Journal of Elasticity最新文献

{"title":"Geometric Interpretability of Hyperelastic Models Fitted to Tissue Biomechanical Data","authors":"Jiabao Tang,&nbsp;Wenyang Liu,&nbsp;Yiqi Mao,&nbsp;Shujuan Hou","doi":"10.1007/s10659-025-10157-1","DOIUrl":"10.1007/s10659-025-10157-1","url":null,"abstract":"<div><p>This work reveals the geometric interpretability of hyperelastic constitutive models fitted to mechanics data of biological tissue, addressing the long-overlooked prediction reliability issue arising from dual constraints of model limitations (structural complexity and physical idealization) and data challenges (finiteness and uncertainty). We evaluate three representative models—the eight-chain model, the Ogden model, and the neural network-derived gray matter model—under Bayesian model calibration, which naturally extends from the inherent uncertainties in biological tissue mechanical response data. By combining diverse mechanics datasets and priors with varying levels of informativeness, we analyze how data and prior constraints influence sloppiness. Posterior samples of model parameters are used to derive the sensitivity matrix of the cost function, uncovering the local geometric features of the cost landscape. Our results demonstrate the pervasive sloppiness in multi-parameter hyperelastic constitutive models, which can only be mitigated by high-quality data and informative priors. Beyond defining robust sloppiness metrics, this work provides actionable insights, such as guiding model selection and offering geometric constraints in machine learning-based automated model discovery.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814348","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":"From Discrete to Continuum: A Generalized Euler–Maclaurin Framework for Scale Effects in Nanomechanics","authors":"G. La Valle,&nbsp;C. Soize","doi":"10.1007/s10659-025-10158-0","DOIUrl":"10.1007/s10659-025-10158-0","url":null,"abstract":"<div><p>This paper introduces a novel approach for constructing, at the same scale, a continuum model equivalent to a given nanoscale discrete system, effectively capturing scale effects. Starting from a general formulation of <span>(m)</span>-particle interaction potentials for discrete particle systems, we propose the use of the Euler–Maclaurin (E–M) summation formula to construct the equivalent continuum model at the same scale. The proposed theory is developed for arbitrary 3D domains. The resulting novel continuum model captures scale effects in both statics and dynamics through additional edge, surface, and volume integrals, which are analytically obtained and driven by the nanostructure. For an arbitrary domain, the proposed approach provides a pathway for its integration into a computational framework. Since nanoscale and microscale systems are inevitably affected by uncertainties, the geometric and constitutive parameters must be modeled as random fields and their identification of must be conducted within a statistical framework. Consequently, we present a discussion on this identification in a probabilistic framework.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814282","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":"Rayleigh Waves: Do They Exist as an Exact Solution of Eringen’s Nonlocal Elasticity Theory in Its Integral Formulation?","authors":"P. A. Martin","doi":"10.1007/s10659-025-10159-z","DOIUrl":"10.1007/s10659-025-10159-z","url":null,"abstract":"<div><p>Eringen’s original linear theory of nonlocal elasticity involves integral operators. We apply it to the problem of waves in an elastic half-space, hoping to find a generalization of Rayleigh waves. We solve the governing equations exactly and show that such a generalization does not exist.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-08-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144814283","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":"Shear Beam Model with Fractional Derivative-Type Internal Dissipation","authors":"Wilson Oliveira,&nbsp;Sebastião Cordeiro,&nbsp;Carlos Alberto Raposo,&nbsp;Dilberto Almeida Júnior","doi":"10.1007/s10659-025-10156-2","DOIUrl":"10.1007/s10659-025-10156-2","url":null,"abstract":"<div><p>This work deals with the well-posedness and asymptotic behavior of a Shear beam model subject to internal dissipation of the fractional derivative-type. The energy functional is presented, and the dissipative property of the system is stablished. We use the semigroup theory in order to deal with the well-posedness and we prove the strong stability of the <span>(C_{0})</span>-semigroup using the Arendt-Batty and Lyubich-Vũ’s general criterion and also we prove the polynomial stability result applying Borichev and Tomilov’s theorem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145171293","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":"Justifying Linearization for Nonlinear Boundary Homogenization on a Grill-Type Winkler Foundation","authors":"Sergey A. Nazarov,&nbsp;Maria-Eugenia Pérez-Martínez","doi":"10.1007/s10659-025-10153-5","DOIUrl":"10.1007/s10659-025-10153-5","url":null,"abstract":"<div><p>We address a nonlinear boundary homogenization problem associated to the deformations of a block of an elastic material with small <i>reaction regions</i> periodically distributed along a plane. We assume a nonlinear Winkler-Robin law which implies that a strong reaction takes place in these reaction regions. Outside, on the plane, the surface is traction-free while the rest of the surface is clamped to an absolutely rigid profile. When dealing with <i>critical sizes</i> of the reaction regions, we show that, asymptotically, they behave as stuck regions, the homogenized boundary condition being a linear one with a new reaction term which contains a <i>capacity matrix</i> depending on the macroscopic variable. This matrix is defined through the solution of a parametric family of microscopic problems, the macroscopic variable being its parameter. Among others, to show the convergence of the solutions, we develop techniques that extend those both for nonlinear scalar problems and linear vector problems in the literature. We also address the <i>extreme cases</i>.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10153-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145170973","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":"Data-Based Approach to Hyperelastic Membranes","authors":"Claudia Grabs,&nbsp;Werner Wirges","doi":"10.1007/s10659-025-10155-3","DOIUrl":"10.1007/s10659-025-10155-3","url":null,"abstract":"<div><p>We study large deformations of hyperelastic membranes using a purely two-dimensional formulation derived from basic balance principles within a modern geometric setting, ensuring a framework that is independent of an underlying three-dimensional formulation. To assess the predictive capabilities of membrane theory, we compare numerical solutions to experimental data from axisymmetric deformations of a silicone rubber film. Five hyperelastic models—Neo-Hookean, Mooney-Rivlin, Gent, Yeoh, and Ogden—are evaluated by fitting their material parameters to our experimental data using TensorFlow. Our results provide a systematic comparison of these models based on their accuracy in capturing observed deformations, establishing a framework for integrating theory, experiment, and data-based parameter identification.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145168041","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":"Bending Shell Theories for Multiscale Materials from (3D) Nonlinear Elasticity","authors":"Tiziana Durante,&nbsp;Luisa Faella,&nbsp;Pedro Hernández-Llanos,&nbsp;Ravi Prakash","doi":"10.1007/s10659-025-10154-4","DOIUrl":"10.1007/s10659-025-10154-4","url":null,"abstract":"<div><p>This article derives homogenized bending shell theories starting from three-dimensional nonlinear elasticity. The original three-dimensional model contains three small parameters: the two homogenization scales <span>(varepsilon )</span> and <span>(varepsilon ^{2})</span> of the material properties and the thickness <span>(h)</span> of the shell. We obtain different limiting behaviors depending on the limit of various ratios of these three parameters.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169094","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":"Harmonic Ellipsoidal Elastic Solid or Liquid Inclusions","authors":"Xu Wang,&nbsp;Peter Schiavone","doi":"10.1007/s10659-025-10152-6","DOIUrl":"10.1007/s10659-025-10152-6","url":null,"abstract":"<div><p>We solve the inverse problem in three-dimensional elasticity associated with the design of a harmonic ellipsoidal isotropic elastic solid or compressible liquid inclusion that does not disturb the first invariant of the stress tensor in the surrounding isotropic elastic matrix subjected to uniform remote normal stresses. In order to achieve the harmonic condition, the two ratios of the remote normal stresses are uniquely determined for given geometric and material parameters.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145169092","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":"Material Tailoring of Linearly Elastic Functionally Graded Rubberlike Cylinders Under Combined Radial Expansion, Extension and Twisting Deformations","authors":"R. C. Batra,&nbsp;G. J. Nie","doi":"10.1007/s10659-025-10151-7","DOIUrl":"10.1007/s10659-025-10151-7","url":null,"abstract":"<div><p>The material tailoring problem for a hollow circular cylinder composed of an isotropic, incompressible, and linearly elastic functionally graded material has been analytically analyzed. The cylinder is deformed by torques and axial loads on the end faces, and pressures on its inner and outer surfaces. The cylinder material has one elastic parameter, the shear modulus <span>(mu left ( r right ) )</span>. For the direct problem it is a known positive and continuously varying function in the radial direction, <span>(r)</span>. For the inverse problem <span>(mu left ( r right ))</span> is a design variable and is found to provide the desired radial variation of either the strain energy density, <span>(W^{def} (r))</span>, or the von Mises stress, <span>(sigma ^{VM} left ( r right ))</span>, for the given loads and the cylinder geometry. If the three loads are simultaneously varied by a factor <span>(gamma )</span> then <span>(W^{def} left ( r right ) )</span> and <span>(sigma ^{VM} left ( r right ) )</span>, respectively, change by <span>(gamma ^{2} )</span> and <span>(gamma )</span> for fixed <span>(mu left ( r right ) )</span> in the direct problem and <span>(mu (r))</span> by <span>(gamma ^{2} )</span> and <span>(gamma )</span> in the inverse problem for preassigned <span>(W^{def} (r) = W_{cr} left ( r right ) )</span> and <span>(sigma ^{VM} left ( r right ) = sigma _{cr}^{VM} left ( r right ))</span>. The <span>(W_{cr} left ( r right ) )</span> and <span>(sigma _{cr}^{VM} left ( r right ))</span> are, respectively, values at failure of the strain energy density and the von Mises stress. For the cylinder material composed of two constituents having positive shear moduli as is often the case in experiments we use a homogenization technique to find the radial variations of their volume fractions and ensure <span>(mu (r))</span> is positive. We review three manufacturing techniques and propose an experimental program to find <span>(W_{cr} left ( r right ))</span> and <span>(sigma _{cr}^{VM} left ( r right ))</span>. The expression for <span>(mu (r))</span> is derived from the solution of the direct problem that has a unique solution. It provides reference solutions for similar nonlinear problems and verification of numerical algorithms. It supports the optimal design of cylinders.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10151-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145162734","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":"Consistent Boundary Element Method for Two-Dimensional Problems of Elasticity with Geometry-Preserving, Homothetic Element Generation","authors":"Ney Augusto Dumont","doi":"10.1007/s10659-025-10150-8","DOIUrl":"10.1007/s10659-025-10150-8","url":null,"abstract":"<div><p>We recently laid down the theoretical basis for the consistent formulation of the collocation boundary element method, as it should have been conceived from the beginning. We proposed a convergence theorem for two- and three-dimensional problems of elasticity and potential, which applies to generally curved elements in the frame of an isoparametric analysis. We also showed that the code implementation leads to controllable, highly precise and accurate results for arbitrarily small source-field distances of two-dimensional problems – limited only by the machine’s capacity to represent numbers. On the other hand, there still is the cost-benefit question of how to adequately describe a real problem’s geometry without increasing the number of degrees of freedom (h- and p-mesh refinement). We are proposing that the isoparametric implementation – with the introduced elegance of a convergence theorem – be replaced with a formulation that preserves the problem’s idealized geometry but is not isoparametric, in general. We also introduce a homothetic approach – for nodes and elements adaptively generated according to the same pattern along a boundary patch –, which is highly cost-effective. We present conceptual formulation, code implementation, and numerical illustrations that go from the simple case of an infinite plate with a circular hole to very challenging – physically unrealistic and only mathematically conceivable – topological applications: a multi-connected domain with generally curved boundary patches and presenting cracks, cusp and reentrant angles of virtually zero magnitude, and a strip of material of zero width. This cannot be manufactured in the real world but can be nevertheless simulated provided we have the proper mathematical tools, as presently proposed.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 3","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145161926","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}