Mathematics and Mechanics of Solids最新文献_第2页

Size-dependent thermoelastic damping analysis of functionally graded polymer micro plate resonators reinforced with graphene nanoplatelets based on three-phase-lag heat conduction model 基于三相滞后热传导模型的功能分级聚合物微板谐振器热弹性阻尼尺寸分析

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-08-08 DOI: 10.1177/10812865241263531

Wei Peng, Xu Zhang, Tianhu He, Yaru Gao, Yan Li

{"title":"Size-dependent thermoelastic damping analysis of functionally graded polymer micro plate resonators reinforced with graphene nanoplatelets based on three-phase-lag heat conduction model","authors":"Wei Peng, Xu Zhang, Tianhu He, Yaru Gao, Yan Li","doi":"10.1177/10812865241263531","DOIUrl":"https://doi.org/10.1177/10812865241263531","url":null,"abstract":"Nanocomposite materials, such as graphene nanoplatelets (GPLs), have been fabricated into high-efficient resonators due to the excellent thermo-mechanical properties. In addition, thermoelastic damping (TED), as a dominant intrinsic dissipation mechanisms, is a major challenge in optimizing high-performance micro-/nano-resonators. Nevertheless, the classical TED models fail on the micro-/nano-scale due to not considering the influences of the size-dependent effect and the thermal lagging effect. To fill these gaps, the present work aims to investigate TED analysis of functionally graded (FG) polymer microplate resonators reinforced with GPLs based on the modified couple stress theory (MCST) and the three-phase-lag (TPL) heat conduction model. Four patterns of GPL distribution including the UD, FG-O, FG-X, and FG-A pattern distributions are taken into account, and the effective mechanical properties of the plate-type nanocomposite are evaluated based on the Halpin-Tsai model. The energy equation and the transverse motion equation in the Kirchhoff microplate model are formulated, and then, the analytical solution of TED is solved by complex frequency method. The influences of the various parameters involving the material length-scale parameter, the phase-lag parameters, and the total weight fraction of GPLs on the TED are discussed in detail. The obtained results show that the effects of the modified parameter on the TED are pronounced. This paper provides a theoretical approach to estimate TED in the design of high-performance micro-resonators.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945978","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

Fractionalization of Forchheimer’s correction to Darcy’s law in porous media in large deformations 大变形多孔介质中达西定律的福克海默修正分数化

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-08-03 DOI: 10.1177/10812865241252577

Sachin Gunda, Alessandro Giammarini, Ariel Ramírez-Torres, Sundararajan Natarajan, Olga Barrera, Alfio Grillo

{"title":"Fractionalization of Forchheimer’s correction to Darcy’s law in porous media in large deformations","authors":"Sachin Gunda, Alessandro Giammarini, Ariel Ramírez-Torres, Sundararajan Natarajan, Olga Barrera, Alfio Grillo","doi":"10.1177/10812865241252577","DOIUrl":"https://doi.org/10.1177/10812865241252577","url":null,"abstract":"This work presents a theoretical and numerical study of the flow of the interstitial fluid saturating a porous medium, principally aimed at modeling a bio-mimetic material and assumed to experience a dynamic regime different from the Darcian one, as is typically hypothesized in biomechanical scenarios. The main aspect of our research is the conjecture according to which, for a particular mechanical state of the porous medium, the fluid exhibits two types of deviation from Darcy’s law. One is due to the inertial forces characterizing the pore scale dynamics of the fluid. This aspect can be resolved by turning to the Forchheimer correction to Darcy’s law, which introduces non-linearities in the relationship between the fluid filtration velocity and the dissipative forces describing the interactions between the fluid and the solid matrix. The second source of discrepancies from classical Darcy’s law emerges, for example, when pore scale disturbances to the flow, such as obstructions of the fluid path or clogging of the pores, result in a time delay between drag force and filtration velocity. Recently, models have been proposed in which such delay is described through constitutive laws featuring fractional operators. Whereas, to the best of our knowledge, the aforementioned behaviors have been studied separately or in small deformations, we present a model of fluid flow in a deformable porous medium undergoing large deformations in which the fluid motion obeys a fractionalized Forchheimer’s correction. After reviewing Forchheimer’s formulation, we present a fractionalization of the Darcy–Forchheimer law, and we explain the numerical procedure adopted to solve the highly non-linear boundary value problem resulting from the presence of the two considered deviations from the Darcian regime. We complete our study by highlighting the way in which the fractional order of the model tunes the magnitude of the pore pressure and fluid filtration velocity.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":2.6,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141945980","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

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":null,"pages":null},"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

A hidden convexity in continuum mechanics, with application to classical, continuous-time, rate-(in)dependent plasticity 连续介质力学中的隐蔽凸性，应用于经典、连续时间、速率（不）相关塑性

IF 2.6 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-31 DOI: 10.1177/10812865241258154

Amit Acharya

引用次数: 0

Mode-III fracture of four cracks emanating from an elliptical hole in one-dimensional orthorhombic quasicrystals with piezoelectric effect 具有压电效应的一维正方体准晶体中由椭圆孔发出的四条裂缝的模式-III断裂

IF 1.7 4区工程技术

Mathematics and Mechanics of Solids Pub Date : 2024-07-28 DOI: 10.1177/10812865241264006

Yuanyuan Gao, Guanting Liu, Zhenping Sun, Yuxin Zhang

{"title":"Mode-III fracture of four cracks emanating from an elliptical hole in one-dimensional orthorhombic quasicrystals with piezoelectric effect","authors":"Yuanyuan Gao, Guanting Liu, Zhenping Sun, Yuxin Zhang","doi":"10.1177/10812865241264006","DOIUrl":"https://doi.org/10.1177/10812865241264006","url":null,"abstract":"In this study, a new generalized conformal mapping is introduced using the generalized complex variable method, focusing on the investigation of the anti-plane problem of an elliptical hole with four cracks in one-dimensional (1D) orthogonal piezoelectric quasicrystals. Under the consideration of electrically impermeable and electrically permeable boundary conditions, the governing equations of the anti-plane problem in 1D orthogonal piezoelectric quasicrystals are successfully simplified into an eighth-order partial differential equation and a fourth-order partial differential equation by introducing a potential function. Based on this, analytical solutions for the stress field and electric field are obtained, and the exact solution for the stress intensity factor (SIF) is derived. In addition, formulas for the electric displacement intensity factor (EDIF) and energy release rate are provided. Subsequently, the influence of geometric parameters and external loads on the field intensity factors and energy release rate is analyzed through numerical examples, providing a theoretical basis for engineering mechanics analysis.","PeriodicalId":49854,"journal":{"name":"Mathematics and Mechanics of Solids","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141796732","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":null,"pages":null},"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":null,"pages":null},"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

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

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

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