Acta Mechanica Sinica最新文献

{"title":"Toughening mechanism of crack bridging in bioinspired Bouligand structures","authors":"Yunqing Nie \u0000 (,&nbsp;),&nbsp;Dongxu Li \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25650-x","DOIUrl":"10.1007/s10409-025-25650-x","url":null,"abstract":"<div><p>The bioinspired Bouligand structure is a hierarchical and non-homogeneous architecture, which has been observed in lamellar bone and the exoskeleton of lobsters. It exhibits excellent damage-resistant performance. However, toughening mechanisms in this structure are still not clear. This paper presents a multiscale fracture model to reveal the toughening mechanisms of crack bridging. Firstly, the anisotropic property is derived based on the micro-structural parameters. Then, the crack-bridging model is established, which systematically considers the toughening effect of the in-plane normal stress and the out-of-plane shear stress in the bridging zone. Finally, the toughening mechanism is investigated. The results demonstrate that the initiation fracture toughness predominantly arises from the enhancement of the intrinsic matrix fracture toughness due to the material anisotropy and heterogeneity. The ascending crack resistance curve is principally associated with the in-plane closing normal stress within the bridging zone. The periodic micro-fluctuations observed in the crack propagation resistance curve are primarily attributed to the out-of-plane shear forces present in the bridging zone. Increasing the fiber slenderness ratio and toughening the interfacial matrix can significantly improve the toughness. These results can not only reveal the toughening mechanism of the Bouligand structure but also provide guidelines for the design of high-performance composites.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 10","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828487","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanobiological response of osteocyte PIEZO1 to induced piezoelectricity of bone matrix","authors":"Yuqing Duanwang \u0000 (,&nbsp;),&nbsp;Yanru Xue \u0000 (,&nbsp;),&nbsp;Zhengbiao Yang \u0000 (,&nbsp;),&nbsp;Shibo Gu \u0000 (,&nbsp;),&nbsp;Yinuo Zhao \u0000 (,&nbsp;),&nbsp;Shuo Gao \u0000 (,&nbsp;),&nbsp;Haochen Li \u0000 (,&nbsp;),&nbsp;Yanqin Wang \u0000 (,&nbsp;),&nbsp;Meng Zhang \u0000 (,&nbsp;),&nbsp;Xiaogang Wu \u0000 (,&nbsp;),&nbsp;Weiyi Chen \u0000 (,&nbsp;),&nbsp;Xiaochun Wei \u0000 (,&nbsp;),&nbsp;Yixian Qin \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25609-x","DOIUrl":"10.1007/s10409-025-25609-x","url":null,"abstract":"<div><p>Osteocytes are the main responders to mechanical stimuli and the primary regulators of bone metabolism and homeostasis. Piezo channels are mechanosensitive, nonselective cation channels. This study constructs an osteocyte model with a piezoelectric bone matrix, including lacuna-canalicular system and various mechanosensors, integrating the complex effects of solid field, flow field, and electric field on osteocytes. By applying triaxial dynamic displacement loads, the mechanical signals of seven mechanosensors, namely PIEZO1, integrins, primary cilia, collagen hillocks, processes, actin filaments, and microtubules, were analyzed and compared. It was shown that PIEZO1 on the cell soma underwent greater stress in areas with higher cell membrane stress or lower cytoskeleton density. Curved PIEZO1 (unactivated state) and flat PIEZO1 (activated state) exhibited distinct stress distribution patterns. Specifically, the stress in flat PIEZO1 was approximately 30% higher than that in curved PIEZO1. The blade of curved PIEZO1 experienced the greatest stress, while the ion channel of flat PIEZO1 experienced the greatest stress. The stress of primary cilia has increased by more than 40 Pa when PIEZO1 was nearby. Piezoelectricity significantly increased the fluid shear stress (FSS) and the stress of mechanosensors, and changed the trend of FSS. Notably, the collagen hillock experienced the highest FSS, and the flat PIEZO1 experienced greater FSS than the curved PIEZO1. Additionally, among the seven mechanosensors, collagen hillocks experienced the greatest stress. Furthermore, PIEZO1, primary cilia, and cytoskeletons all exhibited excellent displacement signal amplification capabilities and high sensitivity to piezoelectric signals. In conclusion, this study quantified the electromechanical signals of osteocytes in a complex microenvironment, offering insights into bone’s mechanotransduction mechanism across multiple scales.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 10","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A new level set structual topology optimization framework enhanced by nested physical informed neural network","authors":"Boxue Wang \u0000 (,&nbsp;),&nbsp;Xihua Chu \u0000 (,&nbsp;),&nbsp;Hui Liu \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25750-x","DOIUrl":"10.1007/s10409-025-25750-x","url":null,"abstract":"<div><p>The physical informed neural network (PINN) has attracted significant interest in the field of topology optimization in recent years. By incorporating physical information into the loss function, the process of the neural network’s loss decreasing is equivalent to the process of approximating the solution of the physical equation. In particular, the loss function can be combined with the objective function in topology optimization. This paper proposes a nested PINN framework based on the level set method (LSM), called LSM-PINN. The key of this framework lies in the algorithm transformation from LSM to PINN. Conventional topology optimization method is based on boundary evolution and may lead to a too scattered structure. In order to reduce this problem in PINN, some restrictions are proposed. During the optimization process, the design domain is discretized into several sample points to participate in the network training. Moreover, the feasibility and potential of the LSM-PINN framework are evaluated through some cases, highlighting the advantages and limitations of the LSM-PINN framework. The results show that the LSM-PINN framework proposed can solve two-dimensional topology optimization problems relatively stably and significantly reduce the dependence on the initial design.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829595","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Identification of rock fracture parameters under non-uniform temperature fields based on physics-informed neural networks","authors":"Yucheng Wu \u0000 (,&nbsp;),&nbsp;Wei Liu \u0000 (,&nbsp;),&nbsp;Zhiqian Zhang \u0000 (,&nbsp;),&nbsp;Bowen Liu \u0000 (,&nbsp;),&nbsp;Houlu Sun \u0000 (,&nbsp;),&nbsp;Guangjin Wang \u0000 (,&nbsp;),&nbsp;Xin Gong \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25672-x","DOIUrl":"10.1007/s10409-025-25672-x","url":null,"abstract":"<div><p>In non-uniform thermal environments, rock fracture behavior is significantly influenced by temperature gradients, localized thermal stresses, and mineral phase transitions, making accurate fracture parameter measurements challenging with conventional experimental methods. To address this, this paper proposes a multi-task (MT) learning approach based on physics-informed neural networks (PINNs), termed MT-PINN, for identifying mixed-mode stress intensity factors (SIFs) in cracked rock specimens under non-uniform temperature fields. First, a heat conduction equation accounting for heat flow disturbances and a thermomechanically coupled phase-field equation incorporating thermal expansion effects are established, which are then embedded into the loss function of a deep neural network framework, constructing the MT-PINN model to predict crack-tip fields and fracture parameters. Second, finite element simulations based on the phase-field method are performed to compute the mechanical response and damage evolution of notched semicircular bending (NSCB) rock specimens under varying non-uniform temperature fields, and the MT-PINN model is trained using datasets generated from these simulations. Finally, three-point bending tests on Fangshan granite NSCB specimens are conducted to measure crack-tip displacement fields and mixed-mode SIFs via digital image correlation, and the practical performance of the PINN model is evaluated. Experimental results are well compared with MT-PINN predictions, demonstrating the model’s effectiveness in identifying rock fracture parameters under non-uniform thermal conditions.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829600","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of strain rate and temperature on the superelastic-plastic behaviors of NiTi polycrystalline-amorphous composite structure based on molecular dynamics","authors":"Xiang Zhu \u0000 (,&nbsp;),&nbsp;Taowei Liu \u0000 (,&nbsp;),&nbsp;Liangliang Chu \u0000 (,&nbsp;),&nbsp;Yaguang Wang \u0000 (,&nbsp;),&nbsp;Guansuo Dui \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25658-x","DOIUrl":"10.1007/s10409-025-25658-x","url":null,"abstract":"<div><p>This study employs molecular dynamics simulations to construct a NiTi polycrystal-amorphous composite structure, and systematically investigates the effects of amorphous layer thickness (1–2.5 nm), strain rate (5×10⁸–2×10⁹ s⁻¹), and temperature (400–500 K) on its superelastic-plastic behaviors. The findings indicate that as the thickness of the amorphous layer thickens, there is an increase in the overall stress level, which encompasses both the critical transformation stress and the yield stress. Furthermore, the incorporation of the amorphous phase leads to an elevation in residual strain. This heightened residual strain is primarily due to the plastic deformation occurring within the amorphous phase, which concurrently obstructs the martensitic reverse transformation. As strain rate increases, the yield strength rises monotonically regardless of amorphous phase presence, while the residual deformation gradually decreases. Meanwhile, grain boundary sliding becomes less prominent at higher strain rates. On unloading to zero stress, the composite structure displays a higher concentration of residual martensite. For the NiTi polycrystalline, the rate of transformation from austenite to martensite slows down as the temperature increases. However, the composite structure with an amorphous layer exhibits minimal fluctuation in martensite transformation suppression between 400–500 K, demonstrating higher thermal stability than the polycrystalline structure. Simultaneously, as the temperature rises, the yield strength decreases while the residual deformation increases.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829337","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Crack propagation in bulk superconductors under field magnetization: a nonlocal damage-electromagnetic coupling model","authors":"Feng Xue \u0000 (,&nbsp;),&nbsp;Jingyu Wang \u0000 (,&nbsp;),&nbsp;Jianmin Long \u0000 (,&nbsp;),&nbsp;Xiaofan Gou \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25627-x","DOIUrl":"10.1007/s10409-025-25627-x","url":null,"abstract":"<div><p>The structural integrity of bulk superconductors functioning as trapped field magnets presents a critical challenge for their engineering applications, where electromagnetic stress concentrations frequently initiate microcracks that propagate into catastrophic fractures during cyclic magnetization processes. To address this failure mechanism, we develop an innovative multiphysics modeling framework combining two computational methodologies: (1) the H-formulation for accurate electromagnetic field analysis in superconducting domains; (2) a nonlocal macro-meso damage model for simulating brittle fracture evolution, which demonstrates superior computational efficiency compared to conventional phase-field models. Systematic quantification reveals the magnetic flux distributions, current density profiles, and associated stress/strain fields in superconducting samples subjected to 10–20 T magnetic loading conditions. The proposed coupled computational platform enables comprehensive visualization of multiphysics interactions, providing critical insights for optimizing the mechanical reliability of superconducting magnet systems.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829596","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Rapid prediction of curved shock flow fields based on deep neural operators","authors":"Zhentao Zhao \u0000 (,&nbsp;),&nbsp;Wei Huang \u0000 (,&nbsp;),&nbsp;Ziyuan Liu \u0000 (,&nbsp;),&nbsp;Zhiping Mao \u0000 (,&nbsp;),&nbsp;Xi He \u0000 (,&nbsp;),&nbsp;Chaoyang Liu \u0000 (,&nbsp;),&nbsp;Yaobin Niu \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25540-x","DOIUrl":"10.1007/s10409-025-25540-x","url":null,"abstract":"<div><p>Currently, utilizing deep learning techniques for flow field prediction has become an important research area. Existing deep learning-based flow field prediction models primarily focus on low-speed flow fields, while research on prediction methods for high-speed flow fields remains relatively scarce. However, predicting high-speed flow fields is crucial for the design and optimization of high-speed aircraft. Therefore, in this work, the vanilla deep operator network (DeepONet) and the Fusion DeepONet, a type of deep neural operator, are employed to predict high-speed flow fields. First, design parameters were sampled, and the open-source software OpenFOAM was used to obtain a dataset of axisymmetric curved shock wave flow fields. The selected design parameters consist of geometric parameters and flow conditions. Keeping the settings of the vanilla DeepONet and Fusion DeepONet identical, a detailed comparative analysis of the prediction accuracy of the two frameworks and their ability to capture curved shock waves was conducted. The results demonstrate that for the prediction of axisymmetric curved shock wave flow fields, the Fusion DeepONet significantly outperforms the vanilla DeepONet in both the prediction accuracy for the overall flow field and the precision of capturing curved shock waves. Additionally, in terms of the generalization (or extrapolation) capability beyond the training parameter space, the Fusion DeepONet also far surpasses the vanilla DeepONet. To gain deeper insights into the Fusion DeepONet framework, we investigated the impact of the levels of information fusion on the model performance and performed an analysis of the model using singular value decomposition. In conclusion, this study confirms the effectiveness of the Fusion DeepONet, a deep neural operator model, in predicting axisymmetric curved shock wave flow fields. It meets the requirements for the design and optimization of high-speed aircraft and holds significant engineering application value.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 10","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147828539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Constant force mechanism to design horizontal quasi-zero stiffness isolators for vibration isolation","authors":"Feng Zhao \u0000 (,&nbsp;),&nbsp;J. C. Ji \u0000 (,&nbsp;),&nbsp;Shuqian Cao \u0000 (,&nbsp;),&nbsp;Jingyang Zheng \u0000 (,&nbsp;),&nbsp;Yanhong Kang \u0000 (,&nbsp;),&nbsp;Quantian Luo \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25520-x","DOIUrl":"10.1007/s10409-025-25520-x","url":null,"abstract":"<div><p>Quasi-zero stiffness (QZS) isolators in the vertical direction have been deeply studied because their working states can be easily achieved through the gravitational force of the loaded mass. However, in the horizontal direction, there is no the constant force similar to the vertical gravitation of the loaded mass to constrain the loaded mass in the working states. Therefore, a novel horizontal isolator composed of a QZS unit and a constant force unit is proposed. The two units respectively consist of oblique bars and tension springs, which can realize the constant force, constant QZS, and nonlinear QZS. The constant force unit enforces the loaded mass in the working state to obtain QZS in the horizontal direction. The parameter conditions of QZS and constant force are derived, and the effects of parameters on QZS features are analyzed. The equation of motion by considering the constant force is solved using an increment harmonic balance method integrated with the arc-length continuation algorithm. The theoretical results show that the isolator has five solutions at one frequency due to the transmissibility bending to left and then to right under the large constant force. A prototype is fabricated and tested to verify the theoretical prediction. The experimental results show that the proposed isolator has more excellent performance with lower transmissibility and wider frequency band than the corresponding linear isolator. This study provides a feasible approach to designing the horizontal QZS isolators.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829246","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Investigating heart failure using a novel whole-heart numerical simulation","authors":"Chang Ruan \u0000 (,&nbsp;),&nbsp;Lu Chen \u0000 (,&nbsp;),&nbsp;Zhuo Zhang \u0000 (,&nbsp;),&nbsp;Xiaobao Tian \u0000 (,&nbsp;),&nbsp;Yu Chen \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25599-x","DOIUrl":"10.1007/s10409-025-25599-x","url":null,"abstract":"<div><p>Heart failure is often accompanied by myocardial dysfunction and cardiac structural remodeling. However, the lack of a comprehensive numerical framework that integrates both electrical and mechanical processes limits our understanding of how structural and material changes drive heart failure progression. Therefore, we developed and validated advanced numerical methods capable of accurately simulating the electromechanical behavior of the heart. We explored and discussed several pathophysiological models of heart failure through comprehensive whole-heart numerical simulations. A full four-chamber heart model, incorporating modified equations for electrical signal diffusion and electromechanical coupling, was employed to achieve more complete and reliable calculations of cardiac active contraction. The computational methods utilized in this study are thoroughly discussed and validated against experimental and clinical data to ensure reliability. Subsequently, different left ventricular dilation models with varying degrees of hypertrophy, along with two pathological myocardial remodeling models representing material property alterations, were developed, and their numerical results were compared and analyzed. The findings confirm that left ventricular dilation impairs diastolic function and, at the numerical level, emphasize that myocardial material properties are critical factors influencing the heart’s pumping function. Mechanically, the study elucidates how structural and material changes contribute to heart failure and demonstrates the applicability and value of the proposed models and computational methods in studying structural heart diseases. These findings offer a fresh perspective on the pathological mechanisms of heart failure, shedding light on the complex interplay between structural and material changes within the heart muscle.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829336","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Topological states in a one-dimensional stepped beam with resonators","authors":"Fang Hong \u0000 (,&nbsp;),&nbsp;Xiangbing Liu \u0000 (,&nbsp;),&nbsp;Yuxin Yao \u0000 (,&nbsp;),&nbsp;Kai Zhang \u0000 (,&nbsp;),&nbsp;Lihua Tang \u0000 (,&nbsp;),&nbsp;Zichen Deng \u0000 (,&nbsp;)","doi":"10.1007/s10409-025-25996-x","DOIUrl":"10.1007/s10409-025-25996-x","url":null,"abstract":"<div><p>Topological metamaterials offer defect-immune edge or interface states for elastic wave control and play an important role in robust waveguiding. One-dimensional topological metamaterial beams with engineered features, such as grooves or resonators, can be tailored to support topological states, offering great potential for advanced mechanical applications. However, most existing works focus on a single type of feature, limiting the number or quality of achievable topological states, especially in terms of low-frequency localization and energy concentration. In this study, a one-dimensional stepped beam structure with resonators is proposed, employing a strategy that integrates both Bragg scattering and local resonance mechanisms to support multiple and highly concentrated topological interface states. First, the hybrid structure is constructed by introducing periodic grooves and attaching subwavelength resonators to the beam, enabling the coexistence of Bragg scattering and local resonance mechanisms. The topological properties of two traditional configurations in one-dimensional beam structures are studied for comparison. The concentration factor is introduced to quantitatively assess the energy localization of the topological states. Subsequently, the finite element simulations for the studied model are performed. The Zak phase calculations and the transmission results indicate the existence and the high localization of topological states. Finally, transmission experiments further confirm the existence and robustness of topological interface states. The results show that the proposed model supports two robust and strongly localized topological states, performing better than traditional designs in terms of energy concentration and structural adaptability. This work offers a practical and flexible strategy for low-frequency vibration control, which has potential for future development of elastic wave sensors and energy harvesting devices.\u0000</p><div><figure><div><div><picture><source><img></source></picture><span>The alternative text for this image may have been generated using AI.</span></div></div></figure></div></div>","PeriodicalId":7109,"journal":{"name":"Acta Mechanica Sinica","volume":"42 9","pages":""},"PeriodicalIF":4.6,"publicationDate":"2026-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147829335","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}