Mathematics and Mechanics of Solids最新文献_第3页

Nonlinear elastic general integral equations in micromechanics of random structure composites 随机结构复合材料微观力学中的非线性弹性一般积分方程

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-31 DOI: 10.1177/10812865241255048

Valeriy A Buryachenko

{"title":"Nonlinear elastic general integral equations in micromechanics of random structure composites","authors":"Valeriy A Buryachenko","doi":"10.1177/10812865241255048","DOIUrl":"https://doi.org/10.1177/10812865241255048","url":null,"abstract":"We consider static problems for composite materials (CMs) with either locally elastic or peridynamic constitutive properties. The general integral equation (GIE) is the exact integral equationWe consider static problems for composite materials connecting the random fields at the point being considered and the surrounding points. There is a very long and colored history of the development of GIE which goes back to Lord Rayleigh. Owing to the new GIE (forming the second background of micromechanics also called the computational analytical micromechanics, CAM), one proved that local micromechanics (LM) and peridynamic micromechanics (PM) are formally similar to each other for CM of random structures. By now, the GIEs are generalized to CMs (of statistically homogeneous and inhomogeneous structures) with the phases described by local models, strongly nonlocal models (strain type and displacement type, peridynamics), and weakly nonlocal models (strain-gradient theories, stress-gradient theories, and higher-order models). However, a fundamental restriction of all mentioned GIEs is their linearity with respect to a primary unknown variable. The goal of this study is obtaining nonlinear GIEs for PM, and, in a particular case, for LM. For the presentation of PM as a unified theory, we describe PM as the formalized schemes of blocked (or modular) structures so that the experts developing one block need not be experts in the underlying another block (this is a good background for effective collaborations of different teams in so many multidisciplinary areas as PM). The opportunity for the creation of this blocked structure of the PM is supported by a critical generalization of CAM which is extremely flexible, robust, and general.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"4 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141873024","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

Transient mode-III problem of the elastic matrix with a line inclusion 带线包容的弹性矩阵的瞬态模态-III 问题

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241262491

YS Wang, BL Wang, KF Wang

{"title":"Transient mode-III problem of the elastic matrix with a line inclusion","authors":"YS Wang, BL Wang, KF Wang","doi":"10.1177/10812865241262491","DOIUrl":"https://doi.org/10.1177/10812865241262491","url":null,"abstract":"The method of pull-out test has been used to identify the mechanical performance of hybrid and fiber-reinforced composite materials. This paper investigates the elastic phase preceding the pull-out of a rigid line inclusion from the polymer matrix with fixed top and bottom surfaces. The mode-III problem is investigated such that the pull-out force is applied from the out-of-plane direction and it can be either transient or static. By applying the singular integral equation technique, the semi-analytical elastic field expressions are obtained. Under the static pull-out force, the stress intensity factor (SIF) near the inclusion tip shows a monotonic increase as the length and height of the matrix increase, whereas for the transient pull-out force, the SIF displays an initial increasing and followed by a decline. The maximum SIF is obtained for (1) the matrix length is 2 to 2.5 times of the inclusion length, and (2) the matrix height is 1 to 2 times of the inclusion length. Moreover, this paper provides a solution approach that incorporates the elasticity of the inclusion, showing that there is an optimal shear stiffness that minimizes the stress singularity of system. The conclusions of this study hold significance for the design and performance evaluation of fiber-reinforced composite materials.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"245 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776123","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

Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation? 弹性电介质断裂力学中的电容器类比模型是否构成适当的近似值？

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241252368

Lennart Behlen, Daniel Wallenta, Andreas Ricoeur

{"title":"Does the capacitor analogy model in fracture mechanics of elastic dielectrics constitute an appropriate approximation?","authors":"Lennart Behlen, Daniel Wallenta, Andreas Ricoeur","doi":"10.1177/10812865241252368","DOIUrl":"https://doi.org/10.1177/10812865241252368","url":null,"abstract":"The analytical solution of an elliptic dielectric cavity in an infinite dielectric plate is taken as basis to investigate a Griffith crack problem which is obtained by letting the semi-minor axis tend towards zero. In the course of this, an erroneous conformal mapping, commonly employed in literature and correctly reproducing the electric field only in a part of the physical space, is rectified. Interpreting the elliptic interface as faces of a mechanically opened crack which is exposed to an oblique remote electric field, surface charges and electrostatic tractions are calculated. In contrast to the established capacitor analogy model, approximately yielding electric charge densities and Coulombic tractions from displacements and electric potentials in the undeformed crack configuration, the work at hand provides exact solutions accounting for different implications of the crack curvature and for the inclination of the electric field. Crack weight functions are finally used to calculate stress and electric displacement intensity factors. As turns out, the surface charges of the capacitor analogy represent an excellent substitute for the exact electric boundary conditions within a relevant range of parameters, whereas inaccurate Coulombic tractions in the vicinity of crack tips may lead to a significantly overestimated mode I stress intensity factor.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"48 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776122","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

Mechanics and mechanobiology of intracranial aneurysms 颅内动脉瘤的力学和力学生物学

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865231219163

JD Humphrey

引用次数: 0

Explicit solutions in Cartesian coordinates for an elliptic hole in an infinite elastic plate 无限弹性板中椭圆孔的直角坐标显解

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241249751

Mordecai Oore, Sageev Oore

引用次数: 0

Transient heat transfer analysis of a sandwich panel with a cracked honeycomb core 带裂纹蜂窝芯的夹芯板的瞬态传热分析

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241261638

Wenzhi Yang, Ruchao Gao, Jinxing Liu, Zengtao Chen

引用次数: 0

Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach 评估基于分解的四阶纤维取向张量插值方法：特征系统方法

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241241002

Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke

{"title":"Evaluation of a decomposition-based interpolation method for fourth-order fiber-orientation tensors: An eigensystem approach","authors":"Julian Karl Bauer, Constantin Krauß, Juliane Blarr, Philipp L Kinon, Luise Kärger, Thomas Böhlke","doi":"10.1177/10812865241241002","DOIUrl":"https://doi.org/10.1177/10812865241241002","url":null,"abstract":"We propose and assess a new decomposition-based interpolation method on fourth-order fiber-orientation tensors. This method can be used to change the resolution of discretized fields of fiber-orientation tensors, e.g., obtained from flow simulations or computer tomography, which are common in the context of short- and long-fiber–reinforced composites. The proposed interpolation method separates information on structure and orientation using a parametrization which is based on tensor components and a unique eigensystem. To identify this unique eigensystem of a given fourth-order fiber-orientation tensor in the absence of material symmetry, we propose a sign convention on tensor coefficients. We explicitly discuss challenges associated with material symmetries, e.g., non-distinct eigenvalues of the second-order fiber-orientation tensor and propose algorithms to obtain a unique set of parameters combined with a minimal number of eigensystems of a given fourth-order fiber-orientation tensor. As a side product, we specify for the first time, parametrizations and admissible parameter ranges of cubic, tetragonal, and trigonal fiber-orientation tensors. Visualizations in terms of truncated Fourier series, quartic plots, and tensor glyphs are compared.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":"61 1","pages":""},"PeriodicalIF":2.6,"publicationDate":"2024-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141776121","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

Transfer matrix for a weakly nonlocal elastic layer and Lamb waves in layered nonlocal composite plates 弱非局部弹性层的传递矩阵和层状非局部复合板中的 Lamb 波

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241258377

Vu Thi Ngoc Anh, Pham Chi Vinh, Tran Thanh Tuan

引用次数: 0

An internal variable model of macroscopic twin boundary dynamics 宏观孪生边界动力学的内变量模型

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-26 DOI: 10.1177/10812865241258723

Arkadi Berezovski

引用次数: 0

Non-coercive problems for elastic plates with thin junction 薄交界弹性板的非强制问题