Acta Mechanica最新文献

{"title":"Elastic anisotropy in heterogeneous materials","authors":"Abhilash Nagaraja","doi":"10.1007/s00707-026-04795-2","DOIUrl":"10.1007/s00707-026-04795-2","url":null,"abstract":"<div><p>Heterogeneous materials exhibit anisotropy induced by factors such as individual phase properties and microstructural configuration that form crucial descriptors of heterogeneity. A review of anisotropy indices proposed in the context of single crystals and composite materials reveals their limitations in quantifying anisotropy in heterogeneous materials. To address this shortcoming, this work presents an approach to quantify elastic anisotropy in heterogeneous materials utilizing their effective elastic properties thereby embodying the effects of heterogeneity. Anisotropy quantification has been demonstrated considering two-phase composite materials highlighting the phenomenon of heterogeneity driven anisotropy and emphasizing the crucial role of constituent volume fractions, reinforcement shape and elastic contrast in influencing the extent of anisotropy. The proposed approach has been extended to quantify anisotropy arising from defects such as porosity and cracks in homogeneous media. Additionally, specific material and microstructural descriptors leading to overall isotropy in composite, porous and cracked materials have been validated. The presented results demonstrate the applicability of the presented anisotropy quantification approach to any class of heterogeneous materials.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"6071 - 6088"},"PeriodicalIF":4.0,"publicationDate":"2026-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188908","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":"Nonlinear dynamics of temperature-dependent fiber-reinforced composite MEMS resonators under multi-harmonic excitations","authors":"Mehdi Alimoradzadeh,&nbsp;Francesco Tornabene,&nbsp;Dimitri Rossana,&nbsp;Ali Asgharpourzadeh","doi":"10.1007/s00707-026-04731-4","DOIUrl":"10.1007/s00707-026-04731-4","url":null,"abstract":"<div><p>This study focuses on the nonlinear vibration of a fully clamped microcomposite beam reinforced by temperature-dependent curvilinear fibers under the double action of a uniform temperature rise and lateral harmonic force in a viscous medium. The Euler–Bernoulli beam theory is used to model the composite microbeam made of a polymer matrix reinforced with temperature-dependent curvilinear fibers. The von Kármán theory is here used to model the geometric nonlinearity, whereas the modified couple stress theory (CST) is employed to derive the partial form of nonlinear equations governing dynamics of the system. The Galerkin approach is used to modify the partial differential equation to a nonlinear ordinary differential equation, which is, then, solved analytically by means of the method of multiple time scale, to investigate the nonlinear dynamic behavior of the system in secondary resonance. Finally, a parametric analysis investigates the effect of different parameters, such as uniform temperature rise, material length scale parameter, fiber path angels, equation of the fiber path angle, and excitation amplitude, on the dynamic behavior of the system in superharmonic and subharmonic resonance, with useful insights for many engineering applications.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5995 - 6016"},"PeriodicalIF":4.0,"publicationDate":"2026-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-026-04731-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Geometry-adaptive nonlinear free vibration modeling of FG-CNTRC plates: a VDQ-transformed TSDT framework","authors":"Y. Gholami,&nbsp;R. Ansari,&nbsp;H. Rouhi","doi":"10.1007/s00707-026-04790-7","DOIUrl":"10.1007/s00707-026-04790-7","url":null,"abstract":"<div><p>This study presents a comprehensive nonlinear free vibration analysis of functionally graded carbon-nanotube-reinforced composite (FG-CNTRC) plates of arbitrary geometries. The proposed numerical formulation integrates the third-order shear deformation theory (TSDT) with a variational differential quadrature-transformed (VDQ-T) technique, enabling precise modeling of complex plate shapes such as rectangular, skew, quadrilateral, and annular sectors without re-derivation of the governing equations for each geometry. The governing equations of motion are obtained from Hamilton’s principle, incorporating geometric nonlinearity of the von Kármán type. The VDQ-transformation facilitates direct discretization of the system energy functionals and leads to a compact matrix formulation suited for high-accuracy vibration calculations. Validation against published results demonstrates excellent agreement of the developed approach. A detailed parametric investigation reveals the pronounced influence of CNT dispersion pattern, plate aspect ratio, and boundary conditions on the nonlinear vibration characteristics. The amplitude-dependent natural frequencies highlight strong coupling between material gradation and geometric nonlinearity. The proposed formulation provides a unified computational framework for nonlinear free vibration analysis of FG-CNTRC plates with various geometrical configurations.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"6017 - 6047"},"PeriodicalIF":4.0,"publicationDate":"2026-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189162","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":"Enriched finite element modeling in nonlinear vibration of porous sandwich beams with GPL reinforcement","authors":"Cong Ich Le,&nbsp;Ngoc Duyen Dang,&nbsp;Thu Nga Dinh,&nbsp;Dinh Kien Nguyen","doi":"10.1007/s00707-026-04818-y","DOIUrl":"10.1007/s00707-026-04818-y","url":null,"abstract":"<div><p>Enriched formulations are efficient in linear analysis, but they are rarely applied to nonlinear vibrations due to the complexity of combining high-order enrichment functions with geometric nonlinearities. This paper bridges this gap by formulating an enriched beam element to study the nonlinear vibration of sandwich beams with a porous core and graphene platelet (GPL) reinforced face layers. The proposed element is based on Euler-Bernoulli theory and von Kármán nonlinearity, using higher-order hierarchical functions to enrich conventional interpolations. Nonlinear frequencies of the sandwich beams with various boundary conditions and sandwich configurations are predicted using a direct iterative method. Extensive parametric studies demonstrate that the proposed element is efficient, providing accurate nonlinear frequencies with substantially fewer elements and shorter computational times than the conventional model. Results reveal that the effect of porosity on nonlinear vibration is coupled with the GPL weight fraction, with the impact of porosity diminishing as GPL content increases. Furthermore, the beam with hinged-hinged ends is to be the most sensitive to variations in the GPL fraction and porosity coefficient, whereas the clamped-clamped beam is the least. The influence of GPL distribution patterns and sandwich configurations on the nonlinear vibration behavior is also examined and highlighted.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"6049 - 6070"},"PeriodicalIF":4.0,"publicationDate":"2026-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189163","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":"Symplectic buckling solutions of L-shaped functionally graded stepped thick plates","authors":"Yingrui Zhang,&nbsp;Zhenhuan Zhou,&nbsp;Yuhang Li,&nbsp;Andi Lai,&nbsp;Jianlong Qu,&nbsp;Xinsheng Xu","doi":"10.1007/s00707-026-04803-5","DOIUrl":"10.1007/s00707-026-04803-5","url":null,"abstract":"<div><p>L-shaped and stepped plates are widely adopted in engineering applications due to their ability to meet strict assembly requirements while achieving significant reductions in weight and material usage. This work derives analytical solutions for the buckling of clamped L-shaped functionally graded material (FGM) stepped thick plates using a symplectic approach within the framework of Hamiltonian system. Three material models are considered to describe the continuous variation of properties through the plate thickness, i.e., the power-law (P-FGM), sigmoid (S-FGM), and exponential (E-FGM) distributions. The overall plate is divided into three rectangular regions with uniform thickness, and the symplectic superposition method is applied to each region, with continuity conditions ensuring compatibility at the interfaces. The accuracy of the analytical solutions is verified through comparisons with literature and finite element results. The effects of step thickness ratio, material gradation laws and material gradient index on the buckling behavior of L-shaped FGM stepped thick plates are discussed. New benchmark data are presented to validate future numerical methods.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5927 - 5950"},"PeriodicalIF":4.0,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188985","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":"Thermo-vibroacoustic response of orthotropic laminated composite plates with fluid–structure interaction","authors":"Neelam Soni,&nbsp;Baij Nath Singh","doi":"10.1007/s00707-026-04819-x","DOIUrl":"10.1007/s00707-026-04819-x","url":null,"abstract":"<div><p>This paper develops a unified thermo-vibroacoustic analytical framework for VERITy-manufactured laminated composite plates. The formulation encompasses temperature-dependent orthotropic stiffness, nonlinear degradation because of void content, and fluid–structure interaction in both air and water acoustic media. The constitutive equations are formulated using Classical Laminated Plate Theory (CLPT) with thermal corrections and then decomposed modally, together with a receptance-based harmonic response analysis. A temperature-dependent viscoelastic damping evolution law is implemented, whereas an extended mode shape representation for simply supported boundary conditions is developed; extension to clamped configurations is formulated but reserved for future validation. Two new design metrics are presented, namely the <i>Thermo-Acoustic Degradation Index</i> (TADI) and the <i>Thermo-Fluid–Structure Integrity Coefficient</i> (TFSIC), which quantify the interacting effects of thermal softening, void-induced stiffness loss, and acoustic loading on vibroacoustic integrity. A comparative analysis with conventional vacuum infusion laminates has shown that VERITy composites have superior thermo-acoustic resilience due to reduced void content and improved resin fiber uniformity. Within the stated modeling assumptions—including CLPT validity, semi-coupled fluid loading, modal truncation up to (<i>m</i>, <i>n</i>) <span>(le )</span> 3, and baffled far-field radiation—the proposed framework provides a benchmarked analytical basis for low-frequency thermo-vibroacoustic estimation of thin orthotropic laminates in aerospace, marine, and noise-critical engineering applications.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5971 - 5994"},"PeriodicalIF":4.0,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188986","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":"Analysis of laminated plates using polyharmonic splines with polynomial augmentation in a radial basis functions - finite differences framework","authors":"A. J. M. Ferreira","doi":"10.1007/s00707-026-04812-4","DOIUrl":"10.1007/s00707-026-04812-4","url":null,"abstract":"<div><p>This paper presents a meshless formulation for the analysis of laminated plates using first-order shear deformation theory (FSDT) combined with a radial basis function–finite difference (RBF-FD) method. The proposed local approximation employs polyharmonic splines (PHS) with polynomial augmentation, which eliminates the need for a shape parameter and provides accurate differentiation on structured and mildly perturbed node sets. Unlike global radial basis function collocation schemes, which typically produce dense and ill-conditioned matrices, the present RBF-FD approach leads to sparse algebraic systems and is compatible with scattered-node discretizations. The laminated plate equilibrium equations are discretized in strong form and applied to static bending and free vibration problems. Numerical results for isotropic and laminated square plates show very good agreement with analytical, elasticity, and benchmark numerical solutions. Additional verification studies are included to document the influence of nodal perturbations, polynomial reproduction, matrix sparsity, conditioning, and the sensitivity of the higher vibration modes.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5951 - 5969"},"PeriodicalIF":4.0,"publicationDate":"2026-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149188984","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":"Thermo-mechanical buckling characteristics of TPMS core sandwich plates incorporating hybrid foam face layers on viscoelastic foundations","authors":"Selman Kahraman,&nbsp;Yusuf Bahcacı,&nbsp;İsmail Esen","doi":"10.1007/s00707-026-04739-w","DOIUrl":"10.1007/s00707-026-04739-w","url":null,"abstract":"<div><p>This study investigates the thermo-mechanical buckling behaviour of functionally graded sandwich plates incorporating triply periodic minimal surface (TPMS) core architectures and hybrid metal–ceramic foam face layers resting on viscoelastic foundations. The novelty of the present study lies in three main aspects: first, a unified analytical framework is developed to analyse thermo-mechanical buckling of TPMS-based sandwich plates with hybrid metal–ceramic foam face layers; second, multiple coupled physical effects including temperature-dependent material properties, foam porosity distribution, magnetic field interaction, and elastic foundation stiffness are simultaneously incorporated into the formulation; and third, a comprehensive parametric investigation is performed to clarify the combined influence of TPMS topology, foam configuration, geometric parameters, and external fields on the thermal stability of sandwich structures. The governing equations are derived using the principle of total potential energy within the framework of higher-order shear deformation theory and solved analytically using a trigonometric solution approach. The results reveal a characteristic non-monotonic thermal buckling response, where the buckling load initially decreases with increasing temperature difference and then increases in the post-critical region. Quantitative results show that TPMS III provides approximately 5–17% higher thermal buckling resistance than TPMS I and about 2–5% higher than TPMS II, depending on the solid volume ratio. In addition, the influence of external fields and foundation conditions is significant. Increasing the magnetic field intensity can modify the buckling response by up to 50%, while increasing the shear foundation stiffness results in variations of approximately 19–56% in the critical buckling parameter. The proposed analytical framework provides an efficient tool for predicting the thermo-mechanical stability of advanced TPMS-based sandwich plates. It offers useful design guidelines for lightweight structural components operating under severe thermal and multi-physical environments.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5839 - 5862"},"PeriodicalIF":4.0,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-026-04739-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189154","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A multiscale prediction model for elastic properties of cement-emulsified asphalt mortar","authors":"Linge Xie,&nbsp;Xianglong Su,&nbsp;Liqun Lu","doi":"10.1007/s00707-026-04807-1","DOIUrl":"10.1007/s00707-026-04807-1","url":null,"abstract":"<div><p>The elastic properties of cement-emulsified asphalt mortar (CAM) are governed by its complex microstructure; however, a clear quantitative relationship between the two remains limited. This work proposes a multiscale model to predict the macro elastic modulus of CAM from nano C–S–H gel. A cement hydration model is used to approximately characterize the microstructure of CAM. Homogenization methods including the Mori–Tanaka, Self-Consistent, and Generalized Self-Consistent methods are employed for upscaling calculation. The evolution law of aspect ratios of asphalt and calcium hydroxide crystals (CH) on asphalt–cement ratio (A/C) is obtained through reverse analysis according to the multiscale model. The multiscale model is validated by comparing with extensive experimental data. The effects of sand particle size, interphase thickness, A/C ratio, water–cement (W/C) ratio and sand–cement (S/C) ratio on the elastic behavior of CAM are studied. Results show that the elastic modulus of CAM is inversely proportional to interphase thickness, W/C, and A/C ratios, but positively correlated with S/C ratio.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5887 - 5904"},"PeriodicalIF":4.0,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189151","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":"Dispersion, instability, and soliton dynamics in nonlocal MEE nanoplates","authors":"R. Karthikeyan,&nbsp;R. Selvamani,&nbsp;Samia Elattar,&nbsp;M. Ijaz Khan","doi":"10.1007/s00707-026-04805-3","DOIUrl":"10.1007/s00707-026-04805-3","url":null,"abstract":"<div><p>This study investigates nonlinear wave propagation in nonlocal magneto-electro-elastic (MEE) sandwich nanoplates using an extended version of the Yan–Dowell framework. The governing equations account for nonlocal elasticity and multiphysical coupling, allowing for a precise description of size-dependent effects and electromechanical interactions at the nanoscale. A harmonic wave approach is used to obtain the dispersion relation, with subsequent analysis of phase and group velocities. Instability of modulation is examined, revealing a bounded instability band shaped by the balance between dispersion and nonlinearity. The impact of the nonlocal parameter and MEE coupling on bandwidth, critical wave number, and growth rate is analyzed. The nonlinear Schrödinger equation is then derived to model envelope dynamics, yielding stable envelope soliton solutions. Numerical findings indicate that soliton width and energy concentration can be adjusted via MEE coupling, enabling targeted control over wave behavior. Compared to linear wave packets, solitons exhibit enhanced localization and stability. The developed model offers a comprehensive approach for studying nonlinear wave phenomena in multifunctional nanostructures for wave guidance, energy transmission, and smart materials applications.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"237 9","pages":"5863 - 5885"},"PeriodicalIF":4.0,"publicationDate":"2026-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149189152","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}