Continuum Mechanics and Thermodynamics最新文献_第10页

Nonlinear and nonlocal models of heat conduction in continuum thermodynamics 连续介质热力学中的非线性和非局部热传导模型

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-01-13 DOI: 10.1007/s00161-025-01443-3

Claudio Giorgi, Federico Zullo

{"title":"Nonlinear and nonlocal models of heat conduction in continuum thermodynamics","authors":"Claudio Giorgi, Federico Zullo","doi":"10.1007/s00161-025-01443-3","DOIUrl":"10.1007/s00161-025-01443-3","url":null,"abstract":"<div><p>The aim of this paper is to develop a general constitutive scheme within continuum thermodynamics to describe the behavior of heat flow in deformable media. Starting from a classical thermodynamic approach, the rate-type constitutive equations are defined in the material (Lagrangian) description where the standard time derivative satisfies the principle of objectivity. All constitutive functions are required to depend on a common set of independent variables and to be consistent with thermodynamics. The statement of the Second Law is formulated in a general nonlocal form, where the entropy production rate is prescribed by a non-negative constitutive function and the extra entropy flux obeys a no-flow boundary condition. The thermodynamic response is then developed based on a variant of the Coleman-Noll procedure. In the local formulation, the free energy potential and the rate of entropy production function are assumed to depend on temperature, temperature gradient and heat-flux vector along with their time derivatives. This approach results in rate-type constitutive equations for the heat-flux vector that are intrinsically consistent with the Second Law and easily amenable to analysis. Many linear and nonlinear models of the rate type are recovered (e.g., Cattaneo-Maxwell’s, Jeffreys-like, Green-Naghdi’s, Quintanilla’s and Burgers-like). Owing to the (weakly) nonlocal formulation of the second law, weakly nonlocal models based on the heat-flux vector and its gradients are obtained within this (classical) thermodynamic framework. In particular, the nonlocal Guyer-Krumhansl model and some nonlinear generalizations devised by Cimmelli and Sellitto are obtained. Finally, we propose a new model where the heat flux dependence on temperature gradients is allowed up to second-order.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 2","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-01-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145950767","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}

引用次数: 0

Multiscale lubrication in rolling and sliding thermo-elastoplastic line contact involving the sandwich and physically adsorbed molecule films 含夹心和物理吸附分子膜的滚动和滑动热弹塑性线接触中的多尺度润滑

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-01-08 DOI: 10.1007/s00161-025-01434-4

Yongbin Zhang

{"title":"Multiscale lubrication in rolling and sliding thermo-elastoplastic line contact involving the sandwich and physically adsorbed molecule films","authors":"Yongbin Zhang","doi":"10.1007/s00161-025-01434-4","DOIUrl":"10.1007/s00161-025-01434-4","url":null,"abstract":"<div><p>The mathematical analysis is presented for calculating the film thickness at the contact center in the hydrodynamic lubricated rolling and sliding steel line contact with the equivalent contact radius on the scale of 100mm by considering the contact thermal and macroscopic elastoplastic deformations where the film thickness is ultra low so that the adsorbed layer-continuum fluid-adsorbed layer sandwich film occurs in the inlet zone and the non-continuum physically adsorbed molecule film occurs in the flattened contact area. The calculation was made for widely varying heavy loads, slide-roll ratios and contact hardness. It was found that the lubrication in the studied contact is qualitatively different from the classical elastohydrodynamic theory description in the condition of very low film thicknesses. The effect of the adsorbed layer makes the film thickness maintained even only with several fluid molecule sizes but much higher than the classical elastohydrodynamic theory calculation. The strong contact-fluid interaction yields the significantly higher film thickness than the weak or medium contact-fluid interactions. Both the increase of the slide-roll ratio and the reduction of the contact hardness rapidly reduce the central film thickness owing to the contact thermal and plastic deformations. The variations of the lubricating film thickness at the contact center with the rolling speed and load no longer follow classical elastohydrodynamic theories because of the strong effects of the adsorbed layer and the contact thermo-elastoplastic deformations. For heavy loads, high rolling speeds and appreciable slide-roll ratios, the effect of the contact thermo-elastoplastic deformation not only largely reduces the central film thickness but also greatly increases the sensitivity of the central film thickness to the load variation.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930626","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}

引用次数: 0

Time reversal and the heat equation 时间反转和热方程

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-01-07 DOI: 10.1007/s00161-025-01441-5

Richard Kaufman, Michael te Vrugt

{"title":"Time reversal and the heat equation","authors":"Richard Kaufman, Michael te Vrugt","doi":"10.1007/s00161-025-01441-5","DOIUrl":"10.1007/s00161-025-01441-5","url":null,"abstract":"<div><p>According to standard thermodynamics, heat spontaneously propagates from hot to cold reservoirs as time progresses towards the future. Consequently, one might assume that for the purpose of describing thermodynamic machines, a world in which heat spontaneously propagates from cold to hot (i.e., a world in which the heat equation has a different sign) would be simply the time reversal of our world. In this article, we explain why this is not the case. Thermodynamics is characterized by the universal approach to equilibrium states from arbitrary initial conditions, such that the final state of a thermodynamic equilibration process does not contain the information necessary to recreate the initial state. In particular, the initial state cannot be recreated by evolving the final state via the rule “heat always propagates from cold to hot”, as this rule would lead to temperature gradients on arbitrarily small scales (which is not a feature that the initial state will generally have had). This toy problem illustrates some general features of the role of the direction of time in thermodynamics. These features are discussed mathematically using the Mori-Zwanzig projection operator formalism.\u0000</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-01-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-025-01441-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145930223","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}

引用次数: 0

Memory-dependent wave dynamics in micropolar thermoelastic solid with Klein-Gordon nonlocal effect 具有Klein-Gordon非局域效应的微极热弹性固体的记忆依赖波动动力学

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-01-06 DOI: 10.1007/s00161-025-01447-z

Abhik Sur, Marin Marin, Sudip Mondal, Murat Yaylacı, Soumik Das

{"title":"Memory-dependent wave dynamics in micropolar thermoelastic solid with Klein-Gordon nonlocal effect","authors":"Abhik Sur, Marin Marin, Sudip Mondal, Murat Yaylacı, Soumik Das","doi":"10.1007/s00161-025-01447-z","DOIUrl":"10.1007/s00161-025-01447-z","url":null,"abstract":"<div><p>This study develops a novel thermoelastic model for an unbounded micropolar half-space produced by a magnetic field having constant intensity. A novel spatiotemporal nonlocal elasticity theory is proposed by taking into account one dynamical scalar nonlocal kernel. In line with the theory, an isotropic nonlocal elasticity model of the Klein-Gordon type is formulated, incorporating both a characteristic internal length scale and an essential internal time scale parameter. The Moore-Gibson-Thompson theory, which is adjacent to the memory responses, governs the micropolar medium’s heat transport mechanism. While the boundary is free of traction, the micropolar medium experiences a time-harmonic thermal loading. The solutions to the governing equations have been obtained using Laplace and Fourier transform techniques. Numerical estimates of each of the physical fields have been performed for the analysis of the effectiveness of the nonlocality parameters of space and time, the micropolar parameters and the time-delay also. The significance of various kernels involved in the heat conduction process and the influence of magnetic field have also been concluded.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2026-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145903760","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}

引用次数: 0

Anti-plane surface waves localized in multi-layered interfaces in square-lattice structures 反平面表面波定域于方晶格结构的多层界面中

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-01-06 DOI: 10.1007/s00161-025-01445-1

Emanuele Reccia

引用次数: 0

On the mathematical foundation of a decoupled directional distortional hardening model for metal plasticity in the framework of rational thermodynamics 合理热力学框架下解耦金属塑性定向变形硬化模型的数学基础

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2025-12-29 DOI: 10.1007/s00161-025-01440-6

Md Mahmudur Rahman, Md Mahmudul Hasan Pathik, Nazrul Islam

{"title":"On the mathematical foundation of a decoupled directional distortional hardening model for metal plasticity in the framework of rational thermodynamics","authors":"Md Mahmudur Rahman, Md Mahmudul Hasan Pathik, Nazrul Islam","doi":"10.1007/s00161-025-01440-6","DOIUrl":"10.1007/s00161-025-01440-6","url":null,"abstract":"<div><p>This study proposes a modification to the yield condition that addresses the mathematical constraints inherent in the Directional Distortional Hardening models developed by Feigenbaum and Dafalias. The modified model resolves both the mathematical inconsistency found in the ’complete model’ and the limitations of the ‘<i>r</i>-model’. In the complete model, inconsistency arises between the distortional term in the yield surface and the plastic part of the free energy in the absence of kinematic hardening. Additionally, the ‘<i>r</i>-model’ fails to capture the flattening of the yield surface in the reverse loading direction due to the absence of a fourth-order anisotropic tensor structure in the distortional term. To address these issues, the proposed model introduces a decoupled distortional hardening term in the yield function. This modification enables the simultaneous representation of both flattening and sharpening of the yield surface, and permits isotropic hardening with distortion even without kinematic hardening. A consistent mathematical formulation based on rational thermodynamics and a corresponding numerical algorithm are also developed, establishing a foundation for future experimental investigations and model validation.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145847296","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}

引用次数: 0

Generalization of Mansfield’s alternative expression of the biharmonic operator 双调和算子的Mansfield替代表达式的推广

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2025-12-08 DOI: 10.1007/s00161-025-01439-z

Gaëtan Hello

{"title":"Generalization of Mansfield’s alternative expression of the biharmonic operator","authors":"Gaëtan Hello","doi":"10.1007/s00161-025-01439-z","DOIUrl":"10.1007/s00161-025-01439-z","url":null,"abstract":"<div><p>The biharmonic operator naturally emerges in the modeling of various physical phenomena and plays, in particular, a prominent role in linear elasticity. Understanding its properties is, therefore, crucial in the consolidation of mechanical science. In his 1984 article, E.H. Mansfield introduced an alternative differential operator that can replace the Laplacian in the expression of the homogeneous biharmonic equation in <span>(mathbb {R}^2)</span>. Despite its potential for further investigations and applications, this result has remained unnoticed so far. The present work generalizes and explores some of the properties of Mansfield’s operator through analytical derivations and symbolic computations. With the proposed generalization of the operator in <span>(mathbb {R}^n)</span>, its essential properties are established, and its expressions in five new coordinate systems are derived. The unique status of the Laplacian and Mansfield’s operator in expressing biharmonic equations in <span>(mathbb {R}^2)</span> is assessed. The interrelation between the kernels of the biharmonic, harmonic, and Mansfield’s operators is demonstrated. Eventually, the structure of the biharmonic terms of the classical Michell solution is clarified through the introduction of the operator. In addition to popularizing and generalizing the original work of E.H. Mansfield, the results and methodologies described in this article can initiate further research, such as the study and extensions of the generalized operator, the reexamination of classical solutions to elasticity problems, and the definition of new polyharmonic operators.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145696998","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}

引用次数: 0

Conductivity and elastic stiffness of isotropic polycrystal featuring general imperfect grain-to-grain bonding 具有一般不完美晶粒键合的各向同性多晶的电导率和弹性刚度

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2025-12-01 DOI: 10.1007/s00161-025-01437-1

Volodymyr I. Kushch

{"title":"Conductivity and elastic stiffness of isotropic polycrystal featuring general imperfect grain-to-grain bonding","authors":"Volodymyr I. Kushch","doi":"10.1007/s00161-025-01437-1","DOIUrl":"10.1007/s00161-025-01437-1","url":null,"abstract":"<div><p>The micromechanical models of the isotropic conductive and elastic polycrystalline solid featuring a general imperfect interface have been developed. In terms of conductivity, the imperfect grain bonding conditions assume a jump of temperature and normal heat flux across the interface. In terms of elasticity, they allow for a jump in displacement and normal traction vectors. The self-consistent homogenization scheme for a polycrystalline solid is formulated in terms of the induced dipole moments and property distribution tensors. The explicit formulas for the effective conductivity and elastic moduli of polycrystalline material are derived from the multipole expansion solution to the model problems under the zero dipole moment condition of the imperfectly bonded inhomogeneity in the effective medium. As a practical application of the developed model, the conductivity and elastic stiffness of the intergranular boundaries of polycrystalline cubic boron nitride are evaluated using the laboratory test data on its macroscopic thermal conductivity and elastic moduli. The interface parameters are found to be strongly dependent on the sintering temperature and hence can serve as an indicator of the consolidation degree of a sintered polycrystalline solid.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145645262","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}

引用次数: 0

WAXD investigations on the effect of loading history on strain-induced crystallization for a fully formulated filled natural rubber WAXD研究了加载历史对全配方填充天然橡胶应变诱导结晶的影响

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2025-11-28 DOI: 10.1007/s00161-025-01435-3

Anthony Le Bihan, Yann Marco, Vincent Le Saux, Laurent Chazeau, Jean-Marc Chenal, Iona Warneboldt, Clement Champy, Pierre Charrier

{"title":"WAXD investigations on the effect of loading history on strain-induced crystallization for a fully formulated filled natural rubber","authors":"Anthony Le Bihan, Yann Marco, Vincent Le Saux, Laurent Chazeau, Jean-Marc Chenal, Iona Warneboldt, Clement Champy, Pierre Charrier","doi":"10.1007/s00161-025-01435-3","DOIUrl":"10.1007/s00161-025-01435-3","url":null,"abstract":"<div><p>Modelling crystallization under stretch is a key topic for fatigue design of rubber-like antivibration parts. Nevertheless, most of the academic studies consider unfilled natural rubber while the industrial materials are fully formulated compounds filled with carbon blacks and exhibit a highly dissipative visco-elastic behavior. This behavior is very useful for antivibration systems but complicates the characterization and modelling of the phase change, as the addition of fillers and additives brings in numerous additional dissipation sources and intricates the time effects on the thermomechanical response and on crystallization. In this study, we use wellresolved WAXD synchrotron measurements to perform in situ measurements under various mechanical protocols. The objective is to characterize the evolution of the triplet {strain, stress, crystallinity index}, and their derivatives, for various time and mechanical solicitations. First, classic load/unload tension tests over a range of strain rates leading to non-equilibrium cases are achieved, to serve as a reference database on the compound studied. Then, a multi-relaxation cyclic test combining static and monotonic steps is applied in order to describe the crystallization state and kinetics around a relaxed state (sometimes called “equilibrium hysteresis”). The results provide a precious database to identify or challenge the existing thermodynamic models, for conditions seldom met in the literature: fully formulated material and various mechanical loading time histories.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611136","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}

引用次数: 0

Analysis of nonlocal thermoviscoelastic diffusion coupling in fractal media for non-integer dimensional spaces 非整数维空间分形介质中的非局部热粘弹性扩散耦合分析

IF 2.2 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2025-11-27 DOI: 10.1007/s00161-025-01431-7

Gulshan Makkad, Lalsingh Khalsa, Abhik Sur, Vinod Varghese

{"title":"Analysis of nonlocal thermoviscoelastic diffusion coupling in fractal media for non-integer dimensional spaces","authors":"Gulshan Makkad, Lalsingh Khalsa, Abhik Sur, Vinod Varghese","doi":"10.1007/s00161-025-01431-7","DOIUrl":"10.1007/s00161-025-01431-7","url":null,"abstract":"<div><p>Motivated by the abundance of fractals within the natural world, the present study deals with a novel extension of classical thermoelasticity to fractal materials by formulating a generalized vector calculus in non-integer dimensional spaces. Fractal media, characterized by complex geometries and anomalous transport behavior, are modeled as continua with non-integer mass dimensions. We develop a comprehensive thermoviscoelastic diffusion framework that incorporates nonlocal elasticity, fractional-order derivatives, and a three-phase-lag heat conduction model. The physical system considered is an infinitely extended Kelvin–Voigt viscoelastic medium with a cylindrical cavity subjected to time-dependent thermal and chemical boundary conditions. The governing equations are transformed into the Laplace domain and solved analytically, with time-domain solutions obtained via Zakian numerical inversion. Numerical simulations reveal the significant influence of fractal geometry, nonlocal effects, and fractal operators on temperature distribution, stress evolution, and diffusion behavior. These findings offer valuable insights for the design of advanced materials and nanoscale systems where classical models fall short.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 1","pages":""},"PeriodicalIF":2.2,"publicationDate":"2025-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145611138","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}

引用次数: 0