling of polycrystalline quasicrystals subjected to hydrogen embrittlement 氢脆作用下多晶准晶相场断裂模拟

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-18 DOI: 10.1016/j.ijsolstr.2026.113853

Hongzhao Li , Raj Kiran , Yu Tan , Haidong Fan , Qingyuan Wang , Peidong Li

Quasicrystals (QCs) have demonstrated excellent hydrogen storage capabilities, making them promising candidates for hydrogen-related applications. However, exposure to hydrogen can significantly affect their mechanical integrity. In this study, a phase-field fracture model (PFM) is proposed to predict fracture behaviors of polycrystalline QCs in a hydrogen-containing environment. The damage-field and interface-field variables are introduced to regularize the cracks and interfaces (or grain boundaries) in QCs, respectively. An equivalent critical energy release rate is introduced to characterize the influence of the interfaces (or grain boundaries) on hydrogen-assisted crack propagation. The present model is numerically implemented in Comsol Multiphysics based on the Weak Form PDE module. Several numerical examples are conducted to validate the ability of the proposed model to predict the fracture behaviors of QCs and to analyze the influence of hydrogen concentration on the fracture mechanism of QCs. Numerical results indicate that the hydrogen concentration and interfaces (or grain boundaries) significantly influence the crack propagation paths and the peak force and failure displacement in the fracture test of QCs. The existence of hydrogen decreases the critical fracture load and promotes the crack propagation in QCs significantly. The developed phase-field framework and numerical implementation approach provide a convenient tool for predicting fracture failure and assessing the service reliability of polycrystalline QCs in complex hydrogen-containing environments.

准晶体（qc）已经证明了出色的储氢能力，使其成为氢相关应用的有希望的候选者。然而，暴露在氢气中会显著影响其机械完整性。本研究提出了一种相场断裂模型（PFM）来预测多晶qc在含氢环境中的断裂行为。引入损伤场和界面场变量分别对裂纹和界面（或晶界）进行正则化。引入等效临界能量释放率来表征界面（或晶界）对氢辅助裂纹扩展的影响。基于弱形式PDE模块，在Comsol Multiphysics中对该模型进行了数值实现。通过数值算例验证了该模型对碳纤维断裂行为的预测能力，并分析了氢浓度对碳纤维断裂机理的影响。数值结果表明，氢浓度和界面（或晶界）对裂纹扩展路径、峰值力和破坏位移有显著影响。氢的存在显著降低了临界断裂载荷，促进了裂纹扩展。所开发的相场框架和数值实现方法为复杂含氢环境下多晶qc的断裂失效预测和使用可靠性评估提供了方便的工具。

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引用次数: 0

Data-Driven-Design (D3) of multi-material systems: A novel framework and its application to viscoelastic metamaterials 多材料系统的数据驱动设计（D3）：一个新的框架及其在粘弹性超材料中的应用

IF 3.8 3区工程技术 Q1 MECHANICS

International Journal of Solids and Structures

Pub Date : 2026-01-17 DOI: 10.1016/j.ijsolstr.2026.113844

Rayehe Karimi Mahabadi, Hossein Salahshoor

While multimaterial additive manufacturing enables finely programmed heterogeneity, there remains no robust and objective-driven framework to assign materials across complex architectures under practical constraints. We introduce Data-Driven-Design (

D^{3}

) as a robust computational framework for multi-material lattice design, optimized with respect to a prescribed performance objective. The framework relies on representing physical constraints, material data, and design objectives as sets in a phase space and formulating the material selection problem as a distance minimization problem among the encoded sets. We showcase the approach in multi-material design of viscoelastic lattices provided with measurements of complex moduli as a function of frequency with the design objective of maximizing dissipation. For our numerical experiments, we import dynamic viscoelasticity measurement for twenty five different materials from literature, and show that multi-material designs can match or outperform the dissipation obtained from homogeneous designs made of the most dissipative material among the data registry. In a finite lattice example, we show that

D^{3}

design yields a mechanical dissipation with 300% increase compared to best homogeneous design from a limited collection of materials. Beyond viscoelastic lattices, the

D^{3}

framework generalizes naturally to multi-physics and multi-objective metastructure design, offering a unified, data-driven approach to optimal material selection under complex constraints.

虽然多材料增材制造能够实现精细编程的异质性，但在实际限制下，仍然没有强大的、客观驱动的框架来跨复杂架构分配材料。我们介绍了数据驱动设计（D3）作为多材料晶格设计的鲁棒计算框架，针对规定的性能目标进行了优化。该框架依赖于将物理约束、材料数据和设计目标表示为相空间中的集合，并将材料选择问题表述为编码集合之间的距离最小化问题。我们展示了粘弹性晶格的多材料设计方法，提供了复模量作为频率函数的测量，设计目标是最大化耗散。在我们的数值实验中，我们从文献中引入了25种不同材料的动态粘弹性测量，并表明多材料设计可以匹配或优于由数据注册表中耗散最大的材料制成的均匀设计所获得的耗散。在一个有限晶格的例子中，我们表明D3设计产生的机械耗散与有限材料的最佳均匀设计相比增加了300%。除了粘弹性网格之外，D3框架还可以自然地推广到多物理场和多目标元结构设计，为复杂约束下的最佳材料选择提供统一的数据驱动方法。

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引用次数: 0