{"title":"Twist deformation of physical trefoil knots","authors":"Taiki Goto , Shunsuke Nomura , Tomohiko G. Sano","doi":"10.1016/j.eml.2025.102369","DOIUrl":"10.1016/j.eml.2025.102369","url":null,"abstract":"<div><div>Knots across various length scales, from micro to macro-scales, such as polymers, DNA, shoelaces, and surgery, serving their unique mechanical properties. The shapes of ideal knots have been extensively studied in the context of knot theory, while those of physical knots have only been recently discussed in the literature. The complex interplay of elasticity and geometry, such as bending, twisting, and contact, needs to be disentangled to predict their deformation. Still, the unified understanding of the deformation of physical knots is insufficient. Here, we focus on the trefoil knot, a closed knot with a nontrivial topology, and study the relationship between the shapes of the trefoil knot and applied physical twists, combining experiments and simulations. As we twist the elastomeric rod, the knot becomes either tightened or loosened, preserving the original three-fold symmetry, and then buckles and exhibits symmetry breaking at critical angles. The curvature profiles computed through the X-ray tomography (<span><math><mi>μ</mi></math></span>CT) analysis also exhibit similar symmetry breaking. The transition would be triggered by the mechanical instability, where the imposed twist energy is converted into the bending energy. The phase transition observed here is analogous to the classical buckling phenomena of elastic rings known as the Michell instability. We find that the twist buckling instability of the trefoil knot results from the interplay of bending, twisting, and contact properties of the rod. In other words, the buckling of the knot is predictable based on the elasticity and geometry of rods, which would be useful in avoiding or even utilizing their buckling in practical engineering applications such as surgery and the shipping industry.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102369"},"PeriodicalIF":4.3,"publicationDate":"2025-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144489504","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}
{"title":"Soft stretchable topological adhesion of hydrogels","authors":"Daochen Yin, Jie Ma, Zihang Shen, Zhi Sheng, Yuren Yin, Zheng Jia","doi":"10.1016/j.eml.2025.102373","DOIUrl":"10.1016/j.eml.2025.102373","url":null,"abstract":"<div><div>Hydrogels are often stretchable and soft. Therefore, when two hydrogels are bonded by an adhesive, the adhesive layer should be stretchable so as not to degrade adhesion during stretching, and should also be soft so as not to affect the mechanical properties (e.g., stress-stretch relationship, modulus, and stretch at rupture) of the hydrogel adherends. Topological adhesion has been one of the state-of-the-art adhesion methods for bonding hydrogels, and stretchable topological adhesion (STA) has been well documented in the literature. However, topological hydrogel adhesion that is both stretchable and soft has not been achieved yet. Here, we demonstrate a soft stretchable topological adhesion (SSTA) strategy using long and flexible stitching polymers that can form topological entanglements with the adherend network as the adhesive. Experimental results indicate that the topological adhesion produced by the SSTA strategy is stretchable, i.e., the adhesion energy is insensitive to applied stretches, and soft, i.e., the application of the adhesive does not alter the stress-stretch relationship, modulus, and stretch at rupture of the hydrogel adherends, which is not possible with existing STA methods for hydrogels. A resistive strain sensor and a soft gripper integrated by the SSTA method are demonstrated.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102373"},"PeriodicalIF":4.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366173","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}
{"title":"Designing hyperelastic and adhesive heterogeneous polymer networks under shear conditions","authors":"Haowei Ruan , Ping Zhang , Canhui Yang","doi":"10.1016/j.eml.2025.102374","DOIUrl":"10.1016/j.eml.2025.102374","url":null,"abstract":"<div><div>Strong adhesion and low hysteresis are essential for the applications of soft polymeric adhesives, but unifying them is challenging due to their contradictory relations with network structures. In this study, we investigate the design principles of hyperelastic and adhesive heterogeneous polymer networks under shear conditions. The heterogeneous polymer networks, composed of two adhesive layers sandwiching a hyperelastic bulk, which are in series upon shear, are generally adhesive but hysteretic. Our theoretical analysis shows that a large thickness ratio and a small shear modulus ratio between the hyperelastic bulk and the adhesive surface are crucial for minimizing hysteresis. We verify the principles by synthesizing heterogeneous polymer networks consisting of a layer of PBA sandwiched between two layers of P(BA-<em>co</em>-IBA-<em>co</em>-AA) and examining their hysteresis via cyclic shear tests. The theoretical predictions agree well with experimental results. We further show that the design criteria for low hysteresis also apply to achieving high creep recovery. This work provides mechanistic insights into the rational design and synthesis of soft polymeric adhesives for applications in flexible electronics, soft robotics, and beyond, where shear loads prevail, and strong adhesion and low hysteresis are mission-critical.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102374"},"PeriodicalIF":4.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144366174","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}
{"title":"Stable self-rotation of liquid crystal elastomer radiating spokes under constant illumination","authors":"Huili Dong , Pengsen Xu , Ming Wang","doi":"10.1016/j.eml.2025.102375","DOIUrl":"10.1016/j.eml.2025.102375","url":null,"abstract":"<div><div>A self-excited system obtains energy from a stable external stimulus and generates and sustains oscillations through its internal mechanisms. However, these oscillations may be detrimental to the stable operation of the structure and can result in fluctuating friction. For enhancing system stability and reducing friction fluctuations, we constructed a stable self-rotation system with liquid crystal elastomer (LCE) radiating spokes under constant illumination. In this paper, we achieve continuous modeling of the illumination distribution by introducing an activation function. Based on the LCE photothermally-responsive model, the temperature field in the LCE rods was analyzed. The actuating rotating moment for the self-rotation of the radiating spokes is generated by the shift in the center of mass due to the photothermally-responsive contraction of the LCE. Subsequently, we provided the equilibrium equation and critical condition for stable self-rotation. Under the mutual influence of the temperature field and the actuating rotating moment, the system eventually achieves stable self-rotation. The system absorbs heat to offset damping dissipation, maintaining continuous self-rotation. Numerical simulations indicate that the stable angular velocity is influenced by parameters including heat flux, contraction coefficient, damping rotating moment, illumination zone, and gravitational acceleration. This stable self-rotation system with LCE radiating spokes shows great promise in soft robotics and energy harvesting due to its low friction fluctuations and high stability.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102375"},"PeriodicalIF":4.3,"publicationDate":"2025-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144501835","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}
{"title":"Exploring the mechanical properties of aperiodic monotile composite family through Gaussian process regression","authors":"Jiyoung Jung, Kundo Park, Grace X. Gu","doi":"10.1016/j.eml.2025.102370","DOIUrl":"10.1016/j.eml.2025.102370","url":null,"abstract":"<div><div>The discovery of the first aperiodic monotile has led to the identification of a family of aperiodic monotiles with varying shape parameters that adjust the length ratio between edges. This finding has inspired the development of novel materials utilizing the structure, with significant interest in its distinctive characteristics. However, while previous studies have primarily focused on the unique features of the aperiodic monotile structures, no systematic studies have been conducted to address the statistical aspects induced by their aperiodic nature, such as the variation in mechanical properties due to the translation and orientation of the pattern. In real-world applications, understanding the statistical variance in the mechanical properties of aperiodic monotiles is crucial for ensuring the reliability and robustness of engineering designs. Motivated by these gaps, we present a Gaussian process regression-based framework to predict the mechanical properties of aperiodic monotile composites for given input parameters, as well as the variance in mechanical properties with respect to different arrangements of the pattern. Validation of the model confirms its ability to successfully predict the mechanical properties and their variance. The proposed regression model is then used to explore the continuous design space of aperiodic monotile composites, revealing that patterns with a tuned shape parameter can offer superior load-bearing capabilities of reinforcements compared to other patterns with different shape parameters. This study contributes to the development of novel composite structures by incorporating both the unique design features and the statistical variation inherent in aperiodic monotile designs.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102370"},"PeriodicalIF":4.3,"publicationDate":"2025-06-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144338378","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}
Wei Zhang , Mingjian Tang , Haoxuan Mu , Xingzi Yang , Xiaowei Zeng , Rui Tuo , Wei (Wayne) Chen , Wei Gao
{"title":"Inverse design of nonlinear mechanics of bio-inspired materials through interface engineering and Bayesian optimization","authors":"Wei Zhang , Mingjian Tang , Haoxuan Mu , Xingzi Yang , Xiaowei Zeng , Rui Tuo , Wei (Wayne) Chen , Wei Gao","doi":"10.1016/j.eml.2025.102359","DOIUrl":"10.1016/j.eml.2025.102359","url":null,"abstract":"<div><div>In many biological materials such as nacre and bone, the material structure consists of hard grains and soft interfaces, with the interfaces playing a significant role in the material’s mechanical behavior. This type of structures has been utilized in the design of various bio-inspired composite materials. Such applications often require the materials to exhibit a specified nonlinear stress–strain relationship. A key challenge lies in identifying appropriate interface properties from an infinite search space to achieve a given target stress–strain curve. This study introduces a Bayesian optimization (BO) framework specifically tailored for the inverse design of interfaces in bio-inspired composites. As a notable advantage, this method is capable of expanding the design space, allowing the discovery of optimal solutions even when the target curve deviates significantly from the initial dataset. Furthermore, our results show that BO can identify distinct interface designs that produce similar target stress–strain responses, yet differ in their deformation and failure mechanisms. These findings highlight the potential of the proposed BO framework to address a wide range of inverse design challenges in nonlinear mechanics problems.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102359"},"PeriodicalIF":4.3,"publicationDate":"2025-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144272571","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}
{"title":"Developing artificial mechanics intuitions from extremely small data","authors":"Jingruo Peng, Shuze Zhu","doi":"10.1016/j.eml.2025.102371","DOIUrl":"10.1016/j.eml.2025.102371","url":null,"abstract":"<div><div>Humans can possess good mechanics intuitions by learning from a few examples, which leads to the question of how to develop artificial mechanics intuitions that can be learned from small data, as we are eagerly entering the era of artificial intelligence. We propose in this Letter the sample-switchable training method, which successfully develops highly-accurate artificial mechanics intuitions that can master brachistochrone problem, catenary problem, and large nonlinear deformation problem of elastic plate by learning from no more than three samples. The model’s intuitive prediction ability increases nonlinearly with respect to the number of training samples, suggesting that superb mechanics intuitions can be in principle achieved based on a finite number of samples, reflecting how human brains form good mechanics intuitions just by learning a few cases. Our current work presents an alternative perspective for educating artificial intelligence capable of intuitively understanding and predicting how materials deform and move, a scenario that has been frequently seen in Science-Fiction movies.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102371"},"PeriodicalIF":4.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144291289","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}
G. Ding , H.B. Zhao , X.H. Jing , X.M. Duan , S.L. Cai , H.B. Zhou , L. Yu , G.H. Duan , J. Duan , R. Li , L.H. Dai , M.Q. Jiang
{"title":"Micro-ballistic impact of a Co33Os20Ta10B37 metallic glass with ultrahigh dynamic strength","authors":"G. Ding , H.B. Zhao , X.H. Jing , X.M. Duan , S.L. Cai , H.B. Zhou , L. Yu , G.H. Duan , J. Duan , R. Li , L.H. Dai , M.Q. Jiang","doi":"10.1016/j.eml.2025.102372","DOIUrl":"10.1016/j.eml.2025.102372","url":null,"abstract":"<div><div>Metallic glasses (MGs) show significant potential for hypervelocity impact protection due to their high hardness and dynamic strength. In this study, the protective performance of a new Co<sub>33</sub>Os<sub>20</sub>Ta<sub>10</sub>B<sub>37</sub> MG was systematically evaluated. Plate impact experiments revealed an ultra-high Hugoniot elastic limit (HEL) up to 19 GPa, setting a new record for metallic materials. Using the laser-induced micro-particle impact test (LIPIT), we characterized the impact response and protective performance of Co<sub>33</sub>Os<sub>20</sub>Ta<sub>10</sub>B<sub>37</sub> subjected to SiO<sub>2</sub> micro-particle impact. The results demonstrated a high coefficient of restitution (COR) and dynamic strength for Co<sub>33</sub>Os<sub>20</sub>Ta<sub>10</sub>B<sub>37</sub>. More importantly, the low impact-mode ratio further indicates that it can efficiently withstand the high-velocity impact of micro-particles, as confirmed by the absence of craters in post-impact surface. These results emphasize the outstanding resistance of Co<sub>33</sub>Os<sub>20</sub>Ta<sub>10</sub>B<sub>37</sub> MG to hypervelocity impact, underscoring its promising potential as an advanced protective material.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102372"},"PeriodicalIF":4.3,"publicationDate":"2025-06-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144262582","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}
Xinwei Yang , Chunwang He , Jie Yang , Yikun Wu , Le Yang , Hao-Sen Chen
{"title":"Data-driven scheme for two-scale chemo-mechanical coupled problem for heterogeneous materials under transient chemical diffusion","authors":"Xinwei Yang , Chunwang He , Jie Yang , Yikun Wu , Le Yang , Hao-Sen Chen","doi":"10.1016/j.eml.2025.102363","DOIUrl":"10.1016/j.eml.2025.102363","url":null,"abstract":"<div><div>This study developed a data-driven computational scheme of multiscale multiphysics coupled problem for heterogeneous materials under transient chemical diffusion. Firstly, the data-driven scheme decouples the multiscale problem into two stages, i.e., offline generation of material constitutive behavior database by microscopic simulation, and online macroscopic boundary value problem (BVP) based on the data-driven mechanical scheme. In addition, data-driven scheme converts the multiphysics coupled constitutive relationship into the material conjugate quantities in database which avoids the poor convergence in multiscale multiphysics coupled calculation. Then, a two-scale chemo-mechanical model with a simple microstructure is validated in two cases: diffusion-induced mechanical deformation and deformation-enhanced chemical diffusion. The results show that the proposed framework can characterize the chemo-mechanical coupled behavior with good convergence and accuracy, which is more efficient than the full-scale finite element simulation. Finally, this data-driven scheme is applied to analyze the multilayer porosity structures for lithium-ion battery cathodes. The results show that cathodes with gradient porosity design can improve the utilization of active materials and enhance the effective capacity.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102363"},"PeriodicalIF":4.3,"publicationDate":"2025-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144253386","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}
Yun Shi , Jiali Cheng , Guangyuan Su , Meiying Zhao , Yongquan Liu , Bing Li
{"title":"Defected elastic metasurfaces for structured focusing with the extension of Babinet principle","authors":"Yun Shi , Jiali Cheng , Guangyuan Su , Meiying Zhao , Yongquan Liu , Bing Li","doi":"10.1016/j.eml.2025.102366","DOIUrl":"10.1016/j.eml.2025.102366","url":null,"abstract":"<div><div>Defects offer a new geometric freedom in metamaterials or phononic crystals to functionally modulate waves, but remain unexplored in a low-dimensional version of artificial structures. We here introduce the concept of a defected metasurface that enables structured focusing by breaking the traditional design notion of perfect metasurfaces for single focus. We theoretically and experimentally demonstrate that the distance between focal points is smaller than the wavelength, which is a challenging task previously. Moreover, the number and the energy distribution of foci can be tailored via integrating defects with the metasurface, which can be well described based on the Babinet principle. We further realize the Talbot effect to generate periodically focusing and digital coding. This defected prototype offers a promising strategy to shape structured elastic waves for nondestructive testing, and may be extended to other fields on the design of efficient acoustic or optical tweezer arrays.</div></div>","PeriodicalId":56247,"journal":{"name":"Extreme Mechanics Letters","volume":"78 ","pages":"Article 102366"},"PeriodicalIF":4.3,"publicationDate":"2025-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144242040","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}