Mathematics and Mechanics of Solids最新文献_第8页

Circular inclusion with a refined linearized version of Steigmann–Ogden model 采用经过改进的线性化 Steigmann-Ogden 模型的圆形包容

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-16 DOI: 10.1177/10812865231213408

Cheng Huang, Ming Dai

{"title":"Circular inclusion with a refined linearized version of Steigmann–Ogden model","authors":"Cheng Huang, Ming Dai","doi":"10.1177/10812865231213408","DOIUrl":"https://doi.org/10.1177/10812865231213408","url":null,"abstract":"The plane deformation of an infinite elastic matrix enclosing a single circular inclusion incorporating stretching and bending resistance for the inclusion–matrix interface is revisited using a refined linearized version of the Steigmann–Ogden model. This refined version of the Steigmann–Ogden model differs from other linearized counterparts in the literature mainly in that the tangential force of the interface defined in this version depends not only on the stretch of the interface but also on the bending moment and initial curvature of the interface (the corresponding bending moment relies on the change in the real curvature of the interface during deformation). Closed-form results are derived for the full elastic field in inclusion–matrix structure induced by an arbitrary uniform in-plane far-field loading. It is identified that with this refined version of the Steigmann–Ogden model a uniform stress distribution could be achieved inside the inclusion for any non-hydrostatic far-field loading when [Formula: see text] (where R is the radius of the inclusion, while [Formula: see text] and [Formula: see text] are the stretching and bending stiffness of the interface). Explicit expressions are also obtained for the effective transverse properties of composite materials containing a large number of unidirectional circular cylindrical inclusions using, respectively, the dilute and Mori–Tanaka homogenization methods. Numerical examples are presented to illustrate the differences between the refined version and two typical counterparts of the Steigmann–Ogden model in evaluating the stress field around a circular nanosized inclusion and the effective properties of the corresponding homogenized composites.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"5 4p2","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138968074","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

Circumferential shear for an incompressible non-Green elastic cylindrical annulus 不可压缩非格林弹性圆柱环的圆周剪切力

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-14 DOI: 10.1177/10812865231207401

R. Bustamante, K. Rajagopal, Oscar Orellana

引用次数: 0

Couple-stress effects in a thin film bonded to a half-space 与半空间粘合的薄膜中的耦合应力效应

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-08 DOI: 10.1177/10812865231209975

MA Güler, Y. Alinia, E. Radi

引用次数: 0

A mathematical mechanics mixed tape: Editor’s foreword to special issue in honor of Alain Goriely 数学力学混合磁带：纪念阿兰-戈里利特刊编者前言

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-08 DOI: 10.1177/10812865231210188

L. A. Mihai

引用次数: 0

An objective and accurate G1-conforming mixed Bézier FE-formulation for Kirchhoff–Love rods 针对基尔霍夫-洛夫棒的客观、精确的 G1-conforming 混合贝塞尔 FE 公式

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-07 DOI: 10.1177/10812865231204972

L. Greco, Domenico Castello, Massimo Cuomo

{"title":"An objective and accurate G1-conforming mixed Bézier FE-formulation for Kirchhoff–Love rods","authors":"L. Greco, Domenico Castello, Massimo Cuomo","doi":"10.1177/10812865231204972","DOIUrl":"https://doi.org/10.1177/10812865231204972","url":null,"abstract":"We present a new invariant numerical formulation suitable for the analysis of Kirchhoff–Love rod model based on the smallest rotation map for which the two kinematic descriptors are the placement of the centroid curve and the rotation angle that describes the orientation of the cross-section. In order to guarantee objectivity with respect to a rigid body motion, the spherical linear interpolation ( slerp) for the rotations is introduced. A new hierarchical interpolation for the rotation angle of the cross-section is proposed, composed by the drilling rotation (with respect to the unit tangent of the centroid curve) contained in the geodetic interpolation of the ends’ rotations plus an additional polynomial correction term. This correction term is needed in order to enhance the accuracy of the proposed finite element (FE) formulation. The FE model implicitly guarantees the G1 continuity conditions, thanks to a change in the parametrization of the centroid curve that leads to a generalization of the one-dimensional (1D) Hermitian interpolation. A mixed formulation is used in order to avoid locking and improve the computational efficiency of the method. A symmetric tangent stiffness operator is obtained performing the second covariant derivative of the mixed functional for which the Levi-Civita connection of the configurations manifold of the rod is needed. The objectivity, the robustness, and accuracy of the G1-conforming formulation are confirmed by means of several numerical examples.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"79 5","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138590683","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

An inverse application of unit cells for extracting fibre properties from effective properties of composites 从复合材料的有效特性中提取纤维特性的单元格逆向应用

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-05 DOI: 10.1177/10812865231212150

Zhenmin Zou, Shuguang Li

{"title":"An inverse application of unit cells for extracting fibre properties from effective properties of composites","authors":"Zhenmin Zou, Shuguang Li","doi":"10.1177/10812865231212150","DOIUrl":"https://doi.org/10.1177/10812865231212150","url":null,"abstract":"A semi-analytical solution is obtained in this paper for the micromechanical analysis of the square and hexagonal unit cells using complex potentials. It provides a means of numerical characterisation of unidirectionally fibre-reinforced composites for their effective properties. This process is considered as the forward problem and its inverse counterpart is also established in this paper to extract fibre properties from effective properties of composites. It is formulated into a mathematical optimisation problem in which the difference between predicted and provided effective properties is employed as the objective function with the fibre properties as the optimisation variables. The attempt of such an inverse problem is to address the lack of fibre properties for many types of composites commonly in use. The novelty of the paper lies in both sides of the analyses, forward and inverse, as none is available in the literature in the forms as presented in this paper and, more importantly, in the objective of this paper as an attempt to address the pressing and yet long-standing issue of lack of fibre properties. As a verification of the forward analysis, the predicted effective properties of a composite match perfectly with the finite element method (FEM) results. The same case is also employed to verify the inverse analysis by turning the prediction the other way round. Both the forward and inverse analyses have been validated against a series of experimental data. While the forward analysis is generally applicable to any input data as the properties of the constituents, the inverse analysis is sensitive to the input data. Potentially, the inverse analysis would offer a much-needed and also effective tool for the characterisation of fibres. However, reasonable predictions of fibre properties can only be obtained if input data are reasonably consistent.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"120 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138599665","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 modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region 涉及残余应力导致的非典型应力-应变关系的单纤维拉拔问题的修正分析模型：完全粘合区域的应力场分析

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-04 DOI: 10.1177/10812865231213022

Pengyu Pei, Guang Yang, Jinyu Zhou, Junfeng Lu

{"title":"A modified analytical model for the single-fiber pullout problem involving non-classical stress–strain relationships due to residual stresses: Analysis of stress field in the fully bonded region","authors":"Pengyu Pei, Guang Yang, Jinyu Zhou, Junfeng Lu","doi":"10.1177/10812865231213022","DOIUrl":"https://doi.org/10.1177/10812865231213022","url":null,"abstract":"Upon reevaluating the influence of residual stresses generated by thermal mismatches in fibrous composites during the curing process, we introduce a modified model for the extraction of a single fiber from an elastic matrix. In contrast to previous models, which solely factored residual stress effects into the boundary conditions at the fiber–matrix interface while omitting them from the constitutive relations, our current model acknowledges bulk residual stress as finite values. Consequently, it yields non-conventional constitutive relations to describe the incremental deformation caused by external pulling forces. We have developed a practical semi-analytical series solution for the radial displacement of the matrix and an exact solution for the radial displacement of the fiber. To validate our modified model, we simplify it to a scenario where the influence of residual stress on the stress–strain relationship is excluded and compare it with results from existing literature. This comparison underscores the soundness of our modified model. We present a phase diagram to illustrate how the impact of residual stress on stress field prediction varies based on the ratio of the fiber modulus to the matrix modulus. This phase diagram serves as a valuable tool for evaluating whether it is advisable to transition from the previous mechanical model, which disregards the influence of residual stress on the stress–strain relationship, to the new model, which takes this influence into account within the stress–strain relationship.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"35 8","pages":""},"PeriodicalIF":2.6,"publicationDate":"2023-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138602600","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

Limit analysis of masonry domes with oculus and lantern: A comparison between different approaches 带圆顶和灯笼的砌体穹顶的极限分析：不同方法的比较

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-04 DOI: 10.1177/10812865231205814

Danila Aita, Gabriele Milani, A. Taliercio

引用次数: 0

Connections between the morphoelastic treatment of growth-induced instabilities and earlier hyperelastic treatments of buckling under thrust 生长诱发不稳定性的形态弹性处理方法与早期推力下屈曲的超弹性处理方法之间的联系

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-12-01 DOI: 10.1177/10812865231200242

T. Pence

引用次数: 0

A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure 考虑纤维分布的胶原结构的人角膜的数值模型

4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2023-11-08 DOI: 10.1177/10812865231202024

Maria Laura De Bellis, Marcello Vasta, Alessio Gizzi, Anna Pandolfi

{"title":"A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure","authors":"Maria Laura De Bellis, Marcello Vasta, Alessio Gizzi, Anna Pandolfi","doi":"10.1177/10812865231202024","DOIUrl":"https://doi.org/10.1177/10812865231202024","url":null,"abstract":"We present a fiber-distributed model of the reinforcing collagen of the human cornea. The model describes the basic connections between the components of the tissue by defining an elementary block (cell) and upscaling it to the physical size of the cornea. The cell is defined by two sets of collagen fibrils running in approximately orthogonal directions, characterized by a random distribution of the spatial orientation and connected by chemical bonds of two kinds. The bonds of the first kind describe the lamellar crosslinks, forming the ribbon-like lamellae; while the bonds of the second kind describe the stacking crosslinks, piling up the lamellae to form the structure of the stroma. The spatial replication of the cell produces a truss structure with a considerable number of degrees of freedom. The statistical characterization of the collagen fibrils leads to a mechanical model that reacts to the action of the deterministic intraocular pressure with a stochastic distribution of the displacements, here characterized by their mean value and variance. The strategy to address the solution of the heavy resulting numerical problem is to use the so-called stochastic finite element improved perturbation method combined with a fully explicit solver. The results demonstrate that the variability of the mechanical properties affects in a non-negligible manner the expected response of the structure to the physiological action.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"105 4","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135342213","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