The presence of an edge dislocation in a surface of a two-dimensional precipitate of square shape embedded in a semi-infinite matrix has been discussed when the precipitate is submitted to misfit strain due to the lattice mismatch between the two phases. Considering any orientation of the precipitate relative to the matrix free-surface, the total force applying on the dislocation has been analytically calculated and its equilibrium position has been determined. The conjugated effects of the precipitate misorientation, of the lattice mismatch and of the precipitate/matrix distance have been finally characterized. A shifting effect on this equilibrium position has been analyzed.
{"title":"Misfit dislocation in a precipitate/matrix interface of any orientation relative to the matrix free-surface","authors":"J. Colin","doi":"10.24423/AOM.3590","DOIUrl":"https://doi.org/10.24423/AOM.3590","url":null,"abstract":"The presence of an edge dislocation in a surface of a two-dimensional precipitate of square shape embedded in a semi-infinite matrix has been discussed when the precipitate is submitted to misfit strain due to the lattice mismatch between the two phases. Considering any orientation of the precipitate relative to the matrix free-surface, the total force applying on the dislocation has been analytically calculated and its equilibrium position has been determined. The conjugated effects of the precipitate misorientation, of the lattice mismatch and of the precipitate/matrix distance have been finally characterized. A shifting effect on this equilibrium position has been analyzed.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"445-464"},"PeriodicalIF":0.8,"publicationDate":"2020-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43651407","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}
J. Yescas, P. Mandal, J. Sinha, R. Snook, J. Hawkes, P. M. Garibaldi, R. Carrera-Espinoza
This paper presents a methodology for the mechanical characterization of agarose millimetric spheres using resonant principles. Detection of the modes of vibration was conducted using a low-cost experimental setup based on an electret microphone adapted with a thin latex elastic membrane for the sensing stage and a piezoelectric actuator driven by a conventional transformer for the excitation stage. The identification of vibration modes is supported through an ANSYS Finite Element model of the experimental setup. Experimental and numerical results demonstrate that two modes of vibration, known as Quadrupole and Octupole, appear in the amplitude spectrum and can be used to obtain stiffness values for the samples. Following this approach, Young’s modulus of 209 ± 19.80, 338 ± 35.30 and 646 ± 109 kPa for 2%, 3% and 4% agarose millimetric spheres were calculated.
{"title":"Mechanical characterization of millimetric agarose spheres using a resonant technique","authors":"J. Yescas, P. Mandal, J. Sinha, R. Snook, J. Hawkes, P. M. Garibaldi, R. Carrera-Espinoza","doi":"10.24423/AOM.3499","DOIUrl":"https://doi.org/10.24423/AOM.3499","url":null,"abstract":"This paper presents a methodology for the mechanical characterization of agarose millimetric spheres using resonant principles. Detection of the modes of vibration was conducted using a low-cost experimental setup based on an electret microphone adapted with a thin latex elastic membrane for the sensing stage and a piezoelectric actuator driven by a conventional transformer for the excitation stage. The identification of vibration modes is supported through an ANSYS Finite Element model of the experimental setup. Experimental and numerical results demonstrate that two modes of vibration, known as Quadrupole and Octupole, appear in the amplitude spectrum and can be used to obtain stiffness values for the samples. Following this approach, Young’s modulus of 209 ± 19.80, 338 ± 35.30 and 646 ± 109 kPa for 2%, 3% and 4% agarose millimetric spheres were calculated.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"217-233"},"PeriodicalIF":0.8,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45164277","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}
This article presents the thermo-diffusion of an isotropic thick circular plate. The Green and Naghdi’s models including the energy dissipation are anticipated in their simple forms. Novel multi single/dual-phase-lag models with higher-order timederivatives are also provided to examine the thermo-diffusion response of the circular plate. The simple and refined forms of Green and Naghdi’s types II and III are investigated in this work. The closed-form solution of thermal diffusion governing equations is attained by taking into account the boundary conditions. A validation examples of outcomes are acceptable by comparing all quantities according to the discussing of all thermoelastic models. The refined forms of Green and Naghdi’s types II and III should be applied to get accurate outcomes.
{"title":"Thermo-diffusion of a thick circular plate via modified Green–Naghdi models","authors":"A. Zenkour","doi":"10.24423/AOM.3533","DOIUrl":"https://doi.org/10.24423/AOM.3533","url":null,"abstract":"This article presents the thermo-diffusion of an isotropic thick circular plate. The Green and Naghdi’s models including the energy dissipation are anticipated in their simple forms. Novel multi single/dual-phase-lag models with higher-order timederivatives are also provided to examine the thermo-diffusion response of the circular plate. The simple and refined forms of Green and Naghdi’s types II and III are investigated in this work. The closed-form solution of thermal diffusion governing equations is attained by taking into account the boundary conditions. A validation examples of outcomes are acceptable by comparing all quantities according to the discussing of all thermoelastic models. The refined forms of Green and Naghdi’s types II and III should be applied to get accurate outcomes.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"235-256"},"PeriodicalIF":0.8,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46919512","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}
In this paper, the work and performance of the premixed methane-air porous axisymmetrical burner have firstly been simulated numerically using the CFD tools. For this purpose the set of governing equations has been enriched by an additional energy equation in porous solid, and the chemical species transport has been extended onto the multi-step mechanism (GRI-2-11). This numerical model has been verified on the base of available benchmark experiments. Next, we have studied the local entropy generation problem taking into account not only classical contributions like viscous and turbulent dissipation but also, the porous combustion of gases. The results showed that the greatest portion of entropy generation in the porous medium burner is related to chemical reactions, followed by heat transfer, mass diffusion (mixing) and friction (viscous dissipation), respectively. According to the results, as the excess air ratio increases, the local entropy generation rate due to heat transfer and friction increases and the local entropy generation rate due to chemical reactions is decreased. Also, by increasing the volumetric heat transfer coefficient, the local entropy generation rate due to heat transfer decreases and the local entropy generation rate due to friction and chemical reactions increases. Also, the local entropy generation rate due to mixing does not show a significant change with the changing excess air ratio and volumetric heat transfer coefficient.
{"title":"A study of the local entropy generation rate in a porous media burner","authors":"I. Mohammadi, J. A. Esfahani, K. C. Kim","doi":"10.24423/AOM.3416","DOIUrl":"https://doi.org/10.24423/AOM.3416","url":null,"abstract":"In this paper, the work and performance of the premixed methane-air porous axisymmetrical burner have firstly been simulated numerically using the CFD tools. For this purpose the set of governing equations has been enriched by an additional energy equation in porous solid, and the chemical species transport has been extended onto the multi-step mechanism (GRI-2-11). This numerical model has been verified on the base of available benchmark experiments. Next, we have studied the local entropy generation problem taking into account not only classical contributions like viscous and turbulent dissipation but also, the porous combustion of gases. The results showed that the greatest portion of entropy generation in the porous medium burner is related to chemical reactions, followed by heat transfer, mass diffusion (mixing) and friction (viscous dissipation), respectively. According to the results, as the excess air ratio increases, the local entropy generation rate due to heat transfer and friction increases and the local entropy generation rate due to chemical reactions is decreased. Also, by increasing the volumetric heat transfer coefficient, the local entropy generation rate due to heat transfer decreases and the local entropy generation rate due to friction and chemical reactions increases. Also, the local entropy generation rate due to mixing does not show a significant change with the changing excess air ratio and volumetric heat transfer coefficient.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"257-279"},"PeriodicalIF":0.8,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42797665","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}
Results of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker–Prager criterion in compression, a formulation coupling elasto-plasticity and damage mechanics and the concrete damaged plasticity (CDP) model implemented in Abaqus. In a softening regime, a non-local theory of integral format is applied to the first three constitutive laws. A fracture energy approach is utilised in CDP model. An ability to reproduce different failure mechanisms observed in experiments for each constitutive model is analysed. A comparison of force-displacement curves and crack patterns between numerical and experimental outcomes is performed.
{"title":"Performance of isotropic constitutive laws in simulating failure mechanisms in scaled RC beams","authors":"I. Marzec, J. Bobiński","doi":"10.24423/AOM.3443","DOIUrl":"https://doi.org/10.24423/AOM.3443","url":null,"abstract":"Results of numerical calculations of reinforced concrete (RC) beams are presented. Based on experimental results on longitudinally reinforced specimens of different sizes and shapes are investigated. Four different continuum constitutive laws with isotropic softening are used: one defined within continuum damage mechanics, an elasto-plastic with the Rankine criterion in tension and the Drucker–Prager criterion in compression, a formulation coupling elasto-plasticity and damage mechanics and the concrete damaged plasticity (CDP) model implemented in Abaqus. In a softening regime, a non-local theory of integral format is applied to the first three constitutive laws. A fracture energy approach is utilised in CDP model. An ability to reproduce different failure mechanisms observed in experiments for each constitutive model is analysed. A comparison of force-displacement curves and crack patterns between numerical and experimental outcomes is performed.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"193-215"},"PeriodicalIF":0.8,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46001229","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}
A. Razeghi-Harikandeei, B. Ganji, R. Jafari-Talookolaei, A. Abdipour
In this paper, the delamination effect on the static and natural frequency response of a microbeam subjected to the nonlinear electrostatic force is studied using a semi-analytical approach for the first time. The Euler–Bernoulli beam assumption along with the non-classical modified couple stress theory is used to obtain the governing differential equation of motion and then a reduced-order model based on Galerkin’s decomposition method is obtained. At first the microbeam with very small delamination like an intact microbeam is solved and then the solution is compared with those reported in the literature and the solution obtained using 3D-coupled electromechanical software. After validation, the effects of delamination length and its locations in thickness and length directions on the microbeam behavior are investigated in details. It is shown that the delamination has remarkable effects on the characteristics of the microbeam, especially near the pull-in voltage. Also, the delaminated microbeam with various thicknesses is studied using both the classical and the non-classical theories. It is found that the difference between the two models is significant for the thin microbeam with a thickness near of below than its material length scale parameter. This investigation is helpful for the nondestructive detection of the delamination in the beams.
{"title":"Static, free and forced vibration analysis of a delaminated microbeam-based MEMS subjected to the electrostatic force","authors":"A. Razeghi-Harikandeei, B. Ganji, R. Jafari-Talookolaei, A. Abdipour","doi":"10.24423/AOM.3529","DOIUrl":"https://doi.org/10.24423/AOM.3529","url":null,"abstract":"In this paper, the delamination effect on the static and natural frequency response of a microbeam subjected to the nonlinear electrostatic force is studied using a semi-analytical approach for the first time. The Euler–Bernoulli beam assumption along with the non-classical modified couple stress theory is used to obtain the governing differential equation of motion and then a reduced-order model based on Galerkin’s decomposition method is obtained. At first the microbeam with very small delamination like an intact microbeam is solved and then the solution is compared with those reported in the literature and the solution obtained using 3D-coupled electromechanical software. After validation, the effects of delamination length and its locations in thickness and length directions on the microbeam behavior are investigated in details. It is shown that the delamination has remarkable effects on the characteristics of the microbeam, especially near the pull-in voltage. Also, the delaminated microbeam with various thicknesses is studied using both the classical and the non-classical theories. It is found that the difference between the two models is significant for the thin microbeam with a thickness near of below than its material length scale parameter. This investigation is helpful for the nondestructive detection of the delamination in the beams.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"169-188"},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43325169","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}
This paper deals with the nonlinear forced vibration of nanocomposite beams resting on a nonlinear viscoelastic foundation and subjected to a transverse periodic excitation. It is considered that the functionally graded carbon nanotubereinforced composite (FG-CNTRC) beam is made of an isotropic matrix reinforced by either aligned- or randomly oriented-straight single-walled carbon nanotubes (SWCNTs) with four types of distributions through the thickness direction of the beam. Both the Eshelby–Mori–Tanaka approach and extended rule of mixtures are used to predict the effective material properties of the FG-CNTRC beams. The mathematical model of the beam is developed based on the Euler–Bernoulli beam theory together with von Karman assumptions. Subsequently, the accurate analytical solutions of the governing equation are obtained through applying the variational iteration method (VIM). Several examples are verified to have higher accuracy than those available in the literature. In addition, a comprehensive investigation into the effect of carbon nanotubes (CNTs) distribution, CNTs volume fraction, end supports, vibration amplitude, and foundation coefficients on the vibrational characteristics of the nanocomposite beam is performed and some new results are presented.
{"title":"An analytical study on the nonlinear forced vibration of functionally graded carbon nanotube-reinforced composite beams on nonlinear viscoelastic foundation","authors":"H. Shafiei, A. Setoodeh","doi":"10.24423/AOM.3268","DOIUrl":"https://doi.org/10.24423/AOM.3268","url":null,"abstract":"This paper deals with the nonlinear forced vibration of nanocomposite beams resting on a nonlinear viscoelastic foundation and subjected to a transverse periodic excitation. It is considered that the functionally graded carbon nanotubereinforced composite (FG-CNTRC) beam is made of an isotropic matrix reinforced by either aligned- or randomly oriented-straight single-walled carbon nanotubes (SWCNTs) with four types of distributions through the thickness direction of the beam. Both the Eshelby–Mori–Tanaka approach and extended rule of mixtures are used to predict the effective material properties of the FG-CNTRC beams. The mathematical model of the beam is developed based on the Euler–Bernoulli beam theory together with von Karman assumptions. Subsequently, the accurate analytical solutions of the governing equation are obtained through applying the variational iteration method (VIM). Several examples are verified to have higher accuracy than those available in the literature. In addition, a comprehensive investigation into the effect of carbon nanotubes (CNTs) distribution, CNTs volume fraction, end supports, vibration amplitude, and foundation coefficients on the vibrational characteristics of the nanocomposite beam is performed and some new results are presented.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"81-107"},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47005815","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}
As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.
{"title":"n-sided polygonal hybrid finite elements involving element boundary integrals only for anisotropic thermal analysis","authors":"R. Cao, X. Zhao, W. Lin, Hui Wang","doi":"10.24423/AOM.3434","DOIUrl":"https://doi.org/10.24423/AOM.3434","url":null,"abstract":"As a combination of the traditional finite element method and boundary element method, the n-sided polygonal hybrid finite element method with fundamental solution kernels, named as HFS-FEM, is thoroughly studied in this work for two-dimensional heat conduction in fully anisotropic media. In this approach, the unknown temperature field within the polygon is represented by the linear combination of anisotropic fundamental solutions of problem to achieve the local satisfaction of the related governing equations, but not the specific boundary conditions and the continuity conditions across the element boundary. To tackle such a shortcoming, the frame temperature field is independently defined on the entire boundary of the polygonal element by means of the conventional one-dimensional shape function interpolation. Subsequently, by the hybrid functional with the assumed intra- and inter-element temperature fields, the stiffness equation can be obtained including the line integrals along the element boundary only, whose dimension is reduced by one compared to the domain integrals in the traditional finite elements. This means that the higher computing efficiency is expected. Moreover, any shaped polygonal elements can be constructed in a unified form with the same fundamental solution kernels, including convex and non-convex polygonal elements, to provide greater flexibility in meshing effort for complex geometries. Besides, the element boundary integrals endow the method higher versatility with a non-conforming mesh in the pre-processing stage of the analysis over the traditional FEM. No modification to the HFS-FEM formulation is needed for the non-conforming mesh and the element containing hanging nodes is treated normally as the one with more nodes. Finally, the accuracy, convergence, computing efficiency, stability of non-convex element, and straightforward treatment of non-conforming discretization are discussed for the present n-sided polygonal hybrid finite elements by a few applications in the context of anisotropic heat conduction.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"109-137"},"PeriodicalIF":0.8,"publicationDate":"2020-04-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49575370","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}
A size-dependent Euler–Bernoulli beam model is derived within the framework of the higher-order nonlocal strain gradient theory. Nonlocal equations of motion are derived by applying Hamilton’s principle and solved with an analytical solution. The solution is obtained using the Navier solution procedure. In the case of simply supported boundary conditions, the analytical solutions of natural frequencies and critical buckling temperature for free vibration problems are obtained. The paper investigates the thermal effects on buckling and free vibrational characteristics of functionally graded size-dependent nanobeams subjected to various types of thermal loading. The influence of higher-order and lower-order nonlocal parameters and strain gradient scale on buckling and vibration are investigated for various thermal conditions. The obtained results are compared with previous research.
{"title":"Thermal buckling and free vibration of Euler–Bernoulli FG nanobeams based on the higher-order nonlocal strain gradient theory","authors":"G. Janevski, Nikola Despenić, I. Pavlović","doi":"10.24423/AOM.3462","DOIUrl":"https://doi.org/10.24423/AOM.3462","url":null,"abstract":"A size-dependent Euler–Bernoulli beam model is derived within the framework of the higher-order nonlocal strain gradient theory. Nonlocal equations of motion are derived by applying Hamilton’s principle and solved with an analytical solution. The solution is obtained using the Navier solution procedure. In the case of simply supported boundary conditions, the analytical solutions of natural frequencies and critical buckling temperature for free vibration problems are obtained. The paper investigates the thermal effects on buckling and free vibrational characteristics of functionally graded size-dependent nanobeams subjected to various types of thermal loading. The influence of higher-order and lower-order nonlocal parameters and strain gradient scale on buckling and vibration are investigated for various thermal conditions. The obtained results are compared with previous research.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"139-168"},"PeriodicalIF":0.8,"publicationDate":"2020-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44799554","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}
We examine the in-plane and anti-plane stress states inside a parabolic inhomogeneity which is bonded to an infinite matrix through an intermediate coating. The interfaces of the three-phase parabolic inhomogeneity are two confocal parabolas. The corresponding boundary value problems are studied in the physical plane rather than in the image plane. A simple condition is found that ensures that the internal stress state inside the parabolic inhomogeneity is uniform and hydrostatic. Furthermore, this condition is independent of the elastic properties of the coating and the two geometric parameters of the composite: in fact, the condition depends only on the elastic constants of the inhomogeneity and the matrix and the ratio between the two remote principal stresses. Once this condition is met, the mean stress in the coating is constant and the hoop stress on the coating side is also uniform along the entire inhomogeneity-coating interface. The unconditional uniformity of stresses inside a three-phase parabolic inhomogeneity is achieved when the matrix is subjected to uniform remote anti-plane shear stresses. The internal uniform anti-plane shear stresses inside the inhomogeneity are independent of the shear modulus of the coating and the two geometric parameters of the composite.
{"title":"Three-phase parabolic inhomogeneities with internal uniform stresses in plane and anti-plane elasticity","authors":"X. Wang, P. Schiavone","doi":"10.24423/AOM.3371","DOIUrl":"https://doi.org/10.24423/AOM.3371","url":null,"abstract":"We examine the in-plane and anti-plane stress states inside a parabolic inhomogeneity which is bonded to an infinite matrix through an intermediate coating. The interfaces of the three-phase parabolic inhomogeneity are two confocal parabolas. The corresponding boundary value problems are studied in the physical plane rather than in the image plane. A simple condition is found that ensures that the internal stress state inside the parabolic inhomogeneity is uniform and hydrostatic. Furthermore, this condition is independent of the elastic properties of the coating and the two geometric parameters of the composite: in fact, the condition depends only on the elastic constants of the inhomogeneity and the matrix and the ratio between the two remote principal stresses. Once this condition is met, the mean stress in the coating is constant and the hoop stress on the coating side is also uniform along the entire inhomogeneity-coating interface. The unconditional uniformity of stresses inside a three-phase parabolic inhomogeneity is achieved when the matrix is subjected to uniform remote anti-plane shear stresses. The internal uniform anti-plane shear stresses inside the inhomogeneity are independent of the shear modulus of the coating and the two geometric parameters of the composite.","PeriodicalId":8280,"journal":{"name":"Archives of Mechanics","volume":"72 1","pages":"27-38"},"PeriodicalIF":0.8,"publicationDate":"2020-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47308853","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}
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