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Flaw sensitivity of stochastic elastic materials 随机弹性材料的缺陷敏感性
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-11-07 DOI: 10.1177/10812865231208174
Shawn R Lavoie, Zhigang Suo
{"title":"Flaw sensitivity of stochastic elastic materials","authors":"Shawn R Lavoie, Zhigang Suo","doi":"10.1177/10812865231208174","DOIUrl":"https://doi.org/10.1177/10812865231208174","url":null,"abstract":"A material-specific length, called the flaw sensitivity length or fractocohesive length, is determined by measuring the strength of samples that contain cracks of various lengths. When the crack length is small compared with the fractocohesive length, the strength is unaffected by the crack. When the crack length is large compared with the fractocohesive length, the strength reduces as the crack length increases. Here we study how the fractocohesive length is affected by the stochastics of the constituents of a material. We simulate a model system, a truss in which the constituents are linearly elastic members forming a geometrically periodic lattice. The stochastics are represented by the scatter of strength among the members. The fractocohesive length scales with the length of each individual member, but the prefactor increases with the degree of scatter in member strength. The fractocohesive length can be much larger than the constituents of a material when the constituents have pronounced statistical variation.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"157 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476272","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
Non-classical theory of electro-thermo-elasticity incorporating local mass displacement and nonlocal heat conduction 结合局部质量位移和非局部热传导的非经典电热弹性理论
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-11-07 DOI: 10.1177/10812865231201132
Olha Hrytsyna, Yuriy Tokovyy, Maryan Hrytsyna
{"title":"Non-classical theory of electro-thermo-elasticity incorporating local mass displacement and nonlocal heat conduction","authors":"Olha Hrytsyna, Yuriy Tokovyy, Maryan Hrytsyna","doi":"10.1177/10812865231201132","DOIUrl":"https://doi.org/10.1177/10812865231201132","url":null,"abstract":"A non-classical local gradient theory of nonferromagnetic thermoelastic dielectrics is presented, incorporating both the local mass-displacement process and the heat-flux gradient effect. The process of local mass displacement is related to the changes in material microstructure. The nonlocal heat conduction law is also addressed in the model. Thus, the generalized relationship between the higher-grade heat and entropy fluxes is adopted. The gradient-type constitutive relations and governing equations are derived using the fundamental principles of continuum mechanics, non-equilibrium thermodynamics, and electrodynamics. Due to the contribution of higher-grade flux, the nonlocal law of heat conduction is obtained. The constitutive relations for isotropic materials with the corresponding additional material constants are derived. To illustrate the local gradient theory and to show the electro-thermo-mechanical coupling effect in isotropic materials, a straightforward problem is analytically solved for a layered non-piezoelectric structure under non-uniform temperature distribution. The analytical results reveal that the thermal polarization effect can also be pronounced in isotropic materials. To illustrate the model considering the effect of nonlocal heat conduction, the propagation of spherical thermoelastic harmonic waves in a homogeneous and isotropic elastic medium with non-classical heat conduction law is studied.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"192 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135476684","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 hierarchy of asymptotic models for a fluid-loaded elastic layer 流体加载弹性层的渐近模型层次
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-11-04 DOI: 10.1177/10812865231201573
Julius Kaplunov, Ludmila Prikazchikova, Sheeru Shamsi
{"title":"A hierarchy of asymptotic models for a fluid-loaded elastic layer","authors":"Julius Kaplunov, Ludmila Prikazchikova, Sheeru Shamsi","doi":"10.1177/10812865231201573","DOIUrl":"https://doi.org/10.1177/10812865231201573","url":null,"abstract":"A hierarchy of asymptotic models governing long-wave low-frequency in-plane motion of a fluid-loaded elastic layer is established. In contrast to a layer with traction-free faces, modelled by Neumann boundary conditions, a fluid-loaded one assumes more involved conditions along the interfaces, dictating a special asymptotic scaling. The latter corresponds to a fluid-borne bending wave, controlled by elastic stiffness of the layer and fluid inertia. In this case, the transverse inertia of the layer and fluid compressibility do not appear at zero-order approximation. The first-order approximation is associated with a Kirchhoff plate, immersed into incompressible fluid. In the studied free vibration setup, the fluid compressibility has to be taken into account only at third order, along with elastic rotary inertia. Transverse shear deformation enters the second-order approximation along with a few other corrections. The conventional impenetrability condition has to be also refined at second order. Dispersion relations corresponding to the developed asymptotic models are compared with the polynomial expansions of the full dispersion relation, obtained from the plane-strain problem of linear elasticity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"11 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135774061","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 computational multiscale approach towards the modelling of microstructures with material interfaces in electrical conductors 电导体材料界面微结构建模的计算多尺度方法
4区 工程技术
Mathematics and Mechanics of Solids Pub Date : 2023-11-03 DOI: 10.1177/10812865231202721
Dilek Güzel, Tobias Kaiser, Andreas Menzel
{"title":"A computational multiscale approach towards the modelling of microstructures with material interfaces in electrical conductors","authors":"Dilek Güzel, Tobias Kaiser, Andreas Menzel","doi":"10.1177/10812865231202721","DOIUrl":"https://doi.org/10.1177/10812865231202721","url":null,"abstract":"Motivated by the change of effective electrical properties grain or phase boundaries, a computational multiscale framework for continua with interfaces at the microscale is proposed. Cohesive-type interfaces are considered at the microscale, such that displacement and electrical potential jumps are accounted for. The governing equations for materials with interfaces under mechanical and electrical loads are provided. Based on these, a computational multiscale formulation is proposed. The coupling between the electrical and mechanical subproblem is established by the constitutive equations at the material interface. In order to investigate deformation-induced property changes at the microscale, the evolution of interface damage is elaborated. The proposed multiscale framework is further examined through various representative boundary value problems so as to identify its key properties.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819865","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
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":"4 4","pages":"0"},"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":"6 1","pages":"0"},"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":"28 1","pages":"0"},"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":"26 1","pages":"0"},"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":"125 1","pages":"0"},"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":"46 1","pages":"0"},"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
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