International Journal of Solids and Structures最新文献

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Dynamic analysis of bi-material interfacial cracks by the high-order GFDM with an enhanced Krylov deferred correction technique
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-11 DOI: 10.1016/j.ijsolstr.2025.113451
Wenxiang Sun , Wenzhen Qu , Yan Gu , Shengdong Zhao
{"title":"Dynamic analysis of bi-material interfacial cracks by the high-order GFDM with an enhanced Krylov deferred correction technique","authors":"Wenxiang Sun ,&nbsp;Wenzhen Qu ,&nbsp;Yan Gu ,&nbsp;Shengdong Zhao","doi":"10.1016/j.ijsolstr.2025.113451","DOIUrl":"10.1016/j.ijsolstr.2025.113451","url":null,"abstract":"<div><div>This work introduces a high-order numerical methodology for simulating interfacial cracks in bi-material media under dynamic loadings. For discretizing the elastodynamic system, the proposed numerical framework utilizes an enhanced Krylov deferred correction (KDC) method for temporal discretization, integrated with the high-order generalized finite difference method (GFDM) for spatial discretization. The enhanced KDC technique incorporates a precise numerical implementation strategy to accurately match the boundary conditions. In the GFDM, the fourth-order Taylor series expansions are utilized near the crack tips, whereas second-order expansions are employed in the far-field. A node refinement technique is applied in vicinity of the crack-tips to improve the numerical accuracy. This integration of the enhanced KDC and the high-order GFDM allows for highly accurate simulations of dynamic interface cracks with large time steps. Extensive numerical experiments validate the effectiveness of this method in addressing bi-material dynamic interface crack problems under impact loadings. Furthermore, the dynamic stress intensity factors (DSIFs) generated through the proposed approach are compared with those obtained from the finite element method (FEM) or the boundary element method (BEM).</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113451"},"PeriodicalIF":3.4,"publicationDate":"2025-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Integrated design of novel composite plate-truss hybrid lattice structures for superior energy absorption
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-09 DOI: 10.1016/j.ijsolstr.2025.113447
Xun Wang , Jian Xiong
{"title":"Integrated design of novel composite plate-truss hybrid lattice structures for superior energy absorption","authors":"Xun Wang ,&nbsp;Jian Xiong","doi":"10.1016/j.ijsolstr.2025.113447","DOIUrl":"10.1016/j.ijsolstr.2025.113447","url":null,"abstract":"<div><div>Conventional truss lattice structures are prone to stress concentration and shear banding under crushing loads, while plate lattice structures suffer from limited mechanical improvement due to narrow crushing spaces and manufacturing defects. A novel composite plate-truss hybrid lattice structure inspired by deep-sea glass sponges addresses these limitations by combining the lightweight performance of truss structures with the robust mechanical properties of plate-lattice structures. It can achieve a high energy absorption capacity by adjusting its geometric parameters. The powerful 3D printing technology of Multi Jet Fusion verified the feasibility of the novel composite square plate-truss hybrid structural design. The theoretical prediction model of the mean crush force of square plate-truss hybrid structure composite was established. Quasi-static compression tests and impact tests confirmed the accuracy of finite element results, while the deformation failure modes and mechanical responses of the new structure were analyzed. Compared to typical lattice structures, the novel composite square plate-truss hybrid structure demonstrates a larger effective crushing region, more stable mechanical response, and superior energy absorption characteristics. The impact of different geometric parameters on the mechanical properties of the proposed structure is discussed through parametric analysis, highlighting the significant influence of wall thickness on bearing and energy absorption characteristics. Furthermore, medium and low-speed impact loads were studied to assess the structural deformation characteristics, mechanical properties, and energy absorption. The results prove the reliability of the design method and show the deformation and energy absorption characteristics of different hybrid structures under different impact velocities. The bionic hybrid design strategy proposed in this study provides a promising way to significantly improve the mechanical properties of lattice structures and impact protection engineering</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113447"},"PeriodicalIF":3.4,"publicationDate":"2025-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Hierarchical micromechanical modeling for CNT-coated fuzzy fiber composites accounting for viscoplasticity and interfacial damage 考虑粘塑性和界面损伤的碳纳米管涂层模糊纤维复合材料分层细观力学建模
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-08 DOI: 10.1016/j.ijsolstr.2025.113409
Ibtissam Hanoun, George Chatzigeorgiou, Fodil Meraghni
{"title":"Hierarchical micromechanical modeling for CNT-coated fuzzy fiber composites accounting for viscoplasticity and interfacial damage","authors":"Ibtissam Hanoun,&nbsp;George Chatzigeorgiou,&nbsp;Fodil Meraghni","doi":"10.1016/j.ijsolstr.2025.113409","DOIUrl":"10.1016/j.ijsolstr.2025.113409","url":null,"abstract":"<div><div>This study investigates fuzzy fiber composites, characterized by a viscoplastic matrix and fuzzy fibers, i.e. fibers coated with radially aligned carbon nanotubes (CNTs). A comprehensive micromechanical framework is developed to model and optimize these composites, with a particular emphasis on interfacial damage mechanisms introduced through microvoids growth in the region between the fuzzy fibers and the matrix. By developing an equivalent fiber model, the complexity of the multi-phase structure is effectively reduced, facilitating efficient parametric analyses. Various homogenization techniques, including Composite Cylinder Assemblage (CCA), Transformation Field Analysis (TFA), and periodic homogenization, are combined to predict the overall stress–strain responses of the equivalent fiber approach and then the full fuzzy fiber composite. The identification of the framework and model parameters enabled a parametric/sensitivity analysis to study the effect of varying key parameters, including the volume fraction. The results of this paper contribute to a deeper understanding of unidirectional fuzzy fiber composites and establish a foundation for future parametric investigations and fuzzy fiber composite applications accounting for nonlinear regimes.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113409"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936773","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Mechanical skin pain and comfort evaluation model applied to skin-integrated electronics 机械皮肤疼痛与舒适评价模型在皮肤集成电子产品中的应用
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-08 DOI: 10.1016/j.ijsolstr.2025.113424
Yunfan Zhu , Dongcan Ji , Yang Wang , Yuhang Li , Min Li , Jiayun Chen , Yinji Ma
{"title":"Mechanical skin pain and comfort evaluation model applied to skin-integrated electronics","authors":"Yunfan Zhu ,&nbsp;Dongcan Ji ,&nbsp;Yang Wang ,&nbsp;Yuhang Li ,&nbsp;Min Li ,&nbsp;Jiayun Chen ,&nbsp;Yinji Ma","doi":"10.1016/j.ijsolstr.2025.113424","DOIUrl":"10.1016/j.ijsolstr.2025.113424","url":null,"abstract":"<div><div>Skin-integrated electronics have received significant attention in medical and health monitoring. Due to improper usage or design, skin pains and discomfort tend to occur in users of skin-integrated electronics, particularly in patients with nervous system damage. This paper presented a theoretical model for evaluating the skin pain and comfort of skin-integrated electronics, based on the physiological process of human pain perception. Additionally, the impact of glial cell reduction on pain caused by damage to the nervous system was analyzed. The simulations were carried out to analyze the skin pain sensation under three different mechanical stimuli from typical skin-integrated electronics, which included: mechanics model of multilayer skin, nerve signal transduction based on Hodgkin-Huxley model, transmission and perception rooted in gate control theory. The stress distribution demonstrated by finite element analysis on the multilayer skin was produced using the viscoelasticity theory. Among three different mechanical stimuli from typical skin-integrated electronics, the numerical experiments obtained the appropriate load for rapid pain response and comfort design, respectively. Furthermore, factors influence the skin pain perception were discussed including skin thickness and number of glial cells, which could contribute to the design of skin-integrated electronics in medical applications.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113424"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Micromechanical modelling of the elastoplasticity and damage in ductile metals 塑性金属弹塑性与损伤的微观力学模拟
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-08 DOI: 10.1016/j.ijsolstr.2025.113437
Ignasi Mundó , Ferhun C. Caner , Antonio Mateo
{"title":"Micromechanical modelling of the elastoplasticity and damage in ductile metals","authors":"Ignasi Mundó ,&nbsp;Ferhun C. Caner ,&nbsp;Antonio Mateo","doi":"10.1016/j.ijsolstr.2025.113437","DOIUrl":"10.1016/j.ijsolstr.2025.113437","url":null,"abstract":"<div><div>Even though the computational constitutive modelling of the mechanical behavior of ductile metals at macroscopic scale has been studied extensively, the complexities in the mechanical behavior of ductile metals continue to challenge the existing models. Ideally the model must predict accurately the elastoplastic behavior of the material under both proportional and non-proportional loadings, its fracturing behavior under both uniaxial and multiaxial stress states as well as its behavior under cyclic loadings. Furthermore, the model must be tested against various test data obtained from specimens made of the same metal alloy. In this study, we present a constitutive model using the microplane approach in which the stress–strain relations are defined on various planes in terms of stress and strain vectors, which are independently activated depending on the strain tensor, effectively creating a multisurface plasticity model. The constitutive relations consist of two separate stress–strain boundaries applied on any given microplane: One for the shear behavior and another for the deviatoric behavior. Data fitting experience revealed that stress triaxiality must be considered only in the deviatoric boundary. Damage evolution is incorporated into both boundaries. The model is calibrated against experimental data obtained from specimens made of Aluminum alloys (6061-T6, 2024-T4 and 7075-T651) and the model predictions are compared against experimental data obtained from specimens made of the same alloy. Furthermore, the model predictions are compared to a different microplane model called the model MPJ2. In addition to test data at various stress triaxialities, test data on Vertex effect and Bauschinger effect are also taken into account.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"317 ","pages":"Article 113437"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143931390","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Reflection and transmission of elastic waves from an immersed Willis slab at oblique incidence
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-07 DOI: 10.1016/j.ijsolstr.2025.113394
Max Gattin , Nicolas Bochud , Giuseppe Rosi , Philip A. Cotterill , William J. Parnell , Salah Naili
{"title":"Reflection and transmission of elastic waves from an immersed Willis slab at oblique incidence","authors":"Max Gattin ,&nbsp;Nicolas Bochud ,&nbsp;Giuseppe Rosi ,&nbsp;Philip A. Cotterill ,&nbsp;William J. Parnell ,&nbsp;Salah Naili","doi":"10.1016/j.ijsolstr.2025.113394","DOIUrl":"10.1016/j.ijsolstr.2025.113394","url":null,"abstract":"<div><div>Elastic metamaterials allow for the control of wave propagation by exploiting local resonances in their internal structure, which leads to unconventional effective properties. However, complex phenomena like non-reciprocity and asymmetry require advanced homogenized models like the Willis model, which introduces additional coupling terms in the elastodynamics equations. The identification of the effective properties of the Willis medium has been predominantly restricted to 1D-wave propagation problems, and therefore here we extend its application to a heterogeneous, viscoelastic meta-slab under oblique wave incidence. In such a configuration, the key challenge in the parameter identification arises from the response of the medium, which is made more complex due to polarization coupling and a larger number of effective parameters. To address this, we adapt the stiffness matrix method to this configuration, enabling the analytical determination of reflection and transmission coefficients. We show how the partial inverse identification of some effective parameters can be analytically obtained by exploiting polarization decoupling at normal incidence. A numerical case study of a meta-slab with a resonant inclusion demonstrates how Willis coupling allows for the prescription of the asymmetric behavior of the meta-slab with a single set of effective parameters. Altogether, the reported methodology and results pave the way towards the complete identification of the effective properties of the Willis medium.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113394"},"PeriodicalIF":3.4,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943453","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An exact small deformation model for a curved planar beam incorporating the bending warping 考虑弯曲翘曲的平面弯曲梁的精确小变形模型
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-06 DOI: 10.1016/j.ijsolstr.2025.113430
G.H. Ma , Y.L. Pei , L.X. Li
{"title":"An exact small deformation model for a curved planar beam incorporating the bending warping","authors":"G.H. Ma ,&nbsp;Y.L. Pei ,&nbsp;L.X. Li","doi":"10.1016/j.ijsolstr.2025.113430","DOIUrl":"10.1016/j.ijsolstr.2025.113430","url":null,"abstract":"<div><div>A planar curved beam is modeled by incorporating transverse shear and bending-warping deformation within the curvilinear coordinates under small deformations. Based on the constrained planar postulate that the deformation of a beam is split into the part of center line and the other part of cross section, the kinematics is orthogonally expanded in terms of the generalized displacements for a curved beam. The resultant stresses and generalized strains are defined and the principle of virtual work is then restated. The lower-order theory is eventually proposed including the equilibrium equations and the boundary conditions. The ordinary differential equations with variable coefficients with variable coefficients are formulated. Bending examples are presented that illustrate the influence of the initial curvature on the deflection and the bending warping.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113430"},"PeriodicalIF":3.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Nonlinear static analysis of metamaterial structures based on the Kagome lattice using beam finite elements and component-wise approach 基于Kagome点阵的超材料结构非线性静力分析
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-06 DOI: 10.1016/j.ijsolstr.2025.113387
R. Augello , E. Carrera , W.Q. Chen , B. Wu , Y.Z. Wang
{"title":"Nonlinear static analysis of metamaterial structures based on the Kagome lattice using beam finite elements and component-wise approach","authors":"R. Augello ,&nbsp;E. Carrera ,&nbsp;W.Q. Chen ,&nbsp;B. Wu ,&nbsp;Y.Z. Wang","doi":"10.1016/j.ijsolstr.2025.113387","DOIUrl":"10.1016/j.ijsolstr.2025.113387","url":null,"abstract":"<div><div>This work numerically investigates the mechanical behavior of metamaterial structures inspired by the Kagome lattice mechanism using the Carrera Unified Formulation (CUF). The proposed numerical model employs enhanced one-dimensional finite elements with three-dimensional capabilities, enabling precise predictions of deformation patterns and stress–strain responses under various loading conditions. With CUF, any three-dimensional effects can be captured, allowing for the analysis of the width direction of these metamaterial structures, potentially accounting for varying geometric properties. The model’s robustness is demonstrated through its ability to capture critical phenomena such as buckling, post-buckling behavior, and rigid-body rotations of lattice triangles, which are hallmarks of the Kagome lattice’s unique mechanical properties. The introduction of stiffer hinges highlights the potential for tailoring mechanical responses to meet specific design requirements, such as enhanced load-carrying capacity and optimized energy absorption. This study demonstrates the versatility of Kagome lattice-based metamaterials and lays the groundwork for future research, including the analysis of 3D Kagome-lattice metamaterials facilitated to the proposed numerical model.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113387"},"PeriodicalIF":3.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143936774","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Predicting nanoscale stress-strain curves: A Gaussian processes within a Bayesian framework 预测纳米尺度应力-应变曲线:贝叶斯框架内的高斯过程
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-06 DOI: 10.1016/j.ijsolstr.2025.113438
Ahmad Altarabsheh , Ibrahim Altarabsheh , Xiang Chen
{"title":"Predicting nanoscale stress-strain curves: A Gaussian processes within a Bayesian framework","authors":"Ahmad Altarabsheh ,&nbsp;Ibrahim Altarabsheh ,&nbsp;Xiang Chen","doi":"10.1016/j.ijsolstr.2025.113438","DOIUrl":"10.1016/j.ijsolstr.2025.113438","url":null,"abstract":"<div><div>This study introduces an innovative method for probabilistically predicting the stress–strain curves of nanoscale materials, with a specific focus on material volume. To achieve this, molecular dynamics (MD) simulations were meticulously conducted across various material sizes to gather stress–strain data. Subsequently, a sophisticated approach was employed, integrating a Gaussian process (GP) within a Bayesian framework to comprehensively model the stress–strain behavior and forecast the complete stress–strain profiles for materials of different sizes. What sets this probabilistic machine learning algorithm apart is its capacity to not only offer precise predictions of material behavior but also to provide a detailed assessment of uncertainty. This feature ensures its effectiveness in generating accurate forecasts of stress–strain characteristics, surpassing the conventional limitations posed by material volume encountered in MD simulations. In doing so, it addresses the crucial challenge of size restrictions inherent to atomistic simulations. To rigorously validate the capabilities of this methodology, we conducted extensive testing using pure copper as our experimental material, benefitting from its comprehensive repository of stress–strain data. It is important to note that this methodology is not restricted to any specific material; instead, it serves as a robust and versatile tool for probabilistically predicting the mechanical properties of nanoscale materials. Consequently, this approach holds immense potential for diverse applications within the field of materials science and engineering, offering researchers an invaluable means to gain insights into the behavior of materials at the nanoscale.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"317 ","pages":"Article 113438"},"PeriodicalIF":3.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143924411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A nonlinear unit cell for adaptive lattice structures with shape-memory-like behaviour
IF 3.4 3区 工程技术
International Journal of Solids and Structures Pub Date : 2025-05-05 DOI: 10.1016/j.ijsolstr.2025.113411
Samuel P. Pickup , Isaac V. Chenchiah , Rainer M.J. Groh
{"title":"A nonlinear unit cell for adaptive lattice structures with shape-memory-like behaviour","authors":"Samuel P. Pickup ,&nbsp;Isaac V. Chenchiah ,&nbsp;Rainer M.J. Groh","doi":"10.1016/j.ijsolstr.2025.113411","DOIUrl":"10.1016/j.ijsolstr.2025.113411","url":null,"abstract":"<div><div>We present and classify a fundamental building block for constructing macro-scale lattice structures with shape-memory-like behaviour. Shape memory alloys (SMAs) are materials that undergo a reversible phase transition at the atomic scale from a high-symmetry crystal structure above a transition temperature to a lower-symmetry crystal structure below the transition temperature, thereby imbuing these alloys with superelastic properties and the ability to recover a previous shape when heated. We present a unit cell for creating latticed metamaterials at the macro- rather than the micro-scale that shows similar smart, adaptive behaviour in two and three spatial dimensions. Specifically, we study a square unit cell with rigid outer edges and two nonlinear springs on the diagonals that undergoes instabilities into planar, rhombic and/or non-planar, folded states. We identify two non-dimensional parameters that govern the planar multistable behaviour, and derive boundaries that split the domain into monostable (square cell), bistable (rhombic cell) and tristable (square and rhombic cells) regimes. Transitions between the square and rhombic configurations can be smooth/soft or sudden/hard. We illustrate how changes in the springs’ rest lengths and stiffness properties define the possible types of phase transitions, irrespective of the physical mechanisms (such as temperature, electromagnetic fields or swelling) driving those changes. In addition to planar multi-stability, we define the parameter regime wherein the initially planar unit cell can deform out of the plane.</div></div>","PeriodicalId":14311,"journal":{"name":"International Journal of Solids and Structures","volume":"318 ","pages":"Article 113411"},"PeriodicalIF":3.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143943450","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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