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Suppressing thermal stress in the vicinity of a circular nano-inhomogeneity via the mechanism of size effects

MATHEMATICS AND MECHANICS OF SOLIDS 2023年第8期28卷 1863-1876页

作者： Huang, Haojie Xing, Shichao Song, Kun Univ Shanghai Sci & Technol Sch Energy & Power Engn Shanghai Peoples R China Shanghai Key Lab Multiphase Flow & Heat Transfer P Shanghai Peoples R China Tongling Univ Key Lab Construction Hydraul Robots Anhui Higher Educ Inst Tongling Peoples R China Nanjing Tech Univ Sch Mech & Power Engn 30 Puzhu South Rd Nanjing 211816 Peoples R China

Thermal stress is one of the main factors threatening the reliability of nanocomposites. In this paper, we propose a set of interfacial conditions to simulate the interfacial phonon scattering and interfacial elasticity in the nanocomposite, and then obtain closed-form solutions for the thermal-elastic fields around the circular nano-inhomogeneity. The results show that the interfacial thermal stress within matrix is more sensitive to interfacial phonon scattering than that in nano-inhomogeneity, while the size change of inhomogeneity has greater impact on the stress of nano-inhomogeneity than that of the matrix. In view of the significant effects of thermal conductivities and thermal expansion coefficients on the thermal stress around inhomogeneity, the maximum von Mises stress is reduced up to three orders of magnitude by adjusting these parameters. More importantly, the thermal stresses within matrix and inhomogeneity can be, respectively, designed as "zero" even though the nanocomposite is subjected to a large thermal loading, which is viewed as an update mechanism of "neutral inhomogeneity." Our work provides guidance for the design of nanocomposites and has important potential applications.

关键词： Thermal stress nano-inhomogeneity interfacial phonon scattering interfacial elasticity complex variable method

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A thin-film-covered mode III crack with dislocation-free zones

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INTERNATIONAL JOURNAL OF FRACTURE 2023年第1期239卷 1-12页

作者： Wang, Xu Schiavone, Peter East China Univ Sci & Technol Sch Mech & Power Engn 130 Meilong Rd Shanghai 200237 Peoples R China Univ Alberta Dept Mech Engn 10-203 Donadeo Innovat Ctr Engn Edmonton AB T6G 1H9 Canada

We use complex variable methods and the theory of singular integral equations to study a thin-film-covered mode III crack with dislocation-free zones (DFZs) under uniform remote anti-plane shear stress. The equilibrium condition is formulated in terms of a single singular integral equation constructed in the image plane via the solution of the problem of a single screw dislocation interacting with a completely coated crack and the method of continuously distributed dislocations. The singular integral equation is solved numerically using the Gauss-Chebyshev integration formula to arrive at the dislocation distribution function, the DFZ condition, the total number of dislocations in the plastic zone and the local mode III stress intensity factor at the crack tip.

关键词： Thin-film-covered crack Plastic zone Dislocation-free zone complex variable method Singular integral equation Dislocation shielding effect

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Analytical approach to estimating the influence of friction slip contact between surrounding rock and concrete lining on mechanical response of deep rheological soft rock tunnels

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APPLIED MATHEMATICAL MODELLING 2023年 113卷 287-308页

作者： Zhao, Nannan Shao, Zhushan Yuan, Bo Chen, Xinyuan Wu, Kui Xian Univ Architecture & Technol Sch Civil Engn Xian 710055 Peoples R China Xian Univ Architecture & Technol Sch Sci Xian 710055 Peoples R China

For a deep-buried tunnel in soft ground, the contact condition between the surrounding rock and lining significantly affects the mechanical response. This is because the slip bond relationship on the contact surface has a direct influence on the tangential slip, result-ing in the redistribution of displacement and stress on the contact surface between the surrounding rock and lining. However, previous studies have not paid sufficient attention to this problem, and a well-established method for quantitatively evaluating this influ-ence remains unavailable. Therefore, the influence of the contact behavior between the surrounding rock and lining was examined in this study using an analytical method. First, the concept of friction slip contact and corresponding theoretical equations are proposed based on the real contact behavior between the surrounding rock and lining. Second, con-sidering the friction slip contact between the surrounding rock and lining, a mechanical model of the tunnel excavation-support process was established, and analytical solutions for the stress and displacement of the tunnel within a viscoelastic rock material were real-ized. Third, the effectiveness and reliability of the proposed solutions were validated. The results could be degenerated to those that do not consider the influence of the mechanical behavior of the contact surface. In addition, there was good agreement between the ana-lytical results and further numerical calculation results. Finally, a comprehensive paramet-ric investigation was conducted, including the influences of the initial release coefficient, friction coefficient, and installation time of the lining. Some useful recommendations for tunnel lining design are provided herein.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Deep soft rock tunnel Time -dependent behavior Friction slip contact complex variable method Analytical solution

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Effect of a gap on the open hole tension strength of carbon fiber reinforced plastic laminates

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JOURNAL OF COMPOSITE MATERIALS 2023年第21期57卷 3377-3391页

作者： Suemasu, Hiroshi Aoki, Yuichiro Tateishi, Yasutomo Sugimoto, Sunao Nakamura, Toshiya Japan Aerosp Explorat Agcy Aeronaut Technol Directorate Tokyo Japan Nihon Emsco Co Ltd Tokyo branch Off Tokyo Japan Japan Aerosp Explorat Agcy Aeronaut Technol Directorate 6-13-1 Osawa Mitaka Tokyo 1810015 Japan

Tensile tests of quasi-isotropic laminates with a circular open hole, which include a gap in the hole area, were conducted to demonstrate the effect of the gap on the strength. The test showed that the reduction in the open-hole strength owing to the gap was less significant than that in the no-hole tensile strength. A two-dimensional mechanical model of quasi-isotropic laminates with an arbitrary inclined gap was proposed and analytically solved to obtain a closed-form expression for the stress concentration. An approximate expression was provided as the sum of the global uniform stress field and the local stress field near the open hole, which was solved based on a complex variable method. The present analytical solution agrees well with the corresponding two-dimensional finite element solutions. The solution indicated that the stress increase owing to the gap is limited at the stress concentration area. The analytical results were consistent with the experimental results.

关键词： Structural composites automated fiber placement technique defects stress concentrations complex variable method finite element method

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Analytical solutions on non-Darcy seepage of grouted and lined subsea tunnels under dynamic water levels

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OCEAN ENGINEERING 2023年 267卷

作者： Liu, Xiang Wang, Dongchi Zhang, Yu Jiang, Annan Fang, Qian Zhang, Rui Dalian Maritime Univ Coll Transportat Engn Dalian 116026 Peoples R China Beijing Jiaotong Univ Key Lab Urban Underground Engn Minist Educ Beijing 100044 Peoples R China Beijing Urban Construct Grp Co Ltd Beijing 100088 Peoples R China

For the grouted and lined subsea tunnels, the fluid in the low permeability media follows non-Darcy's law rather than Darcy's law. To address this, we provide analytical solutions for the grouted and lined subsea tunnel with dynamic water levels. Our method uses complex variable functions and Hansbo non-Darcy seepage model. The analytical solutions divide into three cases according to the critical water inflow and can degenerate into the traditional method following Darcy's law. The numerical simulation, experimental data, in-situ data, and other analytical solutions are adopted to verify our proposed method. The calculated results subjected to non-Darcy seepage are close to the in-situ data compared with other analytical solutions. When degenerating into the traditional method, the results agree well with those of previous methods following Darcy's law. It reveals that our method is suitable and universal. The parametric analyses of the non-linear flow index m, the critical hydraulic gradient il, the dynamic water level xi ci, the thickness of lining zone tl, and the relative permeability coefficient ratio of the grouting zone and lining zone kg/kl are carried out. The results show that non-linear seepage parameters and dynamic water levels significantly affect the water inflow and water head. The denser grouting material can apportion more water heads and make the lining apportion fewer water heads to protect the lining from fluctuation influencing of dynamic water levels.

关键词： Subsea tunnel Non -Darcy seepage Grouting and lining Dynamic water level complex variable method

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A screw dislocation in a three-phase composite composed of an anisotropic elastic half-plane bonded to an isotropic elastic half-plane reinforced by a circular inhomogeneity

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MATHEMATICS AND MECHANICS OF SOLIDS 2023年第8期28卷 1834-1844页

Using complex variable techniques, we solve the problem in anti-plane elasticity associated with a screw dislocation in a three-phase composite which is composed of an anisotropic elastic half-plane perfectly bonded to an isotropic elastic half-plane containing a circular elastic inhomogeneity. Analytical solutions are obtained for three typical cases: a screw dislocation in the isotropic half-plane in the exterior of the circular inhomogeneity, a screw dislocation inside the circular elastic inhomogeneity, a screw dislocation within the anisotropic half-plane. Explicit expressions of the image force acting on the screw dislocation are derived for each of the three cases. The numerical results indicate that at least one equilibrium position for the screw dislocation co-exists in each phase under certain conditions on the elastic constants.

关键词： Three-phase composite screw dislocation image force complex variable method equilibrium position anisotropic elasticity isotropic elasticity

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Using Laurent's series in the theoretical solution to estimate the stress resultants of FG-CNTRC plates weakened by a central cutout at different temperatures

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INTERNATIONAL JOURNAL FOR COMPUTATIONAL methodS IN ENGINEERING SCIENCE & MECHANICS 2023年第4期24卷 227-246页

作者： Zeighami, Vahid Jafari, Mohammad Jafari, Mohammad Shahrood Univ Technol Dept Mech & Mechatron Engn Shahrood Iran New Jersey Inst Technol Dept Mech & Ind Engn Newark NJ USA

Conventional ordinary materials have many weaknesses when exposed to extreme loadings. Hence, scientists develop novel engineered materials to address these weaknesses. Functionally Graded Carbon Nanotube Reinforced Composites (FG-CNTRCs) are a modern group of materials that have recently flourished thanks to their excellent and unique mechanical properties. One common loading condition is subjecting FG-CNTRC plates containing cutouts to in-plane loadings. The presence of an opening disturbs the stress field, especially in the proximity of the cutout, and creates stress concentration. This study estimates the stress and moment resultants on the edge of elliptical cutouts in asymmetric FG-CNTRC plates under various loading conditions using a new analysis based on Lekhnitskii's complex variables method, mapping function, and Laurent series. Unlike previous studies on perforated asymmetric plates, which were based on numerical methods or the Schwartz formulations, this study presents a new solution using Laurent's series to represent the holomorphic function. In calculating the stress and moment components around the opening, the effect of determining variables is studied. This approach can be generalized to solve different anisotropic body problems (FG_CNTRC, FGM, Laminate composites). Thus, stress and moment components in perforated anisotropic plates can be determined simply and systematically using this method.

关键词： Perforated functionally graded plate potential functions complex variable method stress resultants and moments CNTRC

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Thermoelectric field for a coated hole of arbitrary shape in a nonlinearly coupled thermoelectric material

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Applied Mathematics and Mechanics(English Edition) 2022年第11期43卷 1691-1700页

作者： Xu WANG P.SCHIAVONE School of Mechanical and Power Engineering East China University of Science and TechnologyShanghai 200237China Department of Mechanical Engineering University of Alberta10-203 Donadeo Innovation Center for EngineeringEdmonton T6G 1H9Canada

We study the thermoelectric field for an electrically and thermally insulated coated hole of arbitrary shape embedded in an infinite nonlinearly coupled thermoelectric material subject to uniform remote electric current density and uniform remote energy flux.A conformal mapping function for the coating and matrix is introduced,which simultaneously maps the hole boundary and the coating-matrix interface onto two concentric circles in the image *** analytic continuation,we derive a general solution in terms of two auxiliary *** general solution satisfies the insulating conditions along the hole boundary and all of the continuity conditions across the perfect coating-matrix *** the two auxiliary functions have been obtained in the elementary-form,the four original analytic functions in the coating and matrix characterizing the thermoelectric fields are completely and explicitly *** design of a neutral coated circular hole that does not disturb the prescribed thermoelectric field in the thermoelectric matrix is achieved when the relative thickness parameter and the two mismatch parameters satisfy a simple ***,the neutrality of a coated circular thermoelectric inhomogeneity is also accomplished.

关键词： thermoelectric material nonlinear coupling coated hole of arbitrary shape complex variable method analytic solution neutral coated hole

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Fracturing process and initiation mechanism of hard rock tunnels with different shapes: particle flow modeling and analytical study

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COMPUTATIONAL PARTICLE MECHANICS 2023年第6期10卷 1859-1875页

作者： Wu, Hao Fan, Aoqi Ma, Dan Spearing, A. J. S. Zheng, Zhi China Univ Min & Technol Sch Mines Xuzhou 221116 Peoples R China Guangxi Univ Guangxi Key Lab Disaster Prevent & Engn Safety Nanning 530004 Peoples R China Guangxi Univ Key Lab Disaster Prevent & Struct Safety Minist Educ Nanning 530004 Peoples R China Yunnan Phosphate Chem Grp Co Ltd Kunming 650600 Peoples R China

Rock-related disasters such as roof falls, sidewall spalling, and rock bursts are commonly encountered in hard rock tunnels, resulting in frequent occurrence of tunnel instability in tunneling and mining engineering. To improve the understanding of failure mechanism in hard tunnels, rocks containing one single hole with five cross-sectional shapes (circle, horseshoe, trapezoid, trapezoid and square) were modeled using the PFC (Particle Flow Code) program. Then, a series of biaxial compression tests with confining pressures of 0 MPa, 5 MPa, 10 MPa, 20 MPa and 40 MPa were conducted on these models to explore the influence of cross-sectional shape and stress condition on fracturing behavior of tunnels. Afterward, the analytical solutions of stress around the holes in rocks under different stress states were derived by the complex variable function method to interpret the fracture initiation mechanism. The results show that the mechanical property and fracturing characteristics are highly related to the hole shape and confining pressure. A total of four kinds of fractures emerges in sequence around the holes under uniaxial loading, i.e., primary tensile fracture, spalling fracture, remote fracture and shear fracture. With the growing of confining stress, the formation of tensile fractures is limited, while the initiation of the spalling fracture becomes more severe. Also, the failure mode of the pre-holed models shifts from shear failure to spalling failure. Besides, the analytical results of surrounding stress, namely tensile stress and compressive stress, distribute on the roofs/floors and sides of the holes under low lateral stress, whilst the law in case of high lateral stress is opposite, strongly explain the fracturing behavior. The research results have important guiding value for the comprehension of the fracturing behavior of rock tunnels whose axes are parallel to one of the principal stresses.

关键词： Fracturing process Hard rock tunnel Failure mode PFC modeling complex variable method Stress analysis

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A novel method for estimation of stress concentration factor of central cutouts located in orthotropic plate

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JOURNAL OF THE BRAZILIAN SOCIETY OF MECHANICAL SCIENCES AND ENGINEERING 2021年第7期43卷 1-13页

作者： Abbasnia, Ali Jafari, Mohammad Rohani, Abbas Shahrood Univ Technol Fac Mech & Mechatron Engn Shahrood Iran Ferdowsi Univ Mashhad Dept Biosyst Engn Fac Agr Mashhad Razavi Khorasan Iran

The purpose of this paper is to present a new method based on the regression analysis for estimating stress concentration factor of different cutouts in orthotropic plates. The existence of an explicit relation in terms of mechanical properties can be an approach for analyzing the stress of viscoelastic plates. Little research has been conducted to provide explicit relationships to calculate the theoretical stress concentration. In the present study first, using different values of the mechanical properties of the composites, stress concentration factor was calculated by employing an analytical solution based on the complex variable method. Then, using multiple linear regression, an explicit mathematical relation for different cutouts was presented with the purpose of estimating stress concentration factor in terms of mechanical properties. The results showed that the regression model is able to predict circumferential stress with a maximum error of 1% for circular, elliptical, triangular and square cutouts. Also, the evaluation of the model with k-fold cross validation method and also comparison with other studies showed that it is possible to rely on the present estimation. Working with the regression models, which are presented in this article, is very simple and can be practical. Graphic abstract

关键词： Stress concentration factor Composites Orthotropic plate Multiple linear regression complex variable method

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