Continuum Mechanics and Thermodynamics最新文献_第2页

Dynamic Green’s functions for lattice systems with frontiers possessing contrasting periodicity and material properties 具有不同周期性和材料性质边界的晶格系统的动态格林函数

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-17 DOI: 10.1007/s00161-026-01493-1

E. Aktunc, M. J. Nieves, G. S. Mishuris

引用次数: 0

Shell energies derived from three-dimensional isotropic strain-gradient elasticity 由三维各向同性应变梯度弹性导出壳能

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-07 DOI: 10.1007/s00161-026-01523-y

C. Balitactac, Y. Canzani, R. S. Hallyburton, J. Mott, C. Rodriguez

{"title":"Shell energies derived from three-dimensional isotropic strain-gradient elasticity","authors":"C. Balitactac, Y. Canzani, R. S. Hallyburton, J. Mott, C. Rodriguez","doi":"10.1007/s00161-026-01523-y","DOIUrl":"10.1007/s00161-026-01523-y","url":null,"abstract":"<div><p>We derive a class of two-dimensional shell energies for thin elastic bodies exhibiting small-length scale effects modeled via strain-gradient elasticity. Building on the final author’s earlier work on plate models, the kinetic and stored surface energies arise as the leading cubic order-in-thickness expressions for three-dimensional kinetic energies with velocity-gradient effects and a broad class of isotropic stored energies, each possessing an intrinsic length scale <span>(ell )</span>. These include both classical Toupin–Mindlin and more recent dilatational strain-gradient elastic stored energies. A key insight of this work is that consistent asymptotic reductions of strain-gradient theories necessarily begin at cubic order-in-thickness due to the natural scaling assumption <span>(ell = O(h))</span> where <i>h</i> is the thickness of the body. In the limit as the intrinsic length scales vanish, the theory reduces to Koiter’s classical shell energy. We illustrate the theory using the shell energy derived from dilatational strain-gradient elasticity, computing the body force, edge tractions and edge double force densities required to support a variety of finite deformations.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148923300","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

On a coupled problem of chemo-mechanics with a viscoelastic reaction product 粘弹性反应产物的化学-力学耦合问题

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-05 DOI: 10.1007/s00161-026-01518-9

Alexander B. Freidin, Aleksandra B. Ivanova

{"title":"On a coupled problem of chemo-mechanics with a viscoelastic reaction product","authors":"Alexander B. Freidin, Aleksandra B. Ivanova","doi":"10.1007/s00161-026-01518-9","DOIUrl":"10.1007/s00161-026-01518-9","url":null,"abstract":"<div><p>A coupled problem “chemistry–mechanics–diffusion” is discussed in an elastic–viscoelastic framework. The competition between chemical and mechanical influences on the chemical reaction is demonstrated and studied. A chemical reaction between an elastic solid constituent and a diffusing constituent is considered. As a result of the reaction, the elastic constituent transforms into a viscoelastic one, which is described by the standard linear solid model (SLSM). The reaction is localized at the reaction front and is accompanied by volume expansion which, in turn, leads to stresses affecting the velocity of the front propagation. Reaction front kinetics is described based on the notion of a chemical affinity tensor. A plane strain problem with a planar reaction front is considered. The system of equations, describing the joint processes of the propagation of the reaction front and the relaxation of stresses generated by the transformation and external strains is derived. The restrictions on stresses at which the front can propagate are found. To cover the range of changes in the viscosity coefficient, the elastic and relaxation limits are introduced for the SLSM. The various regimes of the front propagation and stress relaxation are distinguished. Special attention is paid to the discussion of impossibility of unblocking the blocked front during further relaxation of stress. Finally, a quasi-equilibrium mode of the front propagation is considered. A characteristic number similar to the Damköhler number is introduced to compare the effect of the rate of the diffusion and the reaction rate on the propagation velocity of the front. In general, the paper demonstrates a variety of coupled behaviors of the reaction front and relaxing stresses, depending on the elastic parameters of solid constituents, the viscosity coefficient of the transformed material, the chemical energies of the constituents of the reaction and external strains.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894403","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

On large displacements of curved slender beams: novel rate elasticity and numerical experiments 弯曲细长梁大位移：新型速率弹性力学及数值试验

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-05 DOI: 10.1007/s00161-026-01512-1

Daniele Ussorio, Raffaele Barretta

{"title":"On large displacements of curved slender beams: novel rate elasticity and numerical experiments","authors":"Daniele Ussorio, Raffaele Barretta","doi":"10.1007/s00161-026-01512-1","DOIUrl":"10.1007/s00161-026-01512-1","url":null,"abstract":"<div><p>Non-linear mechanics of elastic <span>Bernoulli</span>-<span>Euler</span> curved beams is investigated within 4-D spacetime geometric framework. Large displacements of such structures are addressed by novel rate elasticity methodology, avoiding finite deformation approaches and linearization of nonlinear kinematic relations common in literature. The variational rate virtual power principle (RVPP) is formulated and ensuing notion of effective stress rate leveraged. A rate form of nonlinear elasticity for planar curved beams is consequently established, and application of the RVPP yields the consistent elastic stiffness operator governing the structural evolution problem. Straightforward and computationally efficient incremental procedure is implemented in the brand new automatic program named REBUV. An enhanced version of the <span>Riks</span>-<span>Crisfield</span> arc-length method is developed by exploiting the derived expression of the stiffness operator and is successfully applied to the investigated highly nonlinear benchmark problems. Comparison with analytical finite deformation approaches and established computational methods is carried out, supporting effectiveness of the presented approach. This paper provides significant extension to curved beams of a methodology proved capable of solving problems and limitations affecting conventional analytical and computational approaches.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01512-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894404","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

Extended tolerance modelling of dynamic problems for thin transversally graded cylindrical shells 横向梯度圆柱薄壳动力问题的扩展公差建模

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-02 DOI: 10.1007/s00161-026-01525-w

B. Tomczyk, M. Gołąbczak, M. Nagirniak

{"title":"Extended tolerance modelling of dynamic problems for thin transversally graded cylindrical shells","authors":"B. Tomczyk, M. Gołąbczak, M. Nagirniak","doi":"10.1007/s00161-026-01525-w","DOIUrl":"10.1007/s00161-026-01525-w","url":null,"abstract":"<div><p>The objects of consideration are thin, linearly elastic, Kirchhoff–Love-type, open, circular cylindrical shells having a functionally (transversally) graded macrostructure and a tolerance-periodic microstructure in the circumferential direction. At the same time, the shells have constant geometrical, elastic and inertial properties in the axial direction. The aim of this contribution is to formulate and discuss <i>a new, mathematical, averaged, non-asymptotic model for the analysis of selected dynamic problems for such shells</i>. This, so-called, <i>general</i> (<i>or extended</i>) <i>tolerance model</i> will be derived by applying <i>a certain extended version of the well-known tolerance modelling technique.</i> The starting equations are the well-known governing equations of linear Kirchhoff–Love theory of thin, elastic cylindrical shells. For the functionally graded shells under consideration, the starting equations have highly oscillating, non-continuous and tolerance-periodic coefficients in the circumferential direction, whereas <i>equations of the proposed model have continuous and slowly changing coefficients in this direction</i>. Moreover, some <i>of these coefficients depend on a microstructure size</i>. It means that the proposed model makes it possible to study the effect of a microstructure size on the shell dynamics (<i>the length-scale effect</i>). The main similarities and differences between <i>the general tolerance model</i> derived here and <i>the corresponding</i>, <i>known</i>, <i>standard tolerance model</i> derived by means of the classical tolerance modelling technique will be discussed. It will be shown that in the framework of both the general and standard tolerance models <i>not only the fundamental cell-independent, but also the new, additional, cell-dependent free vibration frequencies can be derived and analysed.</i></p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01525-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148883492","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

Internal thermo-elasticity and band gap in the mass-in mass metamaterial 质量-质量超材料的内部热弹性和带隙

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-09-02 DOI: 10.1007/s00161-026-01527-8

A. V. Porubov, A. M. Krivtsov

引用次数: 0

Galerkin-projected evolution equations for reduced 1D thermal stress resultant model derived from transient 2D thermoelasticity 二维瞬态热弹性的一维热应力合成模型的galerkin投影演化方程

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-08-29 DOI: 10.1007/s00161-026-01524-x

Emin Kocbay

{"title":"Galerkin-projected evolution equations for reduced 1D thermal stress resultant model derived from transient 2D thermoelasticity","authors":"Emin Kocbay","doi":"10.1007/s00161-026-01524-x","DOIUrl":"10.1007/s00161-026-01524-x","url":null,"abstract":"<div><p>A framework for the dimensional reduction of transient thermo-structural problems is presented in which the cross-sectional heat diffusion is encoded as an autonomous evolution system for the thermal stress resultants. A through-the-thickness temperature ansatz satisfying the essential boundary conditions is postulated and the heat equation is projected via a weighted-residual Galerkin method, yielding coupled first-order evolution equations for the thermally induced membrane force and bending moment. The resulting 1D model requires no resolved cross-sectional temperature computation at runtime, yet preserves the diffusive time scales of the parent 2D problem; the structural response follows from Euler–Bernoulli beam theory driven by the evolved thermal resultants. The projection procedure is methodologically general; its accuracy is demonstrated here for a homogeneous rectangular beam under mixed Dirichlet–Neumann thermal conditions, for which an exact 2D Fourier series solution is derived independently. A three-way numerical validation against the exact solution and a high-fidelity 2D finite element reference confirms that the reduced 1D model reproduces deformationfields to within a few percent, although the reconstructed cross-sectional stress underestimates the peak thermal eigenstress by approximately 43% due to the quadratic temperature approximation. For the present constant-coefficient problem, the reduced evolution system admits a closed-form eigenfunction expansion, rendering the model entirely mesh-free and yielding wall-clock speedups exceeding three orders of magnitude; for variable-coefficient or nonlinear problems, the dimensional reduction still provides substantial computational savings.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01524-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148894406","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

A note on representation-dependent Onsager closures for thermo-diffusive coupling 热扩散耦合中依赖表征的Onsager闭包的注释

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-08-27 DOI: 10.1007/s00161-026-01511-2

Andreas Prahs

{"title":"A note on representation-dependent Onsager closures for thermo-diffusive coupling","authors":"Andreas Prahs","doi":"10.1007/s00161-026-01511-2","DOIUrl":"10.1007/s00161-026-01511-2","url":null,"abstract":"<div><p>Non-isothermal diffusion can be formulated within different mixture-level approaches that account for diffusion-related transport either through an extended energy flux or through an extended entropy flux. This note compares two prominent approaches: the Gurtin approach, in which diffusion enters the energy balance through an additional diffusive energy flux, and the Müller approach, in which the classical energy balance is retained while diffusion enters through an extended entropy flux. The comparison clarifies how the way diffusion-related transport is represented in each approach and the adopted thermodynamic force basis affect a subsequent Onsager-type closure. In the selected Müller-type force basis, the diffusion-related thermodynamic force contains a temperature-gradient contribution. Consequently, a diagonal Onsager closure in this basis yields a diffusion flux with an apparent Soret-type contribution while the heat flux remains Fourier-like. In the selected Gurtin-type force basis, the corresponding diagonal closure yields uncoupled Fourier and Fick laws, whereas thermo-diffusive coupling appears through non-diagonal Onsager blocks. Thus, the apparent Soret/Dufour structure follows from how diffusion-related transport is represented in the mixture-level approach considered and from the basis of thermodynamic forces used for the Onsager closure. Although diffusion in solids provides the main motivation, the derivation does not rely on a specific constitutive law.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01511-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148838036","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

A note on relations between convexity and concavity of thermodynamic functions 热力学函数的凹凸关系的注解

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-08-25 DOI: 10.1007/s00161-026-01522-z

Mária Lukáčová-Medvid’ová, Ferdinand Thein, Gerald Warnecke, Yuhuan Yuan

{"title":"A note on relations between convexity and concavity of thermodynamic functions","authors":"Mária Lukáčová-Medvid’ová, Ferdinand Thein, Gerald Warnecke, Yuhuan Yuan","doi":"10.1007/s00161-026-01522-z","DOIUrl":"10.1007/s00161-026-01522-z","url":null,"abstract":"<div><p>The paper is concerned with proving the equivalence of convexity or concavity properties of thermodynamic functions, such as energy and entropy, depending on different sets of variables. These variables are the basic thermodynamic state variables, specific state variables or the densities of state variables that are used in continuum mechanics. We prove results for transformations of variables and functions in conjunction with convexity properties. We are concerned with convexity, strict convexity, positive definite Hessian matrices and the analogous forms of concavity. The main results are equivalence relations for these properties between functions. These equivalences are independent of the equations of state since they only use general properties of them. The results can be used for instance to easily prove that the entropy density function for the Euler equations in conservative variables in three space dimensions is strictly concave or even has a negative definite Hessian matrix. Further, we show how various equations of state imply these properties and how these properties are relevant to mathematical analysis.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00161-026-01522-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837508","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

Tolerance envelopes of P-wave band gaps in 1D periodic concrete–rubber layered foundations 一维周期混凝土-橡胶层状基础p波带隙的公差包络

IF 3 4区工程技术

Continuum Mechanics and Thermodynamics Pub Date : 2026-08-19 DOI: 10.1007/s00161-026-01517-w

Vladyslav Danishevskyy, Denys Volchok, Dmytro Bezverkhyi, Illia Kuchyn

{"title":"Tolerance envelopes of P-wave band gaps in 1D periodic concrete–rubber layered foundations","authors":"Vladyslav Danishevskyy, Denys Volchok, Dmytro Bezverkhyi, Illia Kuchyn","doi":"10.1007/s00161-026-01517-w","DOIUrl":"10.1007/s00161-026-01517-w","url":null,"abstract":"<div><p>Periodic concrete-rubber layered foundations can act as mechanical filters that open low-frequency band gaps and thus provide seismic and vibration isolation. Their engineering performance, however, depends on how sensitive these band gaps are to unavoidable material variability. This study presents a tolerance analysis of a one-dimensional transfer-matrix model of a periodic two-layer cell under longitudinal excitation. Using the Floquet-Bloch approach, the boundaries of the first two band gaps and the frequency of maximum spatial attenuation were identified. A parametric sweep with ± 20% variations in layer densities and Young’s moduli was then used to construct tolerance envelopes for these frequency characteristics. The results reveal a clear parameter hierarchy governed by the strong stiffness contrast between concrete and rubber. Variations in concrete stiffness produce a considerably small shift in the band-gap metrics. In contrast, change of rubber stiffness causes an almost uniform frequency scaling, leading to shifts of about 10%. The densities of both phases independently control different band-gap edges. The tolerance information is additionally expressed as possibility distributions of the band-gap metrics by treating each material parameter as a triangular fuzzy number, and the corresponding defuzzified expected values are reported. These results indicate that, within the adopted model, the dominant sources of variability are the rubber stiffness and the densities of both phases, whereas the influence of the concrete stiffness is nearly negligible in the investigated frequency range.</p></div>","PeriodicalId":525,"journal":{"name":"Continuum Mechanics and Thermodynamics","volume":"38 5","pages":""},"PeriodicalIF":3.0,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148768965","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