Mechanics of Materials最新文献

{"title":"The dynamic Eshelby problem: nucleation and growth of a phase change defect as the mechanism of deep earthquakes and failure waves","authors":"Xanthippi Markenscoff","doi":"10.1016/j.mechmat.2025.105385","DOIUrl":"10.1016/j.mechmat.2025.105385","url":null,"abstract":"<div><div>A defect of phase change in density and change in moduli modeled as a self-similarly dynamically expanding Eshelby ellipsoidal inhomogeneous inclusion can nucleate and grow under high pressure at a critical loading. The self-similarly expanding ellipsoid possesses the “lacuna” property, the particle velocity vanishing in the interior domain, which allows the constant stress Eshelby property to be valid in the interior and the inclusion to grow as a whole in the presence of inertia. The energetics for nucleation and growth are derived from the energy-momentum tensor and first principles and generalize in the presence of inertia the “force on an interface” obtained in statics by Eshelby based on a thought experiment. The solution obtains the flow of energies across the moving phase boundary of an inhomogeneous inclusion, at the balancing of which, corresponding to the vanishing of the <em>M</em> integral, the interface presents no obstacle, and an arbitrarily small inclusion of phase change nucleates and grows at constant potential energy. The solution explains the generation of a shear seismic source radiation in deep-focus earthquakes and the generation of failure waves producing a zone with micro-fractures under compression in lima glass, and has wider applications to amorphization defects, defects in alloys, laser additive manufacturing, etc.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105385"},"PeriodicalIF":3.4,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143941281","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Deep learning-assisted prediction of mean grain size of polycrystalline materials from ultrasonic wave response","authors":"Anuj Yadav,&nbsp;Kamal Kishor Prajapati,&nbsp;Mira Mitra","doi":"10.1016/j.mechmat.2025.105367","DOIUrl":"10.1016/j.mechmat.2025.105367","url":null,"abstract":"<div><div>This study introduces a novel approach for the non-destructive automated prediction of mean grain size in polycrystalline materials, using ultrasonic testing combined with deep learning (DL) techniques. The proposed approach involves a 1D convolutional neural network (CNN) regression model designed to analyze the ultrasonic longitudinal wave responses of Inconel-600 specimens, with the goal of predicting their mean grain size. These wave responses are generated through Hanning tone burst load excitation. Initially, simulated longitudinal wave responses are obtained through numerical simulations for eight distinct mean grain sizes (ranging from <span><math><mrow><mn>150</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span> to <span><math><mrow><mn>500</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>). Neper software is utilized to generate simulated microstructures with varying mean grain sizes, followed by finite element (FE) simulation using the commercial tool ANSYS-APDL. Subsequently, experimental wave responses are captured for Inconel-600 specimens with three distinct mean grain sizes (<span><math><mrow><mn>20</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>, <span><math><mrow><mn>67</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>, and <span><math><mrow><mn>107</mn><mspace></mspace><mi>μ</mi><mi>m</mi></mrow></math></span>), prepared through the annealing process. The variation in mean grain sizes among the specimens is observed through optical microscopic images. The experiments are conducted on an in-house experimental setup, with piezoelectric wafer transducers used to generate and sense the experimental wave responses. In addition to distinct mean grain sizes, wave responses are captured by varying locations, frequencies, and noise levels to create a comprehensive and diverse database. The complete database comprises 1155 experimental and simulated wave responses across 11 different mean grain sizes. 80% of the complete database is randomly chosen for training a 1D-CNN regression model, while the remaining 20% is used for testing. The model’s architecture is optimized for predictive accuracy, incorporating convolutional layers, activation functions, and a Huber loss metric. Training and validation demonstrate the model’s ability to learn complex patterns and generalize to unseen data effectively. Testing on unseen datasets yields promising results in predicting mean grain size values, with the model achieving an average relative error (ARE) of 6.24%.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105367"},"PeriodicalIF":3.4,"publicationDate":"2025-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143937330","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shock compaction of porous compounds with application to PBX-9501 and HMX","authors":"Dennis Grady","doi":"10.1016/j.mechmat.2025.105386","DOIUrl":"10.1016/j.mechmat.2025.105386","url":null,"abstract":"<div><div>This report pursues assessment and analysis of earlier experimental shock wave studies of HMX based PBX-9501 explosive material, a mixture of HMX molecular crystal and polymer binder. The effort also undertakes exploring underlying physics of the dynamic compaction and deformation of granular mixtures, and in pursuing compaction model improvements relevant to the shock wave equation-of-state. The model development is applied to experimental unreacting shock strength and Hugoniot data on modestly porous PBX-9501 material tested at Los Alamos National Laboratory (LANL) in the 1980's and again in the 1990's. Time-resolved shock wave experiments lend insights into the energy dissipation dynamics. Complementary detailed material microstructure studies constrain dissipation mechanisms on the microscale. Pore compaction is modelled and the potential for heterogeneous hot-spot formation is assessed. Results of the effort uncover details of the unreacting shock compaction response of this mixture material. Specifics of shock wave structure and the dependence of structure on shock amplitude are explored that lend insights into microstructure dissipation mechanisms responsible for onset of reaction. The report closes with a perspective on dissipation dynamics within the unreacting structured shock wave response of PBX 9501 explosive.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105386"},"PeriodicalIF":3.4,"publicationDate":"2025-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144070957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Experimental testing of V notched radially graded materials under static loading","authors":"Suhib Abu-Qbeitah ,&nbsp;Olga Petrenko ,&nbsp;Michele Ciavarella ,&nbsp;Stephan Rudykh","doi":"10.1016/j.mechmat.2025.105364","DOIUrl":"10.1016/j.mechmat.2025.105364","url":null,"abstract":"<div><div>The growing interest in additive manufacturing and printed materials has opened new possibilities for the development and application of Graded Materials (GMs). However, capturing the strength and fracture behavior of GMs presents challenges, as the extent to which classical theories for homogeneous materials apply remains uncertain. For example, it has been recently suggested that in the classical problem of a sharp wedge or crack loaded in-plane (mode I and/or mode II), the stress singularity can be mitigated by grading the elastic properties of the material near the notch tip according to a power-law distribution, <span><math><mrow><mi>E</mi><mo>∼</mo><msup><mrow><mi>r</mi></mrow><mrow><mi>β</mi></mrow></msup></mrow></math></span>. This suggests that sharp geometrical discontinuities can exist without causing sharp stress concentrations. Under these conditions, it is conceivable that structural optimization should aim to achieve uniform stress distribution or, more specifically, consistent strength throughout the material. Since material resistance typically follows a power-law function of the elastic modulus, a state of uniform stress is not optimal. However, a state of uniform strength may also be considered less than ideal with respect to the homogeneous material since the softer material used to reduce stress concentration reduces also the strength of the specimen. Here, we report experiments conducted on V-notched specimens, varying the grading exponent <span><math><mi>β</mi></math></span>, and compare the results for homogeneous material specimens with those of GMs. We find that the cancellation of singularity effect competes with the reduction of strength due to the use of softer materials, but when the latter effect is accounted for or reduced, we observe an improvement compared to the homogeneous V-notched case. Further, when the strength-modulus exponent <span><math><mrow><mi>m</mi><mo>=</mo><mn>0</mn></mrow></math></span>, structural optimization is equivalent to minimizing stress concentration. For most materials with <span><math><mrow><mi>m</mi><mo>&lt;</mo><mn>1</mn></mrow></math></span>, the optimal behavior occurs near this criterion. In our case, we found <span><math><mrow><mi>m</mi><mo>≈</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></math></span>, which is significant because strain energy density, a function of both stress and strain, acts as a dual-purpose criterion. This criterion is similar to the <span><math><mrow><mi>σ</mi><mo>/</mo><msub><mrow><mi>σ</mi></mrow><mrow><mtext>a</mtext></mrow></msub></mrow></math></span> ratio used in homogeneous materials like Rankine or Von Mises. Notably, in fatigue tests, we anticipate that the benefits of material grading will be more pronounced.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105364"},"PeriodicalIF":3.4,"publicationDate":"2025-05-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143922555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Resisting room-temperature creep in titanium alloys by pre-compression","authors":"Ming Li,&nbsp;Zhenghao Zhang,&nbsp;Yeqiang Bu,&nbsp;Haofei Zhou,&nbsp;Hongtao Wang,&nbsp;Wei Yang","doi":"10.1016/j.mechmat.2025.105383","DOIUrl":"10.1016/j.mechmat.2025.105383","url":null,"abstract":"<div><div>For deep-sea submersibles, the service life of titanium alloys in lightweight pressure hulls is dictated by room-temperature creep deformation. Under high stress in deep-sea, the mechanism for room-temperature creep is primarily dominated by dislocation slip in the soft grains. Guided by the principles of dislocation pile-up and back stress hardening, a pre-compression treatment was applied to Ti80 alloy. Via pre-compression, the dislocation density increased significantly by 1.9–2.5 times in some softer grains whereas the average dislocation density only experienced a 22 % increase. This treatment effectively elevated the critical resolved shear stress (CRSS) and enhanced the resistance to dislocation motion. Accordingly, the creep stress threshold is raised by at least 14 % and the total creep strain is reduced by 80 % after 1000 h of creep at 90 % the yield strength. A creep constitutive model based on back stress evolution was developed to accurately describe the creep behavior of Ti80 alloy. That model incorporates an estimation of the initial back stress induced by pre-compression treatment and its effect on dislocation slip. The results demonstrate crucial insights into the optimization of materials for deep-sea pressure hulls and their long-term performance prediction.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105383"},"PeriodicalIF":3.4,"publicationDate":"2025-05-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143948166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of crease angles and defects on membrane tensile behavior","authors":"Qian Zhang ,&nbsp;Qiuyue Zhong ,&nbsp;Hui Qiu ,&nbsp;Shuo Wang ,&nbsp;Jian Feng ,&nbsp;Jianguo Cai","doi":"10.1016/j.mechmat.2025.105365","DOIUrl":"10.1016/j.mechmat.2025.105365","url":null,"abstract":"<div><div>In this study, the mechanical behavior of creased membrane structures under uniaxial tensile tests is investigated after deployment, focusing on the effects of crease formation, crease angles, and induced defects. The results show that crease introduction reduces the fracture strain, although the fracture strength of creased and uncreased membranes remains similar. Moreover, the local elastic modulus of the creased region along the unfolding direction is found to be 69.5% of that of an ideal pure membrane based on the determination of crease influence width. The analysis of crease angle reveals that both fracture strength and strain increase with crease angle. For membranes with a 90°crease, the fracture strength is about 10.9% higher than that of the membrane with a horizontal crease. The elastic modulus in the direction of crease extension and shear modulus can be determined and verified through mechanical testing and finite element analysis of the angled creased membranes, forming an orthotropic elastic parameter model for the creased region. Finally, the introduction of circular holes of various sizes as geometric defects significantly affects wrinkle distribution and out-of-plane deformation, while notably reducing fracture strain and fracture stress, with the impact on fracture strain being particularly pronounced. This study offers crucial insights into the design of creased membranes, particularly for aerospace and space exploration, where performance under complex loading and defects is critical.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105365"},"PeriodicalIF":3.4,"publicationDate":"2025-05-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923177","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Predicting tensile behavior from nanoindentation using gradient plasticity model with neural network and genetic algorithm","authors":"Daxuan Zhu ,&nbsp;Jianfeng Zhao ,&nbsp;Yanan Hu ,&nbsp;Qianhua Kan ,&nbsp;Guozheng Kang ,&nbsp;Xu Zhang","doi":"10.1016/j.mechmat.2025.105368","DOIUrl":"10.1016/j.mechmat.2025.105368","url":null,"abstract":"<div><div>The conventional <em>J</em>₂-flow theory of plasticity fails to account for size-dependent behavior, limiting its ability to describe the mechanical properties of materials at the microscale accurately. In contrast, the strain gradient plasticity theory incorporates strain gradient effect, making it more suitable for capturing the indentation size effect observed in the nanoindentation of materials. This study employs the conventional theory of mechanism-based strain gradient (CMSG) model with a small strain assumption to approximate the indentation problem involving finite deformation. To extract material parameters from nanoindentation experiments, specifically focusing on the CMSG plasticity model, this study introduces an inversion method that integrates a Long Short-Term Memory (LSTM) neural network model with a genetic algorithm. Finite element simulations using the CMSG plasticity model were employed to generate training and validation data for the neural network model, which was then combined with a genetic algorithm for material parameters determination. The method was validated through comparing the simulations with the experimental results from nanoindentation and uniaxial tensile tests on pure copper. The results demonstrate a strong correlation between the experimental data and the simulations, thereby affirming the accuracy of the inversion approach in retrieving strain gradient parameters of the CMSG plasticity model. The study also highlights the critical role of the indentation size effect in microscale material behavior, offering deeper insights into mechanical properties at small scales. Moreover, the results of material parameters of annealed copper films determined by this method further illustrate the universality of the proposed approach.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105368"},"PeriodicalIF":3.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144084657","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effects of grain orientation and confinement on dynamic compressive behavior of highly oriented MAX phase Ta2AlC","authors":"Xingyuan Zhao ,&nbsp;Tarek Aly ElMeligy ,&nbsp;Maxim Sokol ,&nbsp;Michel W. Barsoum ,&nbsp;Leslie Lamberson","doi":"10.1016/j.mechmat.2025.105378","DOIUrl":"10.1016/j.mechmat.2025.105378","url":null,"abstract":"<div><div>MAX phases are unique ternary carbides and nitrides that bridge the gap between metals and ceramics. Specifically, Ta₂AlC, the MAX phase with the highest bulk modulus, offers a unique combination of metallic and ceramic properties, making it particularly well-suited for extreme applications. Fully dense, coarse-grained, and textured Ta₂AlC was fabricated in bulk, achieving a global grain orientation along the c-axis with an orientation factor of 0.63. The uniaxial quasi-static and dynamic, and biaxial dynamic response was evaluated parallel (<span><math><mrow><mo>∥</mo></mrow></math></span>) and perpendicular (⊥) to the c-axis. The average dynamic strength in ⊥ c-axis orientation was 824 <em>±</em> 39 MPa, 19 % higher than the uniaxial quasi-static compressive strength of 690 <em>±</em> 55 MPa in the same orientation. The biaxial dynamic strength in this orientation, when applying a moderate 80 MPa planar confinement along basal planes (<span><math><mrow><msub><mo>⊥</mo><mo>∥</mo></msub></mrow></math></span> c-axis) had the highest average compressive strength of 1097 <em>±</em> 72 MPa. Scanning electron microscopy fractography indicates a consistent fracture mechanism within the grain orientation across different strain rates under uniaxial loading. During biaxial loading, crack propagation was delayed, with qualitative indications of shear band formation. Concurrently, both the quantity and mode of kink band formation appeared to increase, leading to an overall enhancement in final strength. The link between macroscopic failure behavior captured from ultra-high-speed imaging and microscopic fractography is discussed.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105378"},"PeriodicalIF":3.4,"publicationDate":"2025-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A unified thermomechanically-consistent framework for fatigue failure entropy","authors":"Asghar Zajkani ,&nbsp;Michael Khonsari","doi":"10.1016/j.mechmat.2025.105379","DOIUrl":"10.1016/j.mechmat.2025.105379","url":null,"abstract":"<div><div>This paper aims to develop a cyclic thermo-elastoplastic constitutive model to assess entropy generated due to uniaxial fatigue loading. The study is based on a finite element discretization for repetitive loading/unloading cycles to determine the internal dissipation and associated entropy generation. The primary objective of the study is to explore the internal friction effect as a non-destructive dissipative mechanism through the application of two distinct approaches: creep-like entropy for phenomenological yield stress relaxation and an extrapolated scheme from the thermoelastic constitution. The first facilitates a seamless transition for yield stress values, allowing them to pass smoothly from macro-plasticity to microplasticity, while incorporating a unified scheme of deformation-induced internal friction effects into constitutive equations as the material's internal state evolves. A simple self-consistent homogenization scheme is applied to establish a link between the plasticity scale submitted to cyclic loading. The latter was introduced for the first time via a rate-dependent creep-plasticity entropy to account for the non-damaging part of dissipation in both macro- and micro-plastic-dominated fatigue. This establishes a link between the mechanical degradation rate and the progression of the fatigue cycle. An additive decomposition of total entropy can individualize the inelastic entropy rate as an additional thermal part, representing a phenomenological creep-like relaxation, indicative of internal friction. Furthermore, the progression of the thermo-plastic friction effects is evaluated using the dual thermo-elastoplastic tangent modulus to provide the possibility of activating natural cooling, particularly when the mechanical loads are halted. The results of the finite element simulations show that the calculated Fracture Fatigue Entropy (FFE) values fall within a narrow range, confirming its constancy and usefulness as a material property.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105379"},"PeriodicalIF":3.4,"publicationDate":"2025-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144105514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A hyperelastic model for hollow fiber-reinforced composites at finite deformation","authors":"Jialin Wang ,&nbsp;Liangbin Chen ,&nbsp;Meirong Hao ,&nbsp;Yang Chen ,&nbsp;Zaoyang Guo ,&nbsp;Jun Liang","doi":"10.1016/j.mechmat.2025.105376","DOIUrl":"10.1016/j.mechmat.2025.105376","url":null,"abstract":"<div><div>This study introduces a micromechanics-based constitutive model to describe the effective hyperelastic behaviors of hollow fiber-reinforced composites under finite deformation. The multiplicative decomposition approach is employed to decompose a general deformation into three fundamental deformations: isochoric uniaxial deformation along the fiber direction, equi-biaxial deformation on the transverse plane, and pure shear deformation. Based on this multiplicative decomposition, the free energy density function of the composites is thus additively decomposed into the three corresponding components. Subsequently, the effective free energy density functions of the composite for triaxial deformation (composed of the isochoric uniaxial deformation along the fiber direction and equi-biaxial deformation on the transverse plane), along-fiber shear, and transverse shear are derived using a cylindrical composite element model. The total free energy density function of the composite is then obtained by summing the contributions of these decomposed deformations. To validate the proposed model, finite element simulations based on representative volume elements are conducted. The effects of fiber volume fraction, fiber/matrix stiffness ratio, and wall thickness of hollow fiber on the effective mechanical behaviors of the composites are explored. The theoretical predictions show excellent agreement with numerical results for all considered cases, demonstrating that the proposed model reliably predicts the effective mechanical response of hollow fiber-reinforced composites under finite deformation. Finally, to further validate the prediction accuracy and computational efficiency of the developed model, it is applied to the structural analysis of a cantilever beam, with results compared to those obtained using the FE² method. This comparative analysis demonstrates again the accuracy and efficiency of the proposed approach in practical structural analysis.</div></div>","PeriodicalId":18296,"journal":{"name":"Mechanics of Materials","volume":"207 ","pages":"Article 105376"},"PeriodicalIF":3.4,"publicationDate":"2025-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143923176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}