{"title":"Equivalence Groups of Inhomogeneous Hyperelasticity","authors":"Saadet S. Özer","doi":"10.1007/s10659-026-10231-2","DOIUrl":"10.1007/s10659-026-10231-2","url":null,"abstract":"<div><p>Equivalence groups associated with the field equations of arbitrary motions of inhomogeneous hyperelastic solids are investigated. The explicit forms of the infinitesimal generators, namely the components of the isovector field associated with the equivalence groups are derived. Additional constraints on the isovector components are established to ensure that the transformed equations are supported by a strain energy function. Possible mappings between the equations of materials with different properties are examined. Not only the transformations between homogeneous and inhomogeneous hyperelasticity equations, but also the transformations between the equations and strain energy functions of isotropic and anisotropic materials are investigated. The results are illustrated with several examples.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149035369","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":"Surface and Thickness Effects in an Elastic Layer Under Axisymmetric Surface Pressure","authors":"Yushuai Chen, Ning Jia, Xiaodi Wang","doi":"10.1007/s10659-026-10226-z","DOIUrl":"10.1007/s10659-026-10226-z","url":null,"abstract":"<div><p>This paper presents an analysis of a finite elastic layer bonded to a rigid substrate under a prescribed axisymmetric surface pressure acting over a circular region, employing the surface-energy-density-based elasticity theory (C-Y theory). By incorporating modified boundary conditions at the free surface and employing Love’s strain function in conjunction with the Hankel integral transform, analytical integral solutions for the stress and displacement fields are derived. Taking uniform pressure as an example, the influences of surface effect and thickness effect of the elastic layer on the nanocontact behavior are analyzed. The results indicate that due to the reduction of contact radius and layer thickness, the elastic layer will show a hardening trend. On the one hand, at the nanoscale, the surface effect starts to play an indispensable role on the contact behavior, which leads to reduced displacements and lower peak stresses, as well as smoother stress variations near the edges of the loaded area, with the primary influence concentrated in the vicinity of the free surface. On the other hand, when the thickness of the elastic layer decreases, the rigid substrate beneath the elastic layer will enhance the restriction on the displacement of the elastic layer. This model characterizes the hardening behavior of the elastic layer under axisymmetric pressure and provides an analytical framework for elastic layer–substrate systems.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 4","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"149011459","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":"Three-Dimensional Angular Shear Deformation in Finite Elasticity","authors":"Federico Oyedeji Falope, Luca Lanzoni, Angelo Marcello Tarantino","doi":"10.1007/s10659-026-10230-3","DOIUrl":"10.1007/s10659-026-10230-3","url":null,"abstract":"<div><p>Angular shear deformations are based solely on the angular variation of line elements and not on their extension. To describe kinematics, a material cube is considered that transforms into an oblique prism, where two opposite faces are equal and parallel. Using the displacement components of three vertices of the fundamental edges, positioned along the reference axes, the displacement field of the body has been obtained. Then, the deformation tensors have been determined and some general properties for this class of shear deformations have been highlighted. Using a Lagrangian analysis, the boundary value problem for the equilibrium of a cube subjected to a purely angular shear deformation has been formulated. Subsequently, Piola-Kirchhoff and Cauchy stress tensors, together with the normal and tangential Cauchy stress vector components acting on the inclined faces of the deformed cube, have been evaluated.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10230-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148927360","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":"Read–Shockley Formula for a General Bravais Lattice in Two Dimensions","authors":"Lucia Scardia, Edoardo G. Tolotti","doi":"10.1007/s10659-026-10227-y","DOIUrl":"10.1007/s10659-026-10227-y","url":null,"abstract":"<div><p>In this note we consider a two-dimensional semi-discrete dislocation energy and propose a simple and physically motivated construction for the grain boundary between two crystal grains with a small orientation difference. In the case of a general Bravais lattice, the energy of this construction matches the logarithmic scaling predicted by Read and Shockley.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10227-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926652","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}
Bingrui Ju, Yuri V. Petrov, Shixiang Zhao, Yan Gu, Chuanzeng Zhang
{"title":"Shape Optimization of Notches for Minimizing Stress Concentration Under Torsional Loading: Theoretical Analysis and Numerical Simulation","authors":"Bingrui Ju, Yuri V. Petrov, Shixiang Zhao, Yan Gu, Chuanzeng Zhang","doi":"10.1007/s10659-026-10229-w","DOIUrl":"10.1007/s10659-026-10229-w","url":null,"abstract":"<div><p>Stress concentration in notched components under torsional loading can significantly affect structural strength, durability, and fatigue life. In this study, the optimal profile of the right-angle notch is explored with the objective of minimizing stress concentration. Based on the principle of minimum potential energy and complex analysis, the optimal notch profile is derived analytically and identified as an astroid. An advanced boundary element method (BEM) is employed to verify the validity of the theoretical solution and to provide an effective numerical framework. The numerical results indicate that, compared with the circular notch and the hyperelliptic notch, the astroid notch is more effective in reducing stress concentration. In addition, a zero radius of curvature at the notch root does not necessarily lead to severe stress concentration or stress singularity. These findings offer further insight into notch-induced stress amplification and the mechanical behavior of geometric discontinuities.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148926579","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":"An Eulerian Deformable Cosserat Model for Large Deformations of Porous Geomaterials","authors":"M. B. Rubin, Andrea Panteghini","doi":"10.1007/s10659-026-10228-x","DOIUrl":"10.1007/s10659-026-10228-x","url":null,"abstract":"<div><p>The deformable Cosserat theory discussed in this paper models a continuum with interacting macro- and micro-continua. The macro-continuum describes elastic-plastic response, whereas the micro-continuum is represented by a triad of deformable director vectors determined by director momentum equations that include director-gradient effects. One objective of the paper is to modify the elastic measures of the micro-continuum to be independent of the plastic rate characterizing the macro-continuum. To this end, an additional triad of vectors is introduced through Eulerian evolution equations for material line elements. Elastic deformation measures are then defined to model the deformation of the director vectors <i>relative</i> to this triad of material line elements. The nonlinear purely mechanical theory of the resulting deformable Cosserat model is developed for both anisotropic and isotropic response. Limiting attention to elastically isotropic elastic-plastic response of the macro-continuum, specific equations are developed for a generalized yield criterion for geological materials with evacuated pores and dependence on the Lode angle, porosity, pressure, and hardening/softening of the yield strength. Finally, a small-deformation notched-plate example is used to emphasize the importance of the modified measures: the earlier measures lead to mesh-dependent softening responses, whereas the modified measures predict mesh-independent load-displacement curves, dissipated energy, and shear-band width for the single set of parameters considered.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837527","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":"Inhomogeneous Sliding Shear Versus Simple Shear in Linear Elasticity","authors":"Federico Oyedeji Falope, Luca Lanzoni, Angelo Marcello Tarantino","doi":"10.1007/s10659-026-10225-0","DOIUrl":"10.1007/s10659-026-10225-0","url":null,"abstract":"<div><p>The simplest possible shear deformation is obtained when a face of a block is displaced relative to its opposite parallel face. This sliding shear problem is physically different from the classic simple shear problem. In fact, simple shear produces a homogeneous deformation field, which is necessarily maintained by distributions of tangential stresses applied on the external faces of the block. By contrast, the deformation field generated by sliding shear is inhomogeneous, with the lateral faces of the block always remaining traction-free. Few studies have been conducted on the sliding shear, so it can be asserted that many questions related to this basic problem remain unresolved today. In this paper, the sliding shear problem is formulated within the framework of classical linear elasticity for isotropic materials. However, due to its mathematical complexity, only semi-analytical solutions are provided.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10225-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782749","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":"Addendum to Neutral Deformation Modes of Minimal Surfaces","authors":"André M. Sonnet, Epifanio G. Virga","doi":"10.1007/s10659-026-10221-4","DOIUrl":"10.1007/s10659-026-10221-4","url":null,"abstract":"<div><p>We clarify a few issues that could possibly be misunderstood in our paper [J. Elast. <b>158</b>(2), 25 (2026) https://doi.org/10.1007/s10659-026-10201-8].</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782750","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}
Salvatore Di Stefano, Claudia Binetti, Giuseppe Puglisi, Stefano Giordano
{"title":"A Unified Configurational Framework for Interface and Bulk Defects in Eshelbian Linear Elasticity","authors":"Salvatore Di Stefano, Claudia Binetti, Giuseppe Puglisi, Stefano Giordano","doi":"10.1007/s10659-026-10222-3","DOIUrl":"10.1007/s10659-026-10222-3","url":null,"abstract":"<div><p>Within the framework of Eshelbian mechanics and linear elasticity, we develop a kinematic and energetic formulation for treating different classes of defects. Central to the approach is a defect map, through which interface discontinuities and bulk material inhomogeneities are described within a common notation. The driving force is derived as an energy-release rate, leading to a single identity in which defect-dependent mechanical effects, material inhomogeneity, and boundary/interface contributions are explicitly separated. For affine modes of defect evolution—translation, rotation, and dilatation—the formulation recovers the corresponding classical integrals as special cases. In particular, the analysis shows that path independence is not automatic, but follows under the assumptions required for the balance of the different contributions to the driving force. Finally, a prototypical one-dimensional example is discussed to describe the physical meaning of the deduced analytical expression of the total driving force.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10222-3.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782224","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":"Geometric Properties of Euler’s Elastica","authors":"Milan Batista","doi":"10.1007/s10659-026-10224-1","DOIUrl":"10.1007/s10659-026-10224-1","url":null,"abstract":"<div><p>The aim of this article is to provide a concise and coherent summary of existing results on the geometric properties of the planar Euler elastica. No new governing equation or solution family is proposed; the emphasis is on presenting and synthesising established results. Taking the classical equilibrium equation for a planar, inextensible and unshearable elastic rod under terminal loads as a starting point, the article collects closed-form expressions in terms of Jacobi elliptic functions for the tangent angle, curvature, intrinsic coordinates, and internal force components. The elliptic modulus <span>(k)</span> is used as the organising parameter, enabling the inflectional and non-inflectional families, the homoclinic separatrix, and the straight and circular limiting cases to be described within a common notation. The roles of the solution parameters <span>(k)</span>, <span>(lambda )</span>, <span>(C)</span>, <span>(alpha )</span>, and the coordinate constants are clarified in terms of shape, scale, phase, orientation, and position. Symmetries, periodicity, bounds, and characteristic points are summarised, while inflection, compression, and shear points are interpreted geometrically and mechanically. Conditions for self-intersections and self-touching points are presented, and threshold values of <span>(k)</span> are related to changes in topology. Formulae for characteristic dimensions are also collected.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 3","pages":""},"PeriodicalIF":2.1,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-026-10224-1.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782225","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}