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Journal of Elasticity最新文献

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Inclusions with Uniform Stress in a Bounded Elastic Domain 有界弹性域中的均匀应力包裹体
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-07-07 DOI: 10.1007/s10659-023-10025-w
Ming Dai
{"title":"Inclusions with Uniform Stress in a Bounded Elastic Domain","authors":"Ming Dai","doi":"10.1007/s10659-023-10025-w","DOIUrl":"10.1007/s10659-023-10025-w","url":null,"abstract":"<div><p>A single elliptical or ellipsoidal inclusion with an arbitrary uniform eigenstrain is known to achieve a constant stress field when embedded in an elastic medium provided the edge of the medium is sufficiently far from the inclusion (i.e. the interaction between the inclusion and the edge of the medium is negligible). In this paper, we aim to answer the question as to whether there exists an inclusion of certain configuration (with a uniform eigenstrain) that remains to possess a constant stress when embedded in a bounded medium whose edge interacts significantly with it. Specifically, we consider the anti-plane shear case of an inclusion with a uniform eigenstrain in a circular medium with a traction-free edge. We derive a sufficient and necessary condition ensuring the uniformity of the stress within the inclusion, which further leads to a nonlinear system of equations with respect to an infinite group of parameters characterizing the shape of the inclusion. We obtain convergent solutions for the truncated version of the nonlinear system using numerical techniques, and illustrate the corresponding shape of the inclusion in a few numerical examples. Our results for the case corresponding to small inclusion size and small edge-inclusion distance (relative to the radius of the medium) are well-consistent with the existing results for an inclusion with uniform stress in a semi-infinite medium with a traction-free surface, while those for centrally placed inclusions achieving uniform stress capture the classical case of centric circular inclusion accurately. The results presented in this paper provide a strong evidence for the existence of inclusions possessing uniform stress in an elastic bounded domain subjected to common external boundary conditions under anti-plane shear deformation.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 5","pages":"645 - 657"},"PeriodicalIF":1.8,"publicationDate":"2023-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42078161","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
Universal Deformations of Incompressible Nonlinear Elasticity as Applied to Ideal Liquid Crystal Elastomers 不可压缩非线性弹性的普遍变形在理想液晶弹性体中的应用
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-06-07 DOI: 10.1007/s10659-023-10018-9
Victoria A. Lee, K. Bhattacharya
{"title":"Universal Deformations of Incompressible Nonlinear Elasticity as Applied to Ideal Liquid Crystal Elastomers","authors":"Victoria A. Lee, K. Bhattacharya","doi":"10.1007/s10659-023-10018-9","DOIUrl":"https://doi.org/10.1007/s10659-023-10018-9","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":" ","pages":""},"PeriodicalIF":2.0,"publicationDate":"2023-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48704970","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: 3
Singular Points and Singular Curves in von Kármán Elastic Surfaces von Kármán弹性曲面的奇异点和奇异曲线
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-06-06 DOI: 10.1007/s10659-022-09969-2
Animesh Pandey, Anurag Gupta
{"title":"Singular Points and Singular Curves in von Kármán Elastic Surfaces","authors":"Animesh Pandey,&nbsp;Anurag Gupta","doi":"10.1007/s10659-022-09969-2","DOIUrl":"10.1007/s10659-022-09969-2","url":null,"abstract":"<div><p>Mechanical fields over thin elastic surfaces can develop singularities at isolated points and curves in response to constrained deformations (e.g., crumpling and folding of paper), singular body forces and couples, distributions of isolated defects (e.g., dislocations and disclinations), and singular metric anomaly fields (e.g., growth and thermal strains). With such concerns as our motivation, we model thin elastic surfaces as von Kármán plates and generalize the classical von Kármán equations, which are restricted to smooth fields, to fields which are piecewise smooth, and can possibly concentrate at singular curves, in addition to being singular at isolated points. The inhomogeneous sources to the von Kármán equations, given in terms of plastic strains, defect induced incompatibility, and body forces, are likewise allowed to be singular at isolated points and curves in the domain. The generalized framework is used to discuss the singular nature of deformation and stress arising due to conical deformations, folds, and folds terminating at a singular point.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"153 4-5","pages":"681 - 713"},"PeriodicalIF":2.0,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"4261199","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
Nucleation and Development of Multiple Cracks in Thin Composite Fibers via the Inverse-Deformation Approach 反变形法研究复合材料纤维中多重裂纹的形核与发展
3区 工程技术
Journal of Elasticity Pub Date : 2023-06-06 DOI: 10.1007/s10659-023-10019-8
Arnav Gupta, Timothy J. Healey
{"title":"Nucleation and Development of Multiple Cracks in Thin Composite Fibers via the Inverse-Deformation Approach","authors":"Arnav Gupta, Timothy J. Healey","doi":"10.1007/s10659-023-10019-8","DOIUrl":"https://doi.org/10.1007/s10659-023-10019-8","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135493249","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 Second Gradient Theory of Thermoelasticity 热弹性的第二梯度理论
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-05-22 DOI: 10.1007/s10659-023-10020-1
D. Ieşan, R. Quintanilla
{"title":"A Second Gradient Theory of Thermoelasticity","authors":"D. Ieşan,&nbsp;R. Quintanilla","doi":"10.1007/s10659-023-10020-1","DOIUrl":"10.1007/s10659-023-10020-1","url":null,"abstract":"<div><p>This paper is concerned with a linear theory of thermoelasticity without energy dissipation, where the second gradient of displacement and the second gradient of the thermal displacement are included in the set of independent constitutive variables. In particular, in the case of rigid heat conductors the present theory leads to a fourth order equation for temperature. First, the basic equations of the second gradient theory of thermoelasticity are presented. The boundary conditions for thermal displacement are derived. The field equations for homogeneous and isotropic solids are established. Then, a uniqueness result for the basic boundary-initial-value problems is presented. An existence theorem is established for the first boundary value problem. The problem of a concentrated heat source is investigated using a solution of Cauchy-Kowalewski-Somigliana type.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 5","pages":"629 - 643"},"PeriodicalIF":1.8,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46986010","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
Correction to: On the Algebraic Riccati Equations of Finite Elastostatics 更正：论有限弹性力学的里卡蒂代数方程
IF 1.8 3区 工程技术
Journal of Elasticity Pub Date : 2023-05-16 DOI: 10.1007/s10659-023-10021-0
Gearoid Mac Sithigh
{"title":"Correction to: On the Algebraic Riccati Equations of Finite Elastostatics","authors":"Gearoid Mac Sithigh","doi":"10.1007/s10659-023-10021-0","DOIUrl":"10.1007/s10659-023-10021-0","url":null,"abstract":"","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 5","pages":"693 - 693"},"PeriodicalIF":1.8,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136021169","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
Renormalized Energy of a Dislocation Loop in a 3D Anisotropic Body 三维各向异性体中位错环的重整化能量
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-05-09 DOI: 10.1007/s10659-023-10017-w
Miroslav Šilhavý
{"title":"Renormalized Energy of a Dislocation Loop in a 3D Anisotropic Body","authors":"Miroslav Šilhavý","doi":"10.1007/s10659-023-10017-w","DOIUrl":"10.1007/s10659-023-10017-w","url":null,"abstract":"<div><p>The paper presents a rigorous analysis of the singularities of elastic fields near a dislocation loop in a body of arbitrary material symmetry that extends over the entire three-space. Explicit asymptotic formulas are given for the stress, strain and the incompatible distortion near the curved dislocation. These formulas are used to analyze the main object of the paper, the renormalized energy. The core-cutoff method is used to introduce that notion: first, a core in the form of a curved tube along the dislocation loop is removed; then, the energy of the complement is determined (= the core-cutoff energy). As in the case of a straight dislocation, the core-cutoff energy has a singularity that is proportional to the logarithm of the core radius. The renormalized energy is the limit, as the radius tends to 0, of the core-cutoff energy minus the singular logarithmic part. The main result of the paper are novel formulas for the coefficient of logarithmic singularity (the ‘prelogarithmic energy factor’) and for the renormalized energy.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"355 - 381"},"PeriodicalIF":2.0,"publicationDate":"2023-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45469882","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
Damage as a Material Phase Transition 损伤作为材料相变
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-04-26 DOI: 10.1007/s10659-023-10014-z
Andrea Bucchi, Domenico De Tommasi, Giuseppe Puglisi, Giuseppe Saccomandi
{"title":"Damage as a Material Phase Transition","authors":"Andrea Bucchi,&nbsp;Domenico De Tommasi,&nbsp;Giuseppe Puglisi,&nbsp;Giuseppe Saccomandi","doi":"10.1007/s10659-023-10014-z","DOIUrl":"10.1007/s10659-023-10014-z","url":null,"abstract":"<div><p>We propose paradigmatic examples to show how material damage phenomena can be efficiently described as a solid-solid phase transition. Starting from the pioneering work of J.L. Ericksen (J. Elast. 5(3):191–201, 1975) and the extensions of R.L. Fosdick and other authors to three-dimensional non linear elasticity, we describe the insurgence of damage as a hard → soft transition between two material states (damage and undamaged) characterized by two different energy wells. We consider the two separate constitutive assumptions of a simple Neo-Hookean type damageable material and a more complex microstructure inspired damageable Gent type material with variable limit threshold of the first invariant. In both cases we study two different deformation shear classes, one homogeneous and the other one inhomogeneous and obtain fully analytic description of the system damage response under cyclic loading. The considered constitutive assumptions and deformation classes are aimed at attaining fully analytic descriptions. On the other hand, we remark that the proposed, Griffith type, variational approach of damage, based on two different energy density functions for the damaged and undamaged material phases, and a resulting non (rank-one) convex energy, can be extended to systems with more complex energy functions, possibly with a larger number of wells representing an increasing degree of damage.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"325 - 344"},"PeriodicalIF":2.0,"publicationDate":"2023-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42465134","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: 2
Relaxation and Domain Wall Structure of Bilayer Moiré Systems 双层摩尔体系的弛豫和畴壁结构
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-04-25 DOI: 10.1007/s10659-023-10013-0
Paul Cazeaux, Drake Clark, Rebecca Engelke, Philip Kim, Mitchell Luskin
{"title":"Relaxation and Domain Wall Structure of Bilayer Moiré Systems","authors":"Paul Cazeaux,&nbsp;Drake Clark,&nbsp;Rebecca Engelke,&nbsp;Philip Kim,&nbsp;Mitchell Luskin","doi":"10.1007/s10659-023-10013-0","DOIUrl":"10.1007/s10659-023-10013-0","url":null,"abstract":"<div><p>Moiré patterns result from setting a 2D material such as graphene on another 2D material with a small twist angle or from the lattice mismatch of 2D heterostructures. We present a continuum model for the elastic energy of these bilayer moiré structures that includes an intralayer elastic energy and an interlayer misfit energy that is minimized at two stackings (disregistries). We show by theory and computation that the displacement field that minimizes the global elastic energy subject to a global boundary constraint gives large alternating regions of one of the two energy-minimizing stackings separated by domain walls.</p><p>We derive a model for the domain wall structure from the continuum bilayer energy and give a rigorous asymptotic estimate for the structure. We also give an improved estimate for the <span>(L^{2})</span>-norm of the gradient on the moiré unit cell for twisted bilayers that scales at most <i>inversely linearly</i> with the twist angle, a result which is consistent with the formation of one-dimensional domain walls with a fixed width around triangular domains at very small twist angles.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"443 - 466"},"PeriodicalIF":2.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45675002","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: 6
Mechanical Response of Metal Solenoids Subjected to Electric Currents 电流作用下金属螺线管的机械响应
IF 2 3区 工程技术
Journal of Elasticity Pub Date : 2023-04-25 DOI: 10.1007/s10659-023-10015-y
R. S. Elliott, N. Triantafyllidis
{"title":"Mechanical Response of Metal Solenoids Subjected to Electric Currents","authors":"R. S. Elliott,&nbsp;N. Triantafyllidis","doi":"10.1007/s10659-023-10015-y","DOIUrl":"10.1007/s10659-023-10015-y","url":null,"abstract":"<div><p>Solenoids, ubiquitous in electrical engineering applications, are devices formed from a coil of wire that use electric current to produce a magnetic field. In contrast to typical electrical engineering applications that pertain to their magnetic field, of interest here is their use as actuators by studying their mechanical deformation. An analytically tractable model of parallel, coaxial circular rings is used to find the solenoid’s axial deformation when subjected to a combined electrical (current) and mechanical (axial force) loading. Both finite and infinite solenoids are considered and their equilibrium configurations as well as their stability are investigated as functions of their geometry and applied current intensity.</p></div>","PeriodicalId":624,"journal":{"name":"Journal of Elasticity","volume":"154 1-4","pages":"407 - 419"},"PeriodicalIF":2.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43239215","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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