Acta Mechanica最新文献

{"title":"Thermoelastic and electromagnetic effects in a semiconducting medium","authors":"N. Islam,&nbsp;B. Das,&nbsp;G. C. Shit,&nbsp;A. Lahiri","doi":"10.1007/s00707-025-04267-z","DOIUrl":"10.1007/s00707-025-04267-z","url":null,"abstract":"<div><p>This paper addresses the generalized electromagnetothermoelastic problem for a homogeneous and isotropic thin circular semiconductor. We consider the non-local heat conduction equation due to the miniaturization of modern electronic devices and the prevalent use of ultrashort lasers in environments with extremely high-temperature gradients, along with the presence of a primary electromagnetic field. We assume that while heat propagation exhibits non-local properties, deformation behaves locally. The curved surface of the semiconductor is subjected to an exponentially time-dependent thermal and mechanical load. We employ a finite difference method utilizing the Crank–Nicolson implicit scheme to solve the governing coupled linear equations of hyperbolic type for extremely short-time actions and small microstructured sizes. Our study investigates the impact of the chemical concentration and the physical field variables of the diffusive material to predict the thermoelastic behavior within the nanostructured semiconducting medium. We present numerical computations of the chemical concentration, temperature distribution, chemical potential, deformation, and stress components for fixed values of physical parameters. The results indicate that the non-local parameter significantly smooths out sudden changes in thermal and stress gradients. The phase-lag parameters associated with heat flux and temperature gradient both have finite-speed thermal wave propagation and account for thermal inertia effects. These mechanisms collectively contribute to a reduction in surface resistance. Such factors are essential for precisely capturing ultrashort thermoelastic responses under rapid thermal loading, enabling improved predictions of material behavior in extreme conditions. These findings are crucial for designing and processing nanoelectromechanical systems (NEMS).</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2171 - 2191"},"PeriodicalIF":2.3,"publicationDate":"2025-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638502","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":"Geometry-dependent reduced-order models for the computation of homogenized transfer properties in porous media, part II: electrical double layer effects","authors":"Antoine Moreau,&nbsp;Cyrille Allery,&nbsp;Olivier Millet,&nbsp;Antoine Falaize","doi":"10.1007/s00707-024-04196-3","DOIUrl":"10.1007/s00707-024-04196-3","url":null,"abstract":"<div><p>A reduced-order model (ROM) based on proper orthogonal decomposition (POD) is proposed to solve fastly the strongly nonlinear elementary cell problem derived from the periodic homogenization of the Nernst-Planck-Poisson-Boltzmann equations. In previous works, multiscale models have been developed, in order to take separately into account the macro- and microscopical aspects of ionic diffusion, under the assumption that the porous medium consists of the periodic repetition of a single microscopic representative elementary volume (REV). More recently, a numerical method based on POD-ROM has been developed in order to take into account the variability of the REV at the macroscopical scale, which involves the numerical resolution of a large amount of instances of the cell problem. Presently, this method is extended to the case where the REV’s size is of the order of the Debye length and where the adsorption during the transfer of ions by the solid–fluid interface is considered.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2119 - 2148"},"PeriodicalIF":2.3,"publicationDate":"2025-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-024-04196-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638473","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":"The mechanics of bidirectionally reinforced elastomeric sheet subjected to the combination of lateral pressure and bilateral stretch","authors":"Wenhao Yao,&nbsp;Yaoning Sun,&nbsp;Chun I. L. Kim","doi":"10.1007/s00707-025-04264-2","DOIUrl":"10.1007/s00707-025-04264-2","url":null,"abstract":"<div><p>A three-dimensional continuum model is illustrated to analyze the mechanics of fiber-reinforced composites (FRC) subjected to a combination of lateral pressure and bilateral extension. This model incorporates the Neo-Hookean strain energy function for the matrix material and considers the kinematic contribution of bidirectional reinforcing fibers. The strain energy of the bidirectional fibers is characterized by accounting for the stretching, bending, and twisting responses being computed through first- and second-order gradient deformation. To derive the equilibrium equations, differential geometry is employed to define the FRC surface configurations, while the variational principle is used to establish the Euler equation and boundary conditions. Numerical results demonstrate the model’s validation in analyzing both out-of-plane and in-plane deformations of the matrix material, as well as the bending, twisting, and stretching of the bidirectional fiber network. The novelty of this research lies in its theoretical framework for understanding the mechanics of FRC subjected to simultaneous lateral pressure and bilateral stretching, particularly addressing the effects of interaction between lateral pressure and bilateral extension on the FRC deformation via the characterization of both matrix material and fiber meshwork deformation. The findings reveal that increased lateral pressure leads to greater out-of-plane deformation and strain (<span>(varepsilon _{1})</span>), while bilateral stretching reduces out-of-plane deformation and transverse strain (<span>(varepsilon _{1})</span>), while longitudinal strain (<span>(varepsilon _{2})</span>) distribution remains unchanged. Additionally, the top and bottom boundaries of the FRC exhibit the most pronounced curvatures due to the shrinking effects at these boundaries. Bias extension test results further showcase significant shear strain in the central domain, with the resultant forces from lateral pressure tension and bilateral stretch affecting the shear angle’s enlargement or reduction. The theoretical analysis of fiber unit extension and flexure provides a coherent explanation for the overall deformation of the fiber meshwork, supporting the hypothesis that the fibers’ microstructural deformations govern the macroscopic deformation of the FRC meshwork. The continuum model demonstrates its practical validity by providing reasonable explanations for the shaping process of woven fabrics, Sikken-type stiffeners, fiber-reinforced thermoplastics, and bamboo polylactic acid (PLA) composites.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2089 - 2118"},"PeriodicalIF":2.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638396","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":"An analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere","authors":"Xin Huang,&nbsp;Adil El Baroudi,&nbsp;Amine Ammar","doi":"10.1007/s00707-025-04258-0","DOIUrl":"10.1007/s00707-025-04258-0","url":null,"abstract":"<div><p>In this article, an analytical approach to characterize the breathing mode vibration for thermoelastic nanosphere using the coupled thermoelastic theory is developed. In other words, the inclusion of the temperature field takes into account the concept of heat wave and the energy equation of heat conduction is combined with the elastic theory. The frequency equation is derived from the solution of bi-harmonic function. Two different boundary conditions in the temperature field are considered, insulated and isothermal. The validation of the frequency equation is confirmed by the simulation of COMSOL. Two dimensionless parameters, thermoelastic coupling constant <span>(epsilon )</span> and Peclet number <i>Pe</i>, are introduced to study their influences on the frequencies and quality factors of the nanosphere vibration. Furthermore, the effects of thermodynamic parameters, such as the reference temperature, the coefficient of linear expansion, the thermal conductivity, and the heat capacity, are also studied in this article. Some parameters have monotonic effect on the frequency and quality factors, while others are more complex. The Peclet number plays a role as thermal damping factor in the model. The concise frequency equations obtained during the analysis could be a useful guide for interpreting the experimental observation and measurement of thermoelastic nanosphere vibrations.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2077 - 2088"},"PeriodicalIF":2.3,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638249","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":"Approximate Noether’s symmetry and conservation laws for approximate Lagrangian systems on time scales","authors":"S. X. Jin,&nbsp;X. W. Chen,&nbsp;Y. M. Li","doi":"10.1007/s00707-025-04263-3","DOIUrl":"10.1007/s00707-025-04263-3","url":null,"abstract":"<div><p>In this paper, the approximate Noether symmetries and conservation laws for approximate Lagrangian systems on time scales are discussed and presented. The Hamilton principle of approximate Lagrangian systems on time scales is given, and the approximate Lagrange equations for approximate Lagrangian systems on time scales are established. The Noether identities on time scales are given, the relationship between the approximate Noether symmetries and approximate conservation laws on time scales are established, the approximate inverse Noether theorems on time scales are obtained. Special cases such as the classical approximate Lagrangian systems and the discrete approximate Lagrangian systems are discussed. Finally, one example is given to illustrate the application of the results.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2065 - 2076"},"PeriodicalIF":2.3,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638245","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":"Graphene nanoplates bending under multipart asymmetric conditions based on 3D elasticity and new modified couple stress theories: comparison with the molecular mechanics method","authors":"Amir Reza Golkarian,&nbsp;Mehrdad Jabbarzadeh,&nbsp;Ali Imam,&nbsp;Shahram Etemadi Haghighi","doi":"10.1007/s00707-025-04262-4","DOIUrl":"10.1007/s00707-025-04262-4","url":null,"abstract":"<div><p>The main purpose of the present study is to examine the bending behavior of graphene nanoplates under asymmetric multipart conditions. Efforts have been made to discuss the differences between employing the commonly used modified couple stress theory (MCST) and the new modified couple stress theory (NMCST) in capturing size dependency, as well as to conduct a detailed investigation into the influences of material length scale parameters (MLSPs). For this purpose, the constitutive equations based on the 3D elasticity theory and the NMCST for the nonlinear bending analysis of orthotropic annular micro/nanoplates are initially derived. The rationale for suggesting the use of NMCST, which incorporates three MLSPs, instead of MCST, which uses only one MLSP (suitable for isotropic materials), lies in the non-isotropic nature of graphene nanoplates. This approach allows for the investigation of the potential differential effects of each MLSP under various conditions, particularly asymmetric conditions. Furthermore, employing NMCST provides a better understanding of the influence and dependency of MLSP values on the base material. The 3D elasticity theory is utilized to avoid the common approximations in displacement fields typically introduced by other plate theories. Consequently, the governing equations based on the 3D elasticity theory and NMCST in polar coordinates have been developed for the first time. These equations have been numerically solved using a new semi-analytical polynomial method (SAPM), taking into account the orthotropic properties of graphene. This method is designed to explore numerical solutions under various asymmetric conditions, such as multipart boundary conditions, loading, and elastic foundations. Multipart conditions refer to dividing the nanoplates into different sections and assigning distinct conditions to each section. The fundamentals of this new method are introduced in detail as a powerful semi-analytical approach for solving various partial differential equations under both symmetric and asymmetric conditions. The numerical solution of the derived equations aims to explore the effects of different MLSPs and their influences under various symmetric and asymmetric conditions, thereby providing insights into the nature and behavior of each MLSP. Additionally, the uniqueness or dependency of MLSP values on the base material is investigated. To validate the results, graphene nanoplates have been simulated using the molecular mechanics method (MMM), as there is a lack of information on bending under multipart conditions in the existing literature. All results are compared to ensure accuracy and reliability.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2035 - 2063"},"PeriodicalIF":2.3,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638244","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":"Spectrum of the axially loaded Timoshenko rod","authors":"K. A. Hohls,&nbsp;N. F. J. Van Rensburg","doi":"10.1007/s00707-025-04256-2","DOIUrl":"10.1007/s00707-025-04256-2","url":null,"abstract":"<div><p>The response to excitation in the axially loaded Timoshenko rod is greatly influenced by the type of axial load, which could be compressive or tensile. The results presented in this article have practical applications, particularly when the axial load is compressive, as non-positive eigenvalues indicate possible buckling. The mathematical model leads to an eigenvalue problem. Abstract theory from a recent article is presented and applied, demonstrating that partial sums of modal solutions converge to a solution of the model problem. This enables one to predict the response of a given structure to excitation.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"2011 - 2034"},"PeriodicalIF":2.3,"publicationDate":"2025-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-025-04256-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638243","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":"Application of the modified Wakashima–Tsukamoto model on nonlocal torsional vibration analysis of functionally graded Timoshenko–Gere microbeam","authors":"Juan Wang,&nbsp;Li Tang,&nbsp;D. Dang,&nbsp;M. Li","doi":"10.1007/s00707-025-04221-z","DOIUrl":"10.1007/s00707-025-04221-z","url":null,"abstract":"<div><p>The objective of this study is to assess the nonlocal torsional dynamic characteristics of functionally graded (FG) microscale beams based on Timoshenko–Gere’s theory. In this contribution, the modified Wakashima–Tsukamoto homogenization model is applied to calculate the effective material properties of FG microstructure, while the properties vary in the microbeam thickness direction. To consider the small-scale effect, nonlocal strain gradient theory is developed for the Timoshenko–Gere microbeam. Also, it is assumed that the FG microbeam possesses a rectangular cross section. The governing equation of torsional vibration of FG microbeam is derived with the help of the virtual work’s principle and analytically solved via Galerkin’s method. The numerical comparison between the findings of this study and the former investigation is performed to validate the accuracy of the methodology. Furthermore, two boundary conditions including clamped–free and clamped–clamped are regarded. Finally, the influence of different considerable variants including gradient index, microbeam cross-section geometry parameters, nonlocal and length scale parameters, and length of microbeam on the natural torsional vibration behavior is explored and shown in a group of illustrations and tables.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"1977 - 1989"},"PeriodicalIF":2.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638195","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":"Size-dependent large deformation analysis of microscale functionally graded beams and frames","authors":"Cong Ich Le,&nbsp;Ngoc Duyen Dang,&nbsp;Thi Thu Hoai Bui,&nbsp;Dinh Kien Nguyen","doi":"10.1007/s00707-025-04265-1","DOIUrl":"10.1007/s00707-025-04265-1","url":null,"abstract":"<div><p>The size-dependent large deformation analysis of microscale functionally graded (FG) beam and frame structure is carried out using a corotational beam element. The material properties are graded in the thickness direction according to a power-law distribution in terms of volume fractions of the constituent materials, and they are predicted by Mori–Tanaka homogenization scheme. The element with and without Poisson ratio effect is derived from the modified couple stress theory and Euler–Bernoulli beam theory. To improve the element performance, the solution of the nonlinear equilibrium equations of a beam segment is employed to interpolate the displacement field. An incremental/iterative algorithm is used with the arc-length method to solve the nonlinear equation of the structure and to trace the equilibrium paths. Numerical results reveal that the large deformation is overestimated by ignoring the microstructural size effect and Poisson’s ratio effect. It is also shown that the influence of the power-law index on the large deformation becomes more significant for the structure associated with a higher size scale parameter. The influence of the material gradation, the microstructural size parameter and the Poisson’s ratio effect on the large deformation response of the microscale FG beams and frames is investigated in detail.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"1991 - 2010"},"PeriodicalIF":2.3,"publicationDate":"2025-02-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638194","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":"Approximating the inertia forces in the floating frame of reference formulation using the consistent finite element mass matrix","authors":"Karlijn van Voorthuizen,&nbsp;Mohammed Iqbal Abdul Rasheed,&nbsp;Jurnan Schilder,&nbsp;Marcel Ellenbroek","doi":"10.1007/s00707-025-04247-3","DOIUrl":"10.1007/s00707-025-04247-3","url":null,"abstract":"<div><p>In the floating frame of reference formulation, the exact form of the inertia forces is derived using a continuum-based approach. This yields a mass matrix and quadratic velocity terms containing inertia shape integrals. To avoid these integrals, many implementations of the floating frame formulation approximate the inertia forces by defining the kinetic energy using the lumped finite element mass matrix. This work proposes an alternative approximation of the inertia forces based on the consistent finite element mass matrix for structural elements, addressing cases where the exact solutions available in literature for most solid elements are not applicable. The inertia forces are derived by defining the kinetic energy using the consistent finite element mass matrix or by using the inertia forces from the equation of motion of the corresponding linear finite element model. In this way, the inertia shape integrals are replaced by a readily available mass matrix. In comparison with the lumped approach, the proposed definition yields more accurate results for coarser meshes since a more realistic representation of the mass and inertia properties of the body is used. Furthermore, the proposed approach yields inertia forces similar to the exact continuum-based approach under the assumption of small deformations. If the influence of deformation on the mass matrix is significant or the quadratic velocity terms are important, mesh refinement is required to accurately represent the inertia forces. The accuracy of the proposed definition of the inertia forces is compared to the exact and lumped mass approaches through simulation of flexible systems.</p></div>","PeriodicalId":456,"journal":{"name":"Acta Mechanica","volume":"236 3","pages":"1955 - 1976"},"PeriodicalIF":2.3,"publicationDate":"2025-02-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00707-025-04247-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143638647","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}