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Journal of Elasticity最新文献

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The Nonlinear Partial Differential Equations Governing Anti-Plane Shear and Plane Strain for Isotropic Incompressible Hyperelastic Materials 各向同性不可压缩超弹性材料的反平面剪切和平面应变非线性偏微分方程
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-28 DOI: 10.1007/s10659-025-10182-0
C. O. Horgan
{"title":"The Nonlinear Partial Differential Equations Governing Anti-Plane Shear and Plane Strain for Isotropic Incompressible Hyperelastic Materials","authors":"C. O. Horgan","doi":"10.1007/s10659-025-10182-0","DOIUrl":"10.1007/s10659-025-10182-0","url":null,"abstract":"<div><p>It has long been recognized that the theory of nonlinear elasticity provides a rich framework for a large variety of issues of interest to applied mathematicians. In particular, researchers with primary interest in nonlinear partial differential equations have been attracted to this area of continuum mechanics. However, the detailed theoretical background giving rise to the governing partial differential equations is not always familiar to non-specialists. The purpose of the present expository note is to attempt to alleviate this situation by describing a variety of nonlinear partial differential equations that have been found to govern the deformations of anti-plane shear and plane strain for isotropic incompressible hyperelastic solids in equilibrium.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10182-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145612929","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}
引用次数: 0
Celebrating the Legacy of Professor Patrick Selvadurai (1942 – 2023) 庆祝帕特里克·塞尔瓦杜莱教授的遗产（1942 - 2023）
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-19 DOI: 10.1007/s10659-025-10181-1
Zhongqi Quentin Yue, Parham Samea, Shunde Yin, Leo Rothenburg
{"title":"Celebrating the Legacy of Professor Patrick Selvadurai (1942 – 2023)","authors":"Zhongqi Quentin Yue,&nbsp;Parham Samea,&nbsp;Shunde Yin,&nbsp;Leo Rothenburg","doi":"10.1007/s10659-025-10181-1","DOIUrl":"10.1007/s10659-025-10181-1","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145561008","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}
引用次数: 0
The Effective Energy of a Lattice Metamaterial 晶格超材料的有效能
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-18 DOI: 10.1007/s10659-025-10175-z
Xuenan Li, Robert V. Kohn
{"title":"The Effective Energy of a Lattice Metamaterial","authors":"Xuenan Li,&nbsp;Robert V. Kohn","doi":"10.1007/s10659-025-10175-z","DOIUrl":"10.1007/s10659-025-10175-z","url":null,"abstract":"<div><p>We study the sense in which the continuum limit of a broad class of discrete materials with periodic structure can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more general and more physical than those in the literature. Indeed, it applies to a broad class of systems including ones that possess mechanisms; and we discuss how the degeneracy that plagues prior work in this area can be avoided by penalizing change of orientation. A key motivation for this work is its relevance to mechanism-based mechanical metamaterials. Such systems often have “soft modes”, achieved in typical examples by modulating mechanisms. Our results permit the following more general definition of a soft mode: it is a macroscopic deformation whose effective energy vanishes – in other words, one whose spatially-averaged elastic energy tends to zero in the continuum limit.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533331","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}
引用次数: 0
A Semigroup Approach to a Linear Elastostatic Problem in a Semi-Infinite Strip 半无限带上线性弹性静力问题的半群方法
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-17 DOI: 10.1007/s10659-025-10179-9
Filippo Dell’Oro, Vittorino Pata, Ramon Quintanilla
{"title":"A Semigroup Approach to a Linear Elastostatic Problem in a Semi-Infinite Strip","authors":"Filippo Dell’Oro,&nbsp;Vittorino Pata,&nbsp;Ramon Quintanilla","doi":"10.1007/s10659-025-10179-9","DOIUrl":"10.1007/s10659-025-10179-9","url":null,"abstract":"<div><p>We describe via semigroup techniques the space decaying solutions to the system modeling an isotropic and homogeneous elastostatic semi-infinite band, both in the isothermal case and when thermal effects are present. The semigroup approach allows us to transfer some properties that typically occur in evolution problems to our model, such as analyticity and exponential decay at infinity. These results are closely related to the Saint-Venant principle. We conclude the article by recalling some consequences of the analyticity of the semigroup. The resulting properties are rather innovative compared to the usual results in the literature concerning the spatial decay of solutions.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10179-9.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533332","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}
引用次数: 0
Existence for Accreting Viscoelastic Solids at Large Strains 大应变下粘弹性固体增积的存在性
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-17 DOI: 10.1007/s10659-025-10180-2
Andrea Chiesa, Ulisse Stefanelli
{"title":"Existence for Accreting Viscoelastic Solids at Large Strains","authors":"Andrea Chiesa,&nbsp;Ulisse Stefanelli","doi":"10.1007/s10659-025-10180-2","DOIUrl":"10.1007/s10659-025-10180-2","url":null,"abstract":"<div><p>By revisiting a model proposed in Zurlo and Truskinovsky (Mech. Res. Commun. 93:174–179, 2018), we address the accretive growth of a viscoelastic solid at large strains. The accreted material is assumed to accumulate at the boundary of the body in an unstressed state. The growth process is driven by the deformation state of the solid. The progressive build-up of incompatible strains in the material is modeled by considering an additional backstrain. The model is regularized by postulating the presence of a fictitious compliant material surrounding the accreting body. We show the existence of solutions to the coupled accretion and viscoelastic equilibrium problem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"158 1","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145533330","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}
引用次数: 0
Stability and Numerical Analysis of Micropolar Viscoelastic Systems 微极性粘弹性系统的稳定性及数值分析
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-12 DOI: 10.1007/s10659-025-10178-w
Noelia Bazarra, José R. Fernández, Hugo D. Fernández Sare, Ramón Quintanilla
{"title":"Stability and Numerical Analysis of Micropolar Viscoelastic Systems","authors":"Noelia Bazarra,&nbsp;José R. Fernández,&nbsp;Hugo D. Fernández Sare,&nbsp;Ramón Quintanilla","doi":"10.1007/s10659-025-10178-w","DOIUrl":"10.1007/s10659-025-10178-w","url":null,"abstract":"<div><p>In this work, we consider two dynamic systems arising in micropolar viscoelasticity. In this sense, the material structure is assumed to have macroscopic and microscopic levels. First, an existence and uniqueness result is proved by using the theory of linear semigroups and, secondly, the decay of the solutions to the equilibrium state is shown. Then, the polynomial energy decay is obtained applying a characterization of the system operator. In a second part, we consider the numerical approximation of a variational version of the above problem. This is done by using the finite element method to approximate the spatial variable and the implicit Euler scheme to discretize the time derivatives. A discrete stability property is proved and an a priori error analysis is provided. The linear convergence of the approximations is deduced under some additional regularity conditions on the continuous solution. Finally, some numerical simulations are shown to demonstrate numerical convergence and the behavior of the discrete energy.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510783","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}
引用次数: 0
A Theory of Porous Thermoelastic Solids with the Second Gradient of Temperature 具有第二温度梯度的多孔热弹性固体理论
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-10 DOI: 10.1007/s10659-025-10177-x
D. Ieşan
{"title":"A Theory of Porous Thermoelastic Solids with the Second Gradient of Temperature","authors":"D. Ieşan","doi":"10.1007/s10659-025-10177-x","DOIUrl":"10.1007/s10659-025-10177-x","url":null,"abstract":"<div><p>This paper is concerned with a linear theory of porous thermoelastic materials in which the second temperature gradient is included in the classical set of independent constitutive variables. The paper is based on the theory of microstretch thermoelastic solids, as well as on Green-Naghdi thermomechanics. We use thermal displacement and an entropy production inequality. The introduction of the entropy flux tensor allows the constitutive equations to depend on the second gradient of temperature. We first present the basic equations of the theory as well as the boundary conditions for this class of non-simple materials. We then study the case of isotropic and homogeneous materials and present a general solution of the field equations similar to that obtained by Mindlin in strain gradient elasticity. In the context of anisotropic solids we discuss the uniqueness question appropriate to the fundamental initial-boundary-value problems. The continuous dependence of solutions on initial data and body loads is established. The Mindlin-type solution is used to study the deformation produced by a concentrated heat source in a body occupying an unbounded region.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145510761","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}
引用次数: 0
On a Complex Wave Equation Arising in Isotropic Incompressible Elastodynamics 各向同性不可压缩弹性动力学中的复波动方程
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-11-03 DOI: 10.1007/s10659-025-10176-y
Vincenzo Fazio, Giuseppe Saccomandi, Maria Paola Speciale
{"title":"On a Complex Wave Equation Arising in Isotropic Incompressible Elastodynamics","authors":"Vincenzo Fazio,&nbsp;Giuseppe Saccomandi,&nbsp;Maria Paola Speciale","doi":"10.1007/s10659-025-10176-y","DOIUrl":"10.1007/s10659-025-10176-y","url":null,"abstract":"<div><p>In isotropic and incompressible elastodynamics, Carroll’s solutions for plane, circularly polarized shear waves represent an important class of controllable, non-universal solutions. It has already been shown that these solutions can be obtained in a compact way by rewriting the equations governing transverse waves as a single complex differential wave equation. In this work, we show that a complex wave equation formally identical to Carroll’s one can be used to construct new classes of solutions, still in the isotropic and incompressible setting, but in a more general case involving plane wave superimposed to homogeneous deformations. We analyze these new solutions and observe that they also exist in an interesting asymptotic regime frequently encountered in non-linear acoustics. Moreover, we demonstrate that these solutions are closely linked to symmetry properties of the complex wave equation and satisfy a nonlinear universal relation—a noteworthy and rare result.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10176-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145456099","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}
引用次数: 0
Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress 具有残余应力的可压缩各向同性柯西弹性固体中的普遍变形
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-10-29 DOI: 10.1007/s10659-025-10174-0
Arash Yavari, José Merodio, Mohd H. B. M. Shariff
{"title":"Universal Deformations in Compressible Isotropic Cauchy Elastic Solids with Residual Stress","authors":"Arash Yavari,&nbsp;José Merodio,&nbsp;Mohd H. B. M. Shariff","doi":"10.1007/s10659-025-10174-0","DOIUrl":"10.1007/s10659-025-10174-0","url":null,"abstract":"<div><p>We investigate universal deformations in compressible isotropic Cauchy elastic solids with residual stress, without assuming any specific source for the residual stress. We show that universal deformations must be homogeneous, and the associated residual stresses must also be homogeneous. Since a non-trivial residual stress cannot be homogeneous, it follows that residual stress must vanish. Thus, a compressible Cauchy elastic solid with a non-trivial distribution of residual stress cannot admit universal deformations. These findings are consistent with the results of Yavari and Goriely (Proc. R. Soc. A 472(2196):20160690, 2016), who showed that in the presence of eigenstrains, universal deformations are covariantly homogeneous and in the case of simply-connected bodies the universal eigenstrains are zero-stress (impotent).</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10174-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145405998","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}
引用次数: 0
Universal Deformations in Plane Isotropic Elastostatics 平面各向同性弹性静力学中的通用变形
IF 1.4 3区 工程技术
Journal of Elasticity Pub Date : 2025-10-15 DOI: 10.1007/s10659-025-10172-2
R. J. Knops
{"title":"Universal Deformations in Plane Isotropic Elastostatics","authors":"R. J. Knops","doi":"10.1007/s10659-025-10172-2","DOIUrl":"10.1007/s10659-025-10172-2","url":null,"abstract":"<div><p>A new proof is presented for the plane version of Ericksen’s theorem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"157 4","pages":""},"PeriodicalIF":1.4,"publicationDate":"2025-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-025-10172-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145316199","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}
引用次数: 0
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