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The Euler–Bernoulli Limit of Thin Brittle Linearized Elastic Beams 薄脆线性化弹性梁的Euler-Bernoulli极限
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-11-28 DOI: 10.1007/s10659-023-10040-x
Janusz Ginster, Peter Gladbach
{"title":"The Euler–Bernoulli Limit of Thin Brittle Linearized Elastic Beams","authors":"Janusz Ginster,&nbsp;Peter Gladbach","doi":"10.1007/s10659-023-10040-x","DOIUrl":"10.1007/s10659-023-10040-x","url":null,"abstract":"<div><p>We show that the linear brittle Griffith energy on a thin rectangle <span>(varGamma )</span>-converges after rescaling to the linear one-dimensional brittle Euler–Bernoulli beam energy.</p><p>In contrast to the existing literature, we prove a corresponding sharp compactness result, namely a suitable weak convergence after subtraction of piecewise rigid motions with the number of jumps bounded by the energy.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"125 - 155"},"PeriodicalIF":1.8,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10040-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513226","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
Complete General Solutions for Equilibrium Equations of Isotropic Strain Gradient Elasticity 各向同性应变梯度弹性平衡方程的完全通解
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-11-24 DOI: 10.1007/s10659-023-10039-4
Yury Solyaev
{"title":"Complete General Solutions for Equilibrium Equations of Isotropic Strain Gradient Elasticity","authors":"Yury Solyaev","doi":"10.1007/s10659-023-10039-4","DOIUrl":"10.1007/s10659-023-10039-4","url":null,"abstract":"<div><p>In this paper, we consider isotropic Mindlin–Toupin strain gradient elasticity theory, in which the equilibrium equations contain two additional length-scale parameters and have the fourth order. For this theory, we developed an extended form of Boussinesq–Galerkin (BG) and Papkovich–Neuber (PN) general solutions. The obtained form of BG solution allows to define the displacement field through a single vector function that obeys the eight-order bi-harmonic/bi-Helmholtz equation. The developed PN form of the solution provides an additive decomposition of the displacement field into the classical and gradient parts that are defined through the standard Papkovich stress functions and modified Helmholtz decomposition, respectively. Relations between different stress functions and the completeness theorem for the derived general solutions are established. As an example, it is shown that a previously known fundamental solution within the strain gradient elasticity can be derived by using the developed PN general solution.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"107 - 124"},"PeriodicalIF":1.8,"publicationDate":"2023-11-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138513217","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
Controllable Deformations of Unconstrained Ideal Nematic Elastomers 无约束理想向列弹性体的可控变形
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-10-18 DOI: 10.1007/s10659-023-10038-5
L. Angela Mihai, Alain Goriely
{"title":"Controllable Deformations of Unconstrained Ideal Nematic Elastomers","authors":"L. Angela Mihai,&nbsp;Alain Goriely","doi":"10.1007/s10659-023-10038-5","DOIUrl":"10.1007/s10659-023-10038-5","url":null,"abstract":"<div><p>We establish that, for ideal unconstrained uniaxial nematic elastomers described by a homogeneous isotropic strain-energy density function, the only smooth deformations that can be controlled by the application of surface tractions only and are universal in the sense that they are independent of the strain-energy density are those for which the deformation gradient is constant and the liquid crystal director is either aligned uniformly or oriented randomly in Cartesian coordinates. This result generalizes the classical Ericksen’s theorem for nonlinear homogeneous isotropic hyperelastic materials. While Ericksen’s theorem is directly applicable to liquid crystal elastomers in an isotropic phase where the director is oriented randomly, in a nematic phase, the constitutive strain-energy density must account also for the liquid crystal orientation which leads to significant differences in the analysis compared to the purely elastic counterpart.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"95 - 106"},"PeriodicalIF":1.8,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10038-5.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135888226","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
On the Question of the Sign of Size Effects in the Elastic Behavior of Foams 关于泡沫弹性行为中尺寸效应的符号问题
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-10-06 DOI: 10.1007/s10659-023-10037-6
Stephan Kirchhof, Alfons Ams, Geralf Hütter
{"title":"On the Question of the Sign of Size Effects in the Elastic Behavior of Foams","authors":"Stephan Kirchhof,&nbsp;Alfons Ams,&nbsp;Geralf Hütter","doi":"10.1007/s10659-023-10037-6","DOIUrl":"10.1007/s10659-023-10037-6","url":null,"abstract":"<div><p>Due to their good ratio of stiffness and strength to weight, foam materials find use in lightweight engineering. Though, in many applications like structural bending or tension, the scale separation between macroscopic structure and the foam’s mesostructure like cells size, is relatively weak and the mechanical properties of the foam appear to be size dependent. Positive as well as negative size effects have been observed for certain basic tests of foams, i.e., the material appears either to be more compliant or stiffer than would be expected from larger specimens. Performing tests with sufficiently small specimens is challenging as any disturbances from damage of cell walls during sample preparation or from loading devices must be avoided. Correspondingly, the number of respective data in literature is relatively low and the results are partly contradictory.</p><p>In order to avoid the problems from sample preparation or bearings, the present study employs virtual tests with CT data of real medium-density ceramic foams. A number of samples of different size is “cut” from the resulting voxel data. Subsequently, the apparent elastic properties of each virtual sample are “measured” directly by a free vibrational analysis using finite cell method, thereby avoiding any disturbances from load application or bearings. The results exhibit a large scatter of the apparent moduli per sample size, but with a clear negative size effect in all investigated basic modes of deformation (bending, torsion, uniaxial). Finally, the results are compared qualitatively and quantitatively to available experimental data from literature, yielding common trends as well as open questions.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"79 - 93"},"PeriodicalIF":1.8,"publicationDate":"2023-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10659-023-10037-6.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135346592","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
A Generalized Model for Large Deformations of an Elastically Isotropic Material with Elastic-Inelastic Response 具有弹性-非弹性响应的弹性各向同性材料大变形的广义模型
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-09-13 DOI: 10.1007/s10659-023-10036-7
M. B. Rubin
{"title":"A Generalized Model for Large Deformations of an Elastically Isotropic Material with Elastic-Inelastic Response","authors":"M. B. Rubin","doi":"10.1007/s10659-023-10036-7","DOIUrl":"10.1007/s10659-023-10036-7","url":null,"abstract":"<div><p>The objective of this classroom note is to propose a generalized model for a compressible elastically isotropic material with elastic-inelastic response. The model is generalized for an exponential Fung-type strain energy with a sum of new higher order elastic distortional deformation invariants that can model elastic-inelastic distortional deformation. In contrast with an Ogden-type model, the coefficients of the proposed higher order invariants do not affect the small deformation response. Moreover, there is no need to determine eigenvalues and eigenvectors of the elastic distortional deformation tensor. Examples show that the equations can model preconditioning of biological tissues as well as elastic instability.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"325 - 332"},"PeriodicalIF":1.8,"publicationDate":"2023-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135735410","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
Cauchy Relations in Linear Elasticity: Algebraic and Physics Aspects 线性弹性力学中的柯西关系：代数和物理方面
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-09-07 DOI: 10.1007/s10659-023-10035-8
Yakov Itin
{"title":"Cauchy Relations in Linear Elasticity: Algebraic and Physics Aspects","authors":"Yakov Itin","doi":"10.1007/s10659-023-10035-8","DOIUrl":"10.1007/s10659-023-10035-8","url":null,"abstract":"<div><p>The Cauchy relations distinguish between rari- and multi-constant linear elasticity theories. These relations are treated in this paper in a form that is invariant under two groups of transformations: indices permutation and general linear transformations of the basis. The irreducible decomposition induced by the permutation group is outlined. The Cauchy relations are then formulated as a requirement of nullification of an invariant subspace. A successive decomposition under rotation group allows to define the partial Cauchy relations and two types of elastic materials. We explore several applications of the full and partial Cauchy relations in physics of materials. The structure’s deviation from the basic physical assumptions of Cauchy’s model is defined in an invariant form. The Cauchy and non-Cauchy contributions to Hooke’s law and elasticity energy are explained. We identify wave velocities and polarization vectors that are independent of the non-Cauchy part for acoustic wave propagation. Several bounds are derived for the elasticity invariant parameters.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"39 - 77"},"PeriodicalIF":1.8,"publicationDate":"2023-09-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47277993","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
Construction of Invariant Relations of (n) Symmetric Second-Order Tensors $n$对称二阶张量不变关系的构造
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-08-28 DOI: 10.1007/s10659-023-10031-y
Adair Roberto Aguiar, Gabriel Lopes da Rocha
{"title":"Construction of Invariant Relations of (n) Symmetric Second-Order Tensors","authors":"Adair Roberto Aguiar,&nbsp;Gabriel Lopes da Rocha","doi":"10.1007/s10659-023-10031-y","DOIUrl":"10.1007/s10659-023-10031-y","url":null,"abstract":"<div><p>A methodology is presented to find either implicit or explicit relations, called syzygies, between invariants in a minimal integrity basis for <span>(n)</span> symmetric second-order tensors defined on a three-dimensional euclidean space. The methodology i) yields explicit non-polynomial expressions for certain invariants in terms of the remaining invariants in the integrity basis and ii) allows the construction of the implicit relations. The results of this investigation are important in modeling biological structures, which, in general, are non-homogeneous and made of anisotropic viscoelastic materials that are subjected to large deformations and are modeled through constitutive relations that depend on symmetric tensors.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"45 - 60"},"PeriodicalIF":2.0,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42042772","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
Edge Crack Subject to Anti-Plane Shear Wave in an Orthotropic Strip 正交各向异性带中受反平面剪切波作用的边缘裂纹
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-08-28 DOI: 10.1007/s10659-023-10032-x
Somashri Karan, Sourav Kumar Panja, Sanjoy Basu, Subhas Chandra Mandal
{"title":"Edge Crack Subject to Anti-Plane Shear Wave in an Orthotropic Strip","authors":"Somashri Karan,&nbsp;Sourav Kumar Panja,&nbsp;Sanjoy Basu,&nbsp;Subhas Chandra Mandal","doi":"10.1007/s10659-023-10032-x","DOIUrl":"10.1007/s10659-023-10032-x","url":null,"abstract":"<div><p>In this article, the proposed model analyzed shear wave propagation through an orthotropic strip with an edge crack. Dual integral equations have been developed for solution of the governing mixed boundary value problem with the aid of Hankel transform technique. Then, the dual integral equations have been transformed into a second kind Fredholm integral equation employing Abel’s transformation. The numerical calculations of stress intensity factor and crack opening displacement are performed utilizing the Fox &amp; Goodwin method and displayed graphically. Elastic constants of two orthotropic materials have been used to illustrate the influence of material orthotropy and normalized strip width on SIF and COD.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"156 1","pages":"23 - 37"},"PeriodicalIF":1.8,"publicationDate":"2023-08-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45488335","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
Foreword: In Recognition of the 85th Birthday of Roger L. Fosdick 前言：纪念罗杰·福斯迪克85岁生日
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-08-25 DOI: 10.1007/s10659-023-10033-w
Ryan S. Elliott, Adair R. Aguiar, Yi-Chao Chen, Gianni Royer-Carfangi
{"title":"Foreword: In Recognition of the 85th Birthday of Roger L. Fosdick","authors":"Ryan S. Elliott,&nbsp;Adair R. Aguiar,&nbsp;Yi-Chao Chen,&nbsp;Gianni Royer-Carfangi","doi":"10.1007/s10659-023-10033-w","DOIUrl":"10.1007/s10659-023-10033-w","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"1 - 2"},"PeriodicalIF":2.0,"publicationDate":"2023-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47013595","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 Class of Nonlinear Elasticity Problems with No Local but Many Global Minimizers 一类无局部有多个全局极小值的非线性弹性问题
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-08-04 DOI: 10.1007/s10659-023-10026-9
Yury Grabovsky, Lev Truskinovsky
{"title":"A Class of Nonlinear Elasticity Problems with No Local but Many Global Minimizers","authors":"Yury Grabovsky,&nbsp;Lev Truskinovsky","doi":"10.1007/s10659-023-10026-9","DOIUrl":"10.1007/s10659-023-10026-9","url":null,"abstract":"<div><p>We present a class of models of elastic phase transitions with incompatible energy wells in an arbitrary space dimension, where in a hard device an abundance of Lipschitz global minimizers coexists with a complete lack of strong local minimizers. The analysis is based on the proof that every strong local minimizer in a hard device is also a global minimizer which is applicable much beyond the chosen class of models. Along the way we show that a new demonstration of sufficiency for a subclass of affine boundary conditions can be built around a novel nonlinear generalization of the classical Clapeyron theorem.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"147 - 171"},"PeriodicalIF":2.0,"publicationDate":"2023-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44163270","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
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