Journal of Elasticity最新文献

{"title":"On the Balance of Angular Momentum and the Balances of Director Momentum in a Deformable Cosserat Continuum","authors":"M. B. Rubin","doi":"10.1007/s10659-026-10213-4","DOIUrl":"10.1007/s10659-026-10213-4","url":null,"abstract":"<div><p>This note discusses the balance of angular momentum and the balances of director momentum in a small deformation model of a deformable Cosserat continuum. It is shown that for small deformation elastic response, the deformable Cosserat model in Rubin [14] and the theory of microstructure in Mindlin [8] both satisfy the balance of angular momentum and both predict the same response for the same given strain energy function. This result corrects a discussion in Rubin [14] (Appendix C) related to equations for the microstretch theory in Eringen [3] and the microstructure theory in Mindlin [8].</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-06-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148323205","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":"New Approach for Elastic Collisions with Singular Stress Functions","authors":"Toyohiko Aiki,&nbsp;Chiharu Kosugi","doi":"10.1007/s10659-026-10211-6","DOIUrl":"10.1007/s10659-026-10211-6","url":null,"abstract":"<div><p>A collision of a rubber rod to a hard floor is regarded as a simple example of obstacle problems for elastic material. In this article we have proposed a new mathematical model for the collision phenomenon by applying beam equations with singular stress functions, which is investigated in our recent works. As in the works we have established a mathematical method to deal with the singular stress function. Here, we demonstrate the validity of our modeling through observation to the numerical results. Also, we present existence and uniqueness results of the model given as initial and boundary value problems.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148261883","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":"The Elastic Fluctuation Tensor: Quantifying Stochastic Fluctuations of the Apparent Stiffness of Non-representative Microstructure Volume Elements","authors":"Maximilian Krause,&nbsp;Matti Schneider","doi":"10.1007/s10659-026-10209-0","DOIUrl":"10.1007/s10659-026-10209-0","url":null,"abstract":"<div><p>We introduce the elastic fluctuation tensor to quantify the stochastic fluctuation of the apparent stiffness of finite microstructural volume elements. Typically, in computational homogenization using volume elements of finite size, the apparent stiffness converges to the effective stiffness as the volume element size tends to infinity, such that the material can be approximated as homogeneous on the macroscale. For volume elements of finite size, the apparent stiffness fluctuates on the macroscale. In thermal conductivity homogenization, the fluctuations can be quantified using the fourth-order fluctuation tensor, which computes as the infinite-volume limit of the apparent conductivity covariance, rescaled with the volume. The fluctuation tensor for linear elasticity is of tensor order eight. We show that this fluctuation tensor inherits the symmetry of its ensemble. For instance, rotational statistical symmetry of the ensemble leads to isotropy of the elastic fluctuation tensor. Using results from group representation theory, we define efficient representations of the eighth-order fluctuation tensor for various microstructure symmetry classes and discuss the physical meaning of individual components for the statistically isotropic case. We furthermore leverage symmetry to mitigate numerical errors, thereby reducing the expense of computing the fluctuation tensor. As an example material, we consider polypropylene reinforced by fibers and spherical inclusions. Additionally, we examine polycrystalline copper microstructures. By numerically computing the elastic fluctuation tensor, we confirm theoretical asymptotic convergence rates and symmetry properties. For many of the considered statistically isotropic microstructures, the fluctuations of isotropic stiffness components, which are often the only fluctuations reported, are negligible compared to isotropic fluctuations of the anisotropic stiffness components. Therefore, the full fluctuation tensor must be considered when quantifying the uncertainty of stochastic homogenization.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10209-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172452","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":"Shells as Constrained Fibre Bundles","authors":"Mohammadjavad Javadi,&nbsp;Marcelo Epstein","doi":"10.1007/s10659-026-10207-2","DOIUrl":"10.1007/s10659-026-10207-2","url":null,"abstract":"<div><p>Regarding a shell as the natural restriction of the Euclidean frame bundle to an embedded surface, and further restricting its deformation so that the surface tangent planes be preserved, a first-order (simple) material behaviour leads automatically to a theory that includes strain gradients. Using the principle of virtual work, the weak and strong forms of the shell equilibrium equations and boundary conditions are derived. A comparison with other higher gradient theories is carried out and commented upon. An important outcome of the proposed geometric framework is that the gradient of curvature does not emerge as an independent contribution in the resulting higher-gradient shell formulation.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172338","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":"Multi-Continuum Homogenization for Scale-Dependent Materials in Finite-Sized Structures","authors":"H. C. V. M. Shyam Veluvali,&nbsp;Grigor Nika","doi":"10.1007/s10659-026-10208-1","DOIUrl":"10.1007/s10659-026-10208-1","url":null,"abstract":"<div><p>Classical homogenization is insufficient for finite-sized structures as it does not account for crucial scale-size effects. We develop a thermodynamically consistent model and subsequent two-scale expansion homogenization framework for strain-gradient elasticity that derives scale-dependent effective models complimenting the findings of [58] enabling prediction of finite-size effects in architected metamaterials. Our key result is that the homogenized mechanical properties depend not only on the micro-geometry and volume fraction but also on the absolute size of the underlying constituents. Hence, the homogenized coefficients are not constant (as in classical homogenization) but rather functions of the microstructural size. Numerical validation confirms that the homogenized coefficients converge to the classical ones as the scale-size effects become vanishingly small, providing a critical tool for designing architected materials.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10208-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148172339","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":"Dynamic Micromagnetism à la Ericksen-Leslie, and the Constrained Polar Continuum Mechanics of Hard Magnetic Soft Materials","authors":"Amit Acharya,&nbsp;Siladitya Pal","doi":"10.1007/s10659-026-10205-4","DOIUrl":"10.1007/s10659-026-10205-4","url":null,"abstract":"<div><p>A model of dissipative micromagnetics coupled to (visco-)elasticity is explored, following the procedures of the Ericksen-Leslie theory of nematic liquid crystals allowing for angular momentum due to magnetization. An outcome is the Landau-Lifshitz-Gilbert theory coupled to material spin. A further power-less augmentation to the angular momentum of the theory with classical kinetic energy density is also considered, with a preliminary exploration of its potential in representing the Einstein-de Haas and Barnett effects within continuum mechanics. A treatment of the continuum mechanics of hard magnetic soft materials as a constrained polar material is presented. The models of DeSimone and James [22] and Zhao et al. [66] are discussed as two different, namely energetically and kinematically, constrained models of magnetoelasticity encompassed within the overall framework.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10205-4.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148010078","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":"Revisiting the Stress Field Inside an Elastic Sphere Subjected to a Concentrated Load","authors":"Yosuke Mori,&nbsp;Kiwamu Yoshii,&nbsp;Satoshi Takada","doi":"10.1007/s10659-026-10206-3","DOIUrl":"10.1007/s10659-026-10206-3","url":null,"abstract":"<div><p>We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional linearized elastodynamic equations, the displacement and stress fields are derived using scalar and vector potential representations combined with spherical harmonic expansions. All expansion coefficients are determined explicitly by enforcing the traction boundary conditions. The static elastic solution is obtained rigorously as the long-time limit of the dynamical formulation. Closed-form expressions for all components of the stress tensor are provided, enabling direct evaluation of the principal stresses and their differences throughout the interior of the sphere. The analytical solution is further generalized to arbitrary loading positions by means of rotational transformations, allowing systematic treatment of multiple concentrated loads through superposition.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147938299","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":"Cardiac Mechanics Modeling: Recent Developments and Current Challenges","authors":"Aaron L. Brown,&nbsp;Ju Liu,&nbsp;Daniel B. Ennis,&nbsp;Alison L. Marsden","doi":"10.1007/s10659-026-10204-5","DOIUrl":"10.1007/s10659-026-10204-5","url":null,"abstract":"<div><p>Patient-specific computational models of the heart are powerful tools for cardiovascular research and medicine, with demonstrated applications in treatment planning, device evaluation, and surgical decision-making. Yet constructing such models is inherently difficult, reflecting the extraordinary complexity of the heart itself. Numerous considerations are required, including reconstructing the anatomy from medical images, representing myocardial mesostructure, capturing material behavior, defining model geometry and boundary conditions, coupling multiple physics, and selecting numerical methods. Many of these choices involve a tradeoff between physiological fidelity and modeling complexity. In this review, we summarize recent advances and unresolved questions in each of these areas, with particular emphasis on cardiac tissue mechanics. We argue that clarifying which complexities are essential, and which can be safely simplified, will be key to enabling clinical translation of these models.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147796647","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":"On the Propagation of Acceleration Waves in Circular Cylindrical Elastic Membrane Tubes Subjected to Axial Extension","authors":"Husnu A. Erbay,&nbsp;Saadet Erbay","doi":"10.1007/s10659-026-10202-7","DOIUrl":"10.1007/s10659-026-10202-7","url":null,"abstract":"<div><p>We consider a circular cylindrical elastic membrane tube which is initially at rest and subjected to a given constant axial extension. We then consider the acceleration waves arising from the boundary condition defined for the axial velocity at one end of the tube. Using the singular surface theory, we study the propagation of acceleration waves in the context of nonlinear elasticity. The temporal evolution and propagation speeds are determined for a general incompressible elastic material. We deduce the conditions which determine whether the amplitude of the longitudinal acceleration wave blows up or not. Considering some well-known examples of strain-energy function, our study demonstrates that different constitutive models behave very differently and an amplitude blow-up may occur depending on the magnitude of the initial stretch for some elastic materials. On the other hand, we show that when the state of the medium ahead of the longitudinal acceleration wave is its natural state, an amplitude blow-up does not occur.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147738335","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":"Prestressed Microstretch Elastic Solids","authors":"D. Ieşan","doi":"10.1007/s10659-026-10200-9","DOIUrl":"10.1007/s10659-026-10200-9","url":null,"abstract":"<div><p>The deformation of microstretch elastic solids is described by the displacement vector, the microrotation vector and the microstretch function. This paper presents a theory of prestressed microstretch elastic solids. First, the nonlinear theory of microstretch continua is used to establish the equations governing the infinitesimal deformation superposed on large deformations. Then, the linear theory of microstretch elastic solids with initial stresses and couple stresses is derived. The continuous dependence of solutions upon body loads and initial data is investigated.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 2","pages":""},"PeriodicalIF":1.4,"publicationDate":"2026-04-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"147737936","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}