Mechanics Research Communications最新文献

{"title":"The Fermi–Pasta–Ulam–Tsingou problem extended with viscoelastic effects","authors":"Mads Peter Sørensen ,&nbsp;Peter Leth Christiansen","doi":"10.1016/j.mechrescom.2025.104572","DOIUrl":"10.1016/j.mechrescom.2025.104572","url":null,"abstract":"<div><div>The Fermi–Pasta–Ulam–Tsingou discrete chain is extended to incorporate viscoelastic effects, where the nonlinear elastic springs connecting the particles are supplemented by dissipative dampers arranged in parallel with the springs. These dampers are assumed to be nonlinear, and we propose an interparticle force modeled as a polynomial function of both the particle displacements and their time derivatives, capturing the viscous and damping behavior.</div><div>In the continuum limit, we derive partial differential equations governing the dynamics of the chain. By appropriate scaling of the parameters with respect to the lattice constant, we obtain a nonlinear viscoelastic equation and a viscoelastic Boussinesq equation.</div><div>Traveling waves in form of shock waves are found for the nonlinear viscoelastic equation, where nonlinearity is balanced by viscous dissipation. These traveling waves are interpreted as propagating expansion waves.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104572"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145569264","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the continuum modeling of the foldable rod with rigid links","authors":"Igor Berinskii ,&nbsp;Victor A. Eremeyev","doi":"10.1016/j.mechrescom.2025.104574","DOIUrl":"10.1016/j.mechrescom.2025.104574","url":null,"abstract":"<div><div>We study the small-amplitude motion of a foldable, rod-like structure consisting of rigid links connected by torsional springs. The discrete model of the structure results in two dispersion curves: acoustic and optical. Depending on the structural parameters, stop bands may be observed. Using the long-wave approximation, we introduced a series of continuum models. However, the first-order approximation does not capture the behavior of the discrete model. Interestingly, in some cases, there is only an optical mode. However, higher-order approximations can reproduce behavior similar to that of the discrete model. Therefore, the bending-dominant structure requires an enhanced continuum model.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104574"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145569266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On average stress within sub-regions of granular media","authors":"Matthew R. Kuhn","doi":"10.1016/j.mechrescom.2025.104567","DOIUrl":"10.1016/j.mechrescom.2025.104567","url":null,"abstract":"<div><div>The paper concerns computation of average stress within small sub-regions of a larger static granular assembly, where the sub-region’s boundary is allowed to pass through the assembly’s particles. An exact average is computed for certain stress components and for certain categories of sub-regions. The paper also identifies those choices of sub-regions for which exact stress components may be exactly computed, but when these conditions are not met, provides reasonable bounds on the error.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104567"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520608","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Exploring elements of chaos in driven strings","authors":"Sujit Mainali ,&nbsp;Ashok Puri","doi":"10.1016/j.mechrescom.2025.104576","DOIUrl":"10.1016/j.mechrescom.2025.104576","url":null,"abstract":"<div><div>This paper presents a comprehensive analysis of nonlinear oscillations exhibited by driven strings. We begin with a linear, periodically driven, string in a nonlinear viscoelastic medium. We then show its reduction to the general Duffing oscillator model under the traveling wave assumption, and analyse several cases of the model including a special case corresponding to Ueda oscillator. In addition, we also study a string-oscillator problem involving an exponential (i.e., Toda) nonlinearity. We analyze each system with time series, phase portraits, bifurcation diagrams, Poincaré sections, and Lyapunov exponents. The nonlinear stiffness and driving play a major role in identifying regions of periodic motion and chaos in Duffing type of oscillators. The systematic approach provides an understanding of different elements of chaos in the nonlinear systems considered.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104576"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145569262","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 extension of the arbitrary Lagrange Eulerian (ALE) framework for pavements to nonlocal damage mechanics","authors":"Jakob Platen,&nbsp;Atul Anantheswar,&nbsp;Ines Wollny,&nbsp;Ahmad Chihadeh,&nbsp;Michael Kaliske","doi":"10.1016/j.mechrescom.2025.104580","DOIUrl":"10.1016/j.mechrescom.2025.104580","url":null,"abstract":"<div><div>The arbitrary Lagrange Eulerian (ALE) framework is shown to be well suited to model pavement structures under moving loads with high accuracy and efficiently, since the mesh is restricted to a small region. One downside of the current state is that damage cannot be represented in this approach in a regularized manner. Therefore, an extension of the current ALE framework for pavements is proposed by the modified Helmholtz equation in conjunction with homogeneous Neumann boundary conditions to enable a modeling of regularized damage in this simulation framework.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104580"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145618109","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Free vibration analysis of bi-directional FGM beams based on first-order shear deformation theory","authors":"Youmin Han,&nbsp;Renyu Ge,&nbsp;Jiuyin Cao","doi":"10.1016/j.mechrescom.2025.104559","DOIUrl":"10.1016/j.mechrescom.2025.104559","url":null,"abstract":"<div><div>This paper presents an effective method for calculating the natural frequency of free vibration of a rectangular cross-section beam made of bi-directional functionally graded material by using the interpolation matrix. Firstly, based on the first-order shear deformation theory, the displacement and strain fields at any point on the beam cross-section are presented. Next, the equilibrium equation from the theory of elasticity in stress form is equivalently integrated along the thickness direction to establish a set of variable-coefficient differential equations. In these equations, the natural frequency is the eigenvalue, and the beam's lateral displacement and cross-section rotation are the unknown characteristic functions. Then, the IMM is applied to transform the eigenvalue problem of the variable-coefficient differential equations into a generalized algebraic eigenvalue problem for a set of standard linear equations. Finally, the orthogonal triangular decomposition method (QR) is used to solve these equations, enabling the simultaneous acquisition of several natural frequencies of free vibration of the bi-directional functionally graded material beam and their corresponding mode shapes. The IMM has strong versatility, low computational cost, and high calculation accuracy, and can handle the free vibration problems of beams made of bi-directional functionally graded materials under various boundary conditions. The typical examples in this paper verify the validity and accuracy of the IMM theory.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"150 ","pages":"Article 104559"},"PeriodicalIF":2.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145520609","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Effective toughness estimation by FFT based phase field fracture: Application to composites and polycrystals","authors":"Pedro Aranda ,&nbsp;Javier Segurado","doi":"10.1016/j.mechrescom.2025.104498","DOIUrl":"10.1016/j.mechrescom.2025.104498","url":null,"abstract":"<div><div>An estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative volume elements of the microstructure, controlled by a constant energy dissipation rate using an arc-length type control. The definition of the toughness corresponds to the total energy dissipated after the total fracture of the RVE — which can be accurately obtained thanks to the dissipation control — divided by the RVE transverse area (length in 2D). The proposed estimate accounts for both the effect of heterogeneity in toughness and elastic response on the overall fracture energy and allows as well to account for phases with anisotropic elastic and fracture response (fracture by cleavage). To improve toughness predictions, crack-tip enrichment is used to model initial cracks. The method is applied to obtain the effective toughness of composites and elastic polycrystals in a series of examples. In the two types of materials, it is found that both heterogeneity in elastic response and fracture energy contribute to increase the effective toughness. Microscopically, it is found that toughening mechanisms are related to the propagation of the crack through tougher phases and the deviation of the crack path. It is also found that the latter is the controlling mechanism for cases with marked heterogeneity and high anisotropy, eventually leading to the saturation of the toughening effect for sufficiently high values of heterogeneity or anisotropy.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104498"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 discrete model for elasticity with microstructure","authors":"D. Polyzos ,&nbsp;T.V. Gortsas ,&nbsp;S.V. Tsinopoulos ,&nbsp;D.E. Beskos","doi":"10.1016/j.mechrescom.2025.104510","DOIUrl":"10.1016/j.mechrescom.2025.104510","url":null,"abstract":"<div><div>In the mid-1960s, Mindlin introduced his theory of strain gradient elasticity (SGE), along with one of its most widely recognized simplified versions, known as SGE-Form II. These enhanced theories were motivated by the need to capture dynamic phenomena that classical elasticity fails to address. Although theoretically elegant, the inclusion of numerous material constants and internal length scale parameters makes the practical application of both SGE and SGE-Form II challenging—even for one-dimensional (1D) problems. A practical approach for identifying these parameters involves validating the theories through lattice models, where both the microstructure and macrostructure are materially and geometrically well-defined. Using a simple 1D lattice model with nearest and next-nearest neighbor spring connections and distributed mass, Polyzos and Fotiadis (Int. J. Solids Struct. 49, 470–480, 2012) were the first to successfully validate Mindlin’s SGE-Form II and to interpret the intrinsic parameters introduced by the theory. Despite significant efforts, no lattice model has yet been shown to fully replicate the behavior described by the general SGE theory, even in 1D cases. This gap is addressed in the present work through the use of a simple 1D lattice model and the implementation of a continualization process similar to that employed by Polyzos and Fotiadis (2012).</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104510"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145019992","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Shape optimization of Hencky-type Reddy columns against buckling using genetic algorithms and artificial neural networks","authors":"Ali Forooghi ,&nbsp;Davide Pellecchia ,&nbsp;Eugenio Ruocco","doi":"10.1016/j.mechrescom.2025.104540","DOIUrl":"10.1016/j.mechrescom.2025.104540","url":null,"abstract":"<div><div>The current investigation proposes a computationally efficient framework for optimizing the buckling performance of non-uniform beams by means of an enhanced Hencky bar-chain model (HBM) combined with Reddy’s higher-order beam theory. The model effectively captures shear deformation, making it appropriate for analyzing thick beams where classical models may fall short. To lessen the high computational cost typically associated with iterative buckling analyses, a surrogate model is developed utilizing artificial neural networks (ANNs), trained to forecast critical buckling loads with high precision. The trained ANN is then integrated into a genetic algorithm framework for both single- and multi-objective optimization, which leads to considerable acceleration in the design process. The approach is tested across different boundary conditions, including simply supported, clamped–free, clamped–sliding, and clamped–clamped cases. The obtained results demonstrate that the ANN-based predictions closely match those acquired from high-fidelity eigenvalue solvers while decreasing computational time. In general, the integration of the HBM with machine learning-assisted evolutionary algorithms leads to a dependable approach for the shape optimization of beams under buckling constraints. Such a framework provides precise outcomes with decreased computational effort and can be considered a solid foundation for future developments in structural stability.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104540"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145363341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Energy equivalence-based homogenized micropolar model for 2D high valency architected materials: Periodic, semi-periodic, and aperiodic","authors":"Vardhil Kirtikumar Mehta,&nbsp;Arun R. Srinivasa,&nbsp;J.N. Reddy","doi":"10.1016/j.mechrescom.2025.104530","DOIUrl":"10.1016/j.mechrescom.2025.104530","url":null,"abstract":"<div><div>This study aims to develop a unified method for energy-based homogenization of different classes of architected materials. Unlike the majority of the currently available homogenized models, the proposed model is capable of modeling not only periodic microstructures but also graded, distorted, and random mesostructures. The notion of a <em>non-repeating characteristic cell</em> is introduced to quantify both the geometry and topology of the mesostructures, which helps categorize them into three main classes: periodic, semi-periodic, and aperiodic. The discrete body of an architected material is homogenized at the scale of the characteristic cell by invoking local energy equivalence, resulting in a micropolar continuum at the macroscale with spatially varying material properties. The homogenization process involves obtaining the strain energy of the discrete body (with high valency) using a frame model, performing a homogenization approximation via a physically intuitive limiting process, and finally, obtaining the constitutive relation for the continuum in its unified general form. The finite element model of the micropolar continuum is developed and implemented in a computer program for numerical solutions. First, the periodic and semi-periodic variants of the rectangular mesostructure are analyzed. The efficacy of the homogenized model is tested by comparing the results of a boundary value problem with those of the discrete frame model. Next, for aperiodic mesostructures, a slightly different approach is introduced, involving <em>proxy characteristic cells</em> that significantly reduce the computational complexity of the model. The homogenized model is verified against a sample of five instances of aperiodic mesostructure under a set of boundary value problems. The study also demonstrates that, with fairly good accuracy, the homogenized model incurs an impressive reduction in computational expense compared to the discrete frame model.</div></div>","PeriodicalId":49846,"journal":{"name":"Mechanics Research Communications","volume":"149 ","pages":"Article 104530"},"PeriodicalIF":2.3,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145320586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}