Continuum Mechanics and Thermodynamics最新文献

{"title":"Exact bifurcation analysis of the static response of a Fermi–Pasta–Ulam softening chain with short and long-range interactions","authors":"N. Challamel,&nbsp;C. Combescure,&nbsp;V. Picandet,&nbsp;M. Ferretti,&nbsp;A. Luongo","doi":"10.1007/s00161-024-01356-7","DOIUrl":"10.1007/s00161-024-01356-7","url":null,"abstract":"<div><p>This paper is devoted to the static bifurcation of a nonlinear elastic chain with softening and both direct and indirect interactions. This system is also known as a generalized softening FPU system (Fermi–Pasta–lam nonlinear lattice) with <span>(p = 2)</span> nonlinear interactions (nonlinear direct and second-neighbouring interactions). The static response of this <i>n</i>-degree-of-freedom nonlinear system under pure tension loading is theoretically and numerically investigated. The mathematical problem is equivalent to a nonlinear fourth-order difference eigenvalue problem. The bifurcation parameters are calculated from the exact resolution of the fourth-order linearized difference eigenvalue problem. It is shown that the bifurcation diagram of the generalized softening FPU system depends on the stiffness ratio of both the linear and the nonlinear parts of the nonlinear lattice, which accounts for both short range and long range interactions. This system possesses both a saddle node bifurcation (limit point) and some unstable bifurcation branches for the parameters of interest. We show that for some range of structural parameters, the bifurcations in <i>(n−1)</i> unstable bifurcation branches prevail before the limit point. In the complementary domain of the structural parameters, the bifurcations in <i>(n−1)</i> unstable bifurcation branches prevail after the limit point, which means that the system becomes unstable first, at the limit point. At the border between both domains in the space of structural parameters, the bifurcation in <i>(n−1)</i> unstable bifurcation branches coincide with the limit point, with an addition unstable fundamental branch. This case is the hill-top bifurcation, already analysed by Challamel et al. (Int J Non-Linear Mech 156(104509): 1-11, 2023) in the case <span>(p= 1)</span> interaction. We also numerically highlight the possibility for such a generalized FPU system to possess possible imperfection sensitivity. Numerical results support the fact that the structural boundary of the hill-top bifurcation coincides with the transition between imperfection sensitive to imperfection insensitive systems.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01356-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143071907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Vibration analysis of thermoelastic micro-beams on a Pasternak foundation with two parameters using the Moore–Gibson–Thompson heat conduction model","authors":"Adam Zakria,&nbsp;Ahmed Yahya,&nbsp;Ahmed E. Abouelregal,&nbsp;Muntasir Suhail","doi":"10.1007/s00161-025-01358-z","DOIUrl":"10.1007/s00161-025-01358-z","url":null,"abstract":"<div><p>This study investigated the thermoelastic vibration behavior of microbeams supported by a Pasternak foundation, characterized by two elastic parameters: the shear layer modulus and the Winkler modulus. The thermoelastic behavior of the beam was modeled using the Moore–Gibson–Thompson (MGT) heat conduction theory, which accounted for finite thermal wave speeds and included a higher-order time derivative to effectively address heat conduction dynamics in small-scale structures. The governing equations were derived from the coupled theories of generalized thermoelasticity and beam mechanics, integrating the effects of the foundation. The research examined how foundation parameters, thermal relaxation times, and beam geometry influenced vibration frequency, thermal damping, and the stability of the microbeam. Numerical simulations were performed to demonstrate the effects of material properties, foundation stiffness, and thermal loading on the dynamic behavior of the microbeam. The findings offered valuable insights for the design and optimization of microbeams in advanced engineering applications, such as MEMS devices and nanoscale structures, where thermal effects and foundation interactions were crucial</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143056222","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":"The coupled Legendre-Hadamard condition for fiber-reinforced materials: three-dimensional solids and two-dimensional shells","authors":"Mircea Bîrsan,&nbsp;Milad Shirani,&nbsp;David J. Steigmann","doi":"10.1007/s00161-025-01357-0","DOIUrl":"10.1007/s00161-025-01357-0","url":null,"abstract":"<div><p>Detailed derivations of the Legendre-Hadamard necessary conditions for energy-minimizing states of fiber-reinforced three-dimensional solids and two-dimensional shells are presented. The underlying conceptual framework is Cosserat elasticity theory in which the Cosserat rotation field controls the orientation of the embedded fibers. This is partially coupled to the continuum deformation gradient by the requirement that the fibers convect as material curves with respect to the matrix material in which they are embedded. The conditions obtained combine the effects of deformation and rotation and subsume previously obtained decoupled inequalities involving these effects separately.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01357-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027183","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 model for elastic half space under a visco-elastic layer in generalized thermoelasticity","authors":"S. E. Khader,&nbsp;A. A. Marrouf,&nbsp;M. Khedr","doi":"10.1007/s00161-024-01345-w","DOIUrl":"10.1007/s00161-024-01345-w","url":null,"abstract":"<div><p>We consider a model of two layers for two cases. In the first case, a viscoelastic upper layer over an elastic half-space. In the second case, an elastic upper layer over a viscoelastic half-space. The upper layer’s surface is taken to be traction-free and is subjected to a constant thermal shock. This model is solved in the context of the generalized thermoelasticity theory with one relaxation time. Laplace transform techniques are used. The inverse Laplace transforms are obtained using a numerical method based on the Fourier expansion technique. Numerical results are computed and represented graphically for the temperature, displacement, and stress distributions. This work may be useful in the design of materials used in thermal insulation, vibration reduction, and applications in microelectronics.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01345-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143027149","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 study of a thermoelastic body possessing microtemperatures","authors":"Marin Marin,&nbsp;Andreas Öchsner,&nbsp;Sorin Vlase,&nbsp;Hamid M. Sedighi,&nbsp;Stefan Pirlog","doi":"10.1007/s00161-025-01359-y","DOIUrl":"10.1007/s00161-025-01359-y","url":null,"abstract":"<div><p>In our study we approach a Cosserat thermoelastic body in which we take into account both the usual temperature and the microtemperature, that is, the temperature of the microparticles of the body. After constructing the mixed problem with initial and boundary values, in this context, we define an appropriate Hilbert space in which we obtain a temporal evolutionary equation which is equivalent to the already constructed mixed problem. With the help of some known results from the theory of contraction semigroups we prove both the existence and the uniqueness of the solution of the evolution equation, therefore of the considered mixed problem. Furthermore, the same semigroup theory allows us to obtain the continuous dependence of the solution of the mixed problem, both with respect to the initial data and with respect to the loading.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01359-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142975184","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"Seismic capacity of purely compressed shells based on Airy stress function","authors":"Carlo Olivieri,&nbsp;Sam Cocking,&nbsp;Francesco Fabbrocino,&nbsp;Antonino Iannuzzo,&nbsp;Luca Placidi,&nbsp;Sigrid Adriaenssens","doi":"10.1007/s00161-024-01350-z","DOIUrl":"10.1007/s00161-024-01350-z","url":null,"abstract":"<div><p>Purely compressed shells are often elegant and highly efficient structural forms, but this leanness may create risk if they are subjected to unexpected patterns and magnitudes of loading, such as may arise due to seismic events. In the same way that historic masonry structures were designed to sustain loads by activating purely compressive force paths, a modern metamaterial can be designed for specific purposes following the same logic. Conventional analysis methods for compression-only shells and vaults, often developed for masonry structures, have tended not to model combined vertical and horizontal loads directly. This has created a significant challenge for engineers assessing historic vaults or designing new shells. To address this gap, this paper presents an enhanced method based on membrane equilibrium analysis (MEA) and the static theorem of limit analysis. This approach is the first application of MEA to directly consider vertical and horizontal body forces acting on a compression-only shell through a parametric formulation of an Airy stress function. The method is applied to a case study of a sail vault subjected to vertical and horizontal loads. Moreover, it is demonstrated how this approach can be used to define iso-resistant shapes that offer more sustainable design options while preserving structural capacity.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01350-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939206","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 comprehensive study of simulated cyclic indentation response of linear viscoelastic materials","authors":"Olga Smerdova","doi":"10.1007/s00161-024-01352-x","DOIUrl":"10.1007/s00161-024-01352-x","url":null,"abstract":"<div><p>This paper presents and analyzes the cyclic indentation response of a linear viscoelastic material over the entire time range of the relaxation processes using conical or spherical indenters. Finite Element simulations of cyclic indentation on two Generalized Maxwell materials with different relaxation spectra were performed. A variety of cyclic responses to indentation were generated and analyzed using an analytical method based on elastic contact. It is shown that the elastic contact depth and contact stiffness from the loading curves should be used to identify the relaxation modulus corresponding to the time of loading. The stabilization of the loop has also been studied through the energy ratio, a parameter that describes the evolution of the dissipated energy with cycles. A simple time shift between cyclic creep and monotonous indentation creep of a linear viscoelastic material is demonstrated. The simulated indentation curves and the parameters derived from them were found to be qualitatively similar to the experimental cyclic indentation data on HDPE polymer at different loading rates. Assuming that the first loading is affected by plasticity due to the use of a sharp indenter, a correction was suggested to obtain the elastic relaxation modulus from the experiments. The values of the modulus identified in this way for HDPE compared well with the relaxation modulus identified for this material from previous cyclic tensile experiments. The small discrepancy was attributed to the non-linear viscoelasticity or the viscoplasticity of the polymer.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939207","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":"Dynamic properties of the structures with three level of symmetry","authors":"Sorin Vlase,&nbsp;Andreas Öchsner,&nbsp;Marin Marin","doi":"10.1007/s00161-024-01337-w","DOIUrl":"10.1007/s00161-024-01337-w","url":null,"abstract":"<div><p>In the field of mechanical engineering, structural systems that can present different types of symmetries are frequently encountered. The choice of such solutions with symmetries is generally the result of considering factors such as reducing design and production costs, logistical considerations, but also for aesthetic reasons. The existence of these symmetries inside some structures brings new properties in the mechanical behavior and can be useful in simplifying the calculation, in the static and dynamic case. Symmetries can bring new properties when the problem of studying vibrations is raised. Thus, the dynamic analysis time can be reduced and the designer can get a quick picture of the behavior of the structure in operation. The paper aims to study a special situation of symmetry that can be encountered in engineering practice, namely the existence of three planes of symmetry within a structure. Such structures can be found frequently in the field of mechanical engineering but also in the construction of buildings. The presented properties can contribute to the reduction of dynamic analysis time and therefore to the reduction of design costs. An example from real life is analyzed in the work, highlighting the listed properties.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 2","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01337-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142939208","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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":"On the formulation of evolutive laws and complementarity conditions for non-smooth elastoplastic materials","authors":"Fabio De Angelis","doi":"10.1007/s00161-024-01341-0","DOIUrl":"10.1007/s00161-024-01341-0","url":null,"abstract":"<div><p>In the present work a formulation of evolutive laws and complementarity conditions in non-smooth elastoplasticity is discussed. The treatment addresses the problem of non-smooth elastoplasticity which is represented by functions characterized by singularities and defined by non-smooth yielding limit conditions and non-differentiable functions. The mathematical theory of subdifferential calculus is properly advocated to provide the suitable mathematical framework in order to treat non-differentiable functions and non-smooth problems. Extended expressions of evolutive laws and complementarity conditions in non-smooth elastoplasticity are illustrated within the adopted generalized mathematical treatment. Relations between the presented mathematical formulations and the expressions in classical elastoplasticity are pointed out and discussed. The proposed treatment has significant advantages since it provides a geometrical framework to the maximum dissipation principle for non-smooth problems in elastoplasticity. Furtherly, the proposed treatment gives insights in the interpretation of the adopted geometrical framework for different types of evolutive laws for new materials and solids such as for instance in some types of new metamaterials with non-smooth constitutive behavior. In addition, the present formulation is also useful in the design of metamaterials, such as pantographic ones, where the plasticity of the pivots is relevant.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2025-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142912797","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":"Behaviour of solutions for a thermoelastic Cosserat medium with temperature gradients","authors":"Marin Marin,&nbsp;Sorin Vlase,&nbsp;Andreas Öchsner,&nbsp;O. M. Hapenciuc","doi":"10.1007/s00161-024-01355-8","DOIUrl":"10.1007/s00161-024-01355-8","url":null,"abstract":"<div><p>Our study falls within the linear theory of thermoelasticity of Cosserat media. Unlike other works that fall into similar contexts and that use the entropy balance low, our approach is based on an entropy production inequality. The entropy flux tensor is introduced and thermoelastic media are considered for which the stress tensors are dependent on the temperature gradients. In this way, a fourth-order differential equation satisfied by temperature is obtained. In this context the mixed initial-boundary value problem is formulated for which an uniqueness result regarding the solution of this problem is proven. Also, a continuous dependence result is deduced for the solution of the mixed formulated problem with regard to the charges and the initial values.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"37 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-024-01355-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142888051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}