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Interaction between an edge dislocation and a circular elastic inhomogeneity with Steigmann-Ogden interface. Steigmann-Ogden界面下边缘位错与圆形弹性不均匀性的相互作用
IF 2.6 4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-11-01 Epub Date: 2023-04-26 DOI: 10.1177/10812865231166081
Xu Wang, Peter Schiavone
{"title":"Interaction between an edge dislocation and a circular elastic inhomogeneity with Steigmann-Ogden interface.","authors":"Xu Wang, Peter Schiavone","doi":"10.1177/10812865231166081","DOIUrl":"10.1177/10812865231166081","url":null,"abstract":"<p><p>We propose an effective method for the solution of the plane problem of an edge dislocation in the vicinity of a circular inhomogeneity with Steigmann-Ogden interface. Using analytic continuation, the pair of analytic functions defined in the infinite matrix surrounding the inhomogeneity can be expressed in terms of the pair of analytic functions defined inside the circular inhomogeneity. Once the two analytic functions defined in the circular inhomogeneity are expanded in Taylor series with unknown complex coefficients, the Steigmann-Ogden interface condition can be written explicitly in complex form. Consequently, all of the complex coefficients appearing in the Taylor series can be uniquely determined so that the two pairs of analytic functions are then completely determined. An explicit and general expression of the image force acting on the edge dislocation is derived using the Peach-Koehler formula.</p>","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2023-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10630138/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45543969","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Interaction between an edge dislocation and a circular incompressible liquid inclusion 边缘位错与圆形不可压缩液体包裹体之间的相互作用
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-24 DOI: 10.1177/10812865231202445
Xu Wang, Peter Schiavone
{"title":"Interaction between an edge dislocation and a circular incompressible liquid inclusion","authors":"Xu Wang, Peter Schiavone","doi":"10.1177/10812865231202445","DOIUrl":"https://doi.org/10.1177/10812865231202445","url":null,"abstract":"We use Muskhelishvili’s complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson’s ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135273268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 thermodynamic extremal principles in gradient plasticity with energetic forces 含能梯度塑性的热力学极值原理
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-18 DOI: 10.1177/10812865231196296
Henryk Petryk
{"title":"On thermodynamic extremal principles in gradient plasticity with energetic forces","authors":"Henryk Petryk","doi":"10.1177/10812865231196296","DOIUrl":"https://doi.org/10.1177/10812865231196296","url":null,"abstract":"Incremental energy minimization is revisited as a method of determining an incremental solution for rate-independent dissipative solids undergoing isothermal quasi-static deformation. The incremental minimization is applied to the total internal energy of the compound thermodynamic system that consists of a deforming body with internal variables, a conservative loading device, and an ambient heat reservoir. It is shown that the difference between the virtual and actual dissipation rates plays a fundamental role in this minimization, which is related to thermodynamic extremal principles of local and global type. The analysis is carried out within the gradient plasticity framework with the energetic forces derived as the variational derivative of the Helmholtz free energy depending on the spatial gradient of arbitrary internal variables. Specifications are given for existing models of gradient plasticity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135884460","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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-order model of small-strain incompatible elasticity 小应变不相容弹性的二阶模型
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-16 DOI: 10.1177/10812865231193427
Samuel Amstutz, Nicolas van Goethem
{"title":"A second-order model of small-strain incompatible elasticity","authors":"Samuel Amstutz, Nicolas van Goethem","doi":"10.1177/10812865231193427","DOIUrl":"https://doi.org/10.1177/10812865231193427","url":null,"abstract":"This work deals with the modeling of solid continua undergoing incompatible deformations due to the presence of microscopic defects like dislocations. Our approach relies on a geometrical description of the medium by the strain tensor and the representation of internal efforts using zeroth- and second-order strain gradients in an infinitesimal framework. At the same time, energetic arguments allow to monitor the corresponding moduli. We provide mathematical and numerical results to support these ideas in the framework of isotropic constitutive laws.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077518","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Dispersive transverse waves for a strain-limiting continuum model 应变极限连续介质模型的色散横波
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-15 DOI: 10.1177/10812865231188931
HA Erbay, KR Rajagopal, G Saccomandi, Y Şengül
{"title":"Dispersive transverse waves for a strain-limiting continuum model","authors":"HA Erbay, KR Rajagopal, G Saccomandi, Y Şengül","doi":"10.1177/10812865231188931","DOIUrl":"https://doi.org/10.1177/10812865231188931","url":null,"abstract":"It is well known that propagation of waves in homogeneous linearized elastic materials of infinite extent is not dispersive. Motivated by the work of Rubin, Rosenau, and Gottlieb, we develop a generalized continuum model for the response of strain-limiting materials that are dispersive. Our approach is based on both a direct inclusion of Rivlin–Ericksen tensors in the constitutive relations and writing the linearized strain in terms of the stress. As a result, we derive two coupled generalized improved Boussinesq-type equations in the stress components for the propagation of pure transverse waves. We investigate the traveling wave solutions of the generalized Boussinesq-type equations and show that the resulting ordinary differential equations form a Hamiltonian system. Linearly and circularly polarized cases are also investigated. In the case of unidirectional propagation, we show that the propagation of small-but-finite amplitude long waves is governed by the complex Korteweg–de Vries (KdV) equation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135758630","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Mesoscale analysis of fracture process in brick masonry structures 砖砌体结构断裂过程的细观尺度分析
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-14 DOI: 10.1177/10812865231199067
K Koocheki, S Pietruszczak
{"title":"Mesoscale analysis of fracture process in brick masonry structures","authors":"K Koocheki, S Pietruszczak","doi":"10.1177/10812865231199067","DOIUrl":"https://doi.org/10.1177/10812865231199067","url":null,"abstract":"This paper deals with mesoscale analysis of masonry structures, which involves fracture propagation in brick units as well as along the masonry joints. The brick–mortar interfaces are incorporated in standard finite elements by employing a constitutive law with embedded discontinuity. Macrocracks in bricks are modelled in a discrete way using the same methodology, without any a-priori assumptions regarding their orientation. The proposed approach is computationally efficient as it does not explicitly require the discretization of joints. The accuracy of the approximation is first assessed by comparing the solution with a detailed mesoscale model incorporating interface elements. Later, a numerical study is conducted involving simulation of various experimental tests on small masonry assemblages, as well as single-leaf masonry walls, with running bond pattern, subjected to in-plane loading. The results clearly demonstrate the predictive abilities of the proposed simplified approach.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135803180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid 非格林弹性固体二维梁剪应力的近似测定
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-13 DOI: 10.1177/10812865231201623
Roger Bustamante
{"title":"Approximate determination of shear stresses for a 2D beam made of a non-Green elastic solid","authors":"Roger Bustamante","doi":"10.1177/10812865231201623","DOIUrl":"https://doi.org/10.1177/10812865231201623","url":null,"abstract":"Shear stresses for a two-dimensional (2D) beam are calculated modifying the classical method developed by Jouravski, for the case the linearized strain tensor is assumed to be a nonlinear function of the Cauchy stresses. Two problems are studied, namely, the case of a cantilever beam with a point load on its free edge (considering a rectangular and a circular cross-section) and the three-point flexural test for a beam of rectangular cross-section. Numerical results are obtained for the particular case of a bimodular constitutive model for rock, and the results for the shear stresses are compared with the predictions of the classical theory of strength of materials for such problems, assuming a linearized elastic body.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135858325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Plane deformations of the Varga material Varga材料的平面变形
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-11 DOI: 10.1177/10812865231199460
Daniel J Arrigo, Travis C Chism
{"title":"Plane deformations of the Varga material","authors":"Daniel J Arrigo, Travis C Chism","doi":"10.1177/10812865231199460","DOIUrl":"https://doi.org/10.1177/10812865231199460","url":null,"abstract":"The governing equations for plane deformations of isotropic incompressible hyperelastic materials are highly nonlinear, and consequently, very few exact solutions are known. As far as we are aware, the Varga material is the only material in which results of any generality are known. In this paper, we show that for the Varga material, the full governing equations are in fact linearizable.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136210853","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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: 1
A theoretical model for power generation via liquid crystal elastomers 液晶弹性体发电的理论模型
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-11 DOI: 10.1177/10812865231193735
L Angela Mihai
{"title":"A theoretical model for power generation via liquid crystal elastomers","authors":"L Angela Mihai","doi":"10.1177/10812865231193735","DOIUrl":"https://doi.org/10.1177/10812865231193735","url":null,"abstract":"Motivated by the need for new materials and green energy production and conversion processes, a class of mathematical models for liquid crystal elastomers (LCEs) integrated within a theoretical charge pump electrical circuit is considered. The charge pump harnesses the chemical and mechanical properties of LCEs transitioning from the nematic to isotropic phase when illuminated or heated to generate higher voltage from a lower voltage supplied by a battery. For the material constitutive model, purely elastic and neoclassical-type strain energy densities applicable to a wide range of monodomain nematic elastomers are combined, while elastic and photothermal responses are decoupled to make the investigation analytically tractable. By varying the model parameters of the elastic and neoclassical terms, it is found that LCEs are more effective than rubber when used as dielectric material within a charge pump capacitor.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136063817","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Professor A.P.S. (Patrick) Selvadurai (1942–2023) A.P.S. (Patrick) Selvadurai教授(1942-2023)
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-10-09 DOI: 10.1177/10812865231202871
Peter Schiavone
{"title":"Professor A.P.S. (Patrick) Selvadurai (1942–2023)","authors":"Peter Schiavone","doi":"10.1177/10812865231202871","DOIUrl":"https://doi.org/10.1177/10812865231202871","url":null,"abstract":"","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135141686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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