We use conformal mapping techniques to design two interacting non-elliptical rigid inclusions, each of which is loaded by a couple, which ensure the so-called ?harmonic condition? in which the original mean stress in the matrix remains undisturbed after the introduction of the inclusions. We show that for prescribed Poisson?s ratio and corresponding geometric parameters, several restrictions are necessary on the external loadings to ensure the harmonic condition. It is seen from our analysis that: (i) the interfacial and hoop stresses are uniformly distributed along each of the inclusion-matrix interfaces; (ii) the interfacial normal and hoop stresses along the two interfaces are completely determined by the Poisson?s ratio and the constant mean stress in the matrix whilst the interfacial tangential stress along the two interfaces can be completely determined by the moments of the couples and the areas of the two inclusions; (iii) the existence of the applied couples will influence the non-elliptical shapes of the two rigid harmonic inclusions when the moment to area ratios for the two inclusions differ.
{"title":"Two interacting non-elliptical rigid harmonic inclusions loaded by couples","authors":"Xu Wang, P. Schiavone","doi":"10.2298/tam190228010w","DOIUrl":"https://doi.org/10.2298/tam190228010w","url":null,"abstract":"We use conformal mapping techniques to design two interacting non-elliptical rigid inclusions, each of which is loaded by a couple, which ensure the so-called ?harmonic condition? in which the original mean stress in the matrix remains undisturbed after the introduction of the inclusions. We show that for prescribed Poisson?s ratio and corresponding geometric parameters, several restrictions are necessary on the external loadings to ensure the harmonic condition. It is seen from our analysis that: (i) the interfacial and hoop stresses are uniformly distributed along each of the inclusion-matrix interfaces; (ii) the interfacial normal and hoop stresses along the two interfaces are completely determined by the Poisson?s ratio and the constant mean stress in the matrix whilst the interfacial tangential stress along the two interfaces can be completely determined by the moments of the couples and the areas of the two inclusions; (iii) the existence of the applied couples will influence the non-elliptical shapes of the two rigid harmonic inclusions when the moment to area ratios for the two inclusions differ.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"156 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76095802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. Energy separation is a spontaneous energy redistribution within a fluid flow. As a consequence, there are places with higher and lower val- ues of total temperature in the fluid flow. It is characteristic for many flow geometries. This paper deals with the energy separation in a cylinder wake. Two flow conditions are being considered–transient and steady-state flow in the wake. Two different solvers from the open source package OpenFOAM are used in order to capture the phenomenon of energy separation. One of these solvers is modified for the purpose of calculation in a particular case of the vortex street flow. The energy equation based on the internal energy present in this solver is replaced by the energy equation written in the form of a total enthalpy. The other solver has been previously tested in the vortex tube flow, and can also capture the energy separation in the steady-state wake flow of the cylinder. In both cylinder wake flow conditions, a two-dimensional computational domain is used. Standard 𝑘 − 𝜀 model is used for computations. It is proved that OpenFOAM is capable of capturing the energy separation phenomenon in a proper way in both of the wake flow cases. Good agreement between the experimental results and the ones from computations is obtained in the case of steady-state flow in the wake. Previous research findings are also confirmed in the case of vortex street flow.
{"title":"Energy separation in transient and steady-state flow across the cylinder","authors":"M. Burazer","doi":"10.2298/TAM171130006B","DOIUrl":"https://doi.org/10.2298/TAM171130006B","url":null,"abstract":". Energy separation is a spontaneous energy redistribution within a fluid flow. As a consequence, there are places with higher and lower val- ues of total temperature in the fluid flow. It is characteristic for many flow geometries. This paper deals with the energy separation in a cylinder wake. Two flow conditions are being considered–transient and steady-state flow in the wake. Two different solvers from the open source package OpenFOAM are used in order to capture the phenomenon of energy separation. One of these solvers is modified for the purpose of calculation in a particular case of the vortex street flow. The energy equation based on the internal energy present in this solver is replaced by the energy equation written in the form of a total enthalpy. The other solver has been previously tested in the vortex tube flow, and can also capture the energy separation in the steady-state wake flow of the cylinder. In both cylinder wake flow conditions, a two-dimensional computational domain is used. Standard 𝑘 − 𝜀 model is used for computations. It is proved that OpenFOAM is capable of capturing the energy separation phenomenon in a proper way in both of the wake flow cases. Good agreement between the experimental results and the ones from computations is obtained in the case of steady-state flow in the wake. Previous research findings are also confirmed in the case of vortex street flow.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"165 1","pages":"83-94"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80401752","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This paper presents research regarding the influence of turbulent kinetic energy (TKE) level on accuracy of Reynolds averaged Navier–Stokes (RANS) based turbulence models. A theoretical analysis of influence TKE level on accuracy of the RANS turbulence models has been performed accord- ing to the Boussinesq hypothesis definition. After that, this theoretical analysis has been investigated by comparison of numerically and experimentally obtained results on the test case of a steady-state incompressible swirl-free flow in a straight conical diffuser named Azad diffuser. Numerical calculations have been performed using the OpenFOAM CFD software and first and second-order closure turbulence models. TKE level, velocity profiles and Reynolds stresses have been calculated downstream in four different cross sections of the diffuser. Certain conclusions about modeling turbulent flows by 𝑘 − 𝜀 and LRR turbulence models have been made by comparing the velocity profiles, TKE distribution and Reynolds stresses on the selected cross sections.
{"title":"On the influence of turbulent kinetic energy level on accuracy of k − ε and LRR turbulence models","authors":"M. Novkovic, M. Burazer, S. A. Ćoćić, R. Lecic","doi":"10.2298/TAM171201009N","DOIUrl":"https://doi.org/10.2298/TAM171201009N","url":null,"abstract":". This paper presents research regarding the influence of turbulent kinetic energy (TKE) level on accuracy of Reynolds averaged Navier–Stokes (RANS) based turbulence models. A theoretical analysis of influence TKE level on accuracy of the RANS turbulence models has been performed accord- ing to the Boussinesq hypothesis definition. After that, this theoretical analysis has been investigated by comparison of numerically and experimentally obtained results on the test case of a steady-state incompressible swirl-free flow in a straight conical diffuser named Azad diffuser. Numerical calculations have been performed using the OpenFOAM CFD software and first and second-order closure turbulence models. TKE level, velocity profiles and Reynolds stresses have been calculated downstream in four different cross sections of the diffuser. Certain conclusions about modeling turbulent flows by 𝑘 − 𝜀 and LRR turbulence models have been made by comparing the velocity profiles, TKE distribution and Reynolds stresses on the selected cross sections.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"25 1","pages":"139-149"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85055002","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.
{"title":"Dynamic stability of Timoshenko beams on Pasternak viscoelastic foundation","authors":"R. Pavlović, R. Pavlović","doi":"10.2298/TAM171103005P","DOIUrl":"https://doi.org/10.2298/TAM171103005P","url":null,"abstract":"The dynamic stability problem of a Timoshenko beam supported by a generalized Pasternak-type viscoelastic foundation subjected to compressive axial loading, where rotary inertia is neglected, is investigated. Each axial force consists of a constant part and a time-dependent stochastic function. By using the direct Liapunov method, bounds of the almost sure asymptotic stability of a beam as a function of viscous damping coefficient, variance of the stochastic force, shear correction factor, parameters of Pasternak foundation, and intensity of the deterministic component of axial loading are obtained. With the aim of justifying the use of the direct Liapunov method analytical results are firstly compared with numerically obtained results using Monte Carlo simulation method. Numerical calculations are further performed for the Gaussian process with a zero mean as well as a harmonic process with random phase. The main purpose of the paper is to point at significance damping parameter of foundation on dynamic stability of the structure.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"27 1","pages":"67-81"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79302398","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. To investigate air flow in longitudinally ventilated traffic tunnels, a scaled model of a typical road-traffic tunnel with an appropriate ventilation system based on axial ducted fans, is designed and built in the Lab. The focus of this paper is the airflow in a bi-directional traffic, two-lane tunnel. At the scale ratio of approx. 1:20, at 20 . 52m length it represents ≈ 400m of a real-scale tunnel. The model consists of two parallel tunnel tubes, where the main tunnel (with a hydraulic diameter of 𝐷 ℎ 1 ≈ 0 . 4m ) has the geometry of a scaled road traffic-tunnel. The second tunnel ( 𝐷 ℎ 2 ≈ 0 . 16m ) has a smaller size and is circular in cross-section, used only to simulate airflow towards an evacuation tunnel tube. Thus the two tunnels are connected by the evacuation passages, equipped with adjustable escape doors. By a combination of experimental and numerical work, the air flow-field and the performance of the ventilation sys- tem are investigated. The velocity field and its turbulence properties exiting the fans were determined experimentally using hot-wire anemometry. These data were further processed to be used in the tunnel flow computations by CFD. The efficiency of momentum transfer ( 𝜂 𝑖 , Kempf factor) of the longitu- dinal tunnel ventilation is determined. The effect that the imposed boundary conditions and the level of their detail, have within a CFD computation of tunnel airflow, with respect to accuracy, velocity distribution and computed 𝜂 𝑖 . Finally a traffic-loaded (traffic “jam”) case of flow is studied through ex- periment and CFD. The difficulty in assessing the required thrust of the plant in traffic-jam tunnel conditions is discussed, and the ventilation efficiency is estimated. Based on later results, the two limiting shapes of axial velocity distribution with respect to height above the road, in this type of tunnel and traffic, are estimated. The last result can be used as a realistic boundary condition (as inlet b.c. and/or initial condition) for numerical studies of flow and fire scenarios in such tunnels with the traffic load critical for design.
{"title":"Experimental and numerical analysis of flow field and ventilation performance in a traffic tunnel ventilated by axial fans","authors":"M. Šekularac, Novica Z. Janković","doi":"10.2298/TAM171201010S","DOIUrl":"https://doi.org/10.2298/TAM171201010S","url":null,"abstract":". To investigate air flow in longitudinally ventilated traffic tunnels, a scaled model of a typical road-traffic tunnel with an appropriate ventilation system based on axial ducted fans, is designed and built in the Lab. The focus of this paper is the airflow in a bi-directional traffic, two-lane tunnel. At the scale ratio of approx. 1:20, at 20 . 52m length it represents ≈ 400m of a real-scale tunnel. The model consists of two parallel tunnel tubes, where the main tunnel (with a hydraulic diameter of 𝐷 ℎ 1 ≈ 0 . 4m ) has the geometry of a scaled road traffic-tunnel. The second tunnel ( 𝐷 ℎ 2 ≈ 0 . 16m ) has a smaller size and is circular in cross-section, used only to simulate airflow towards an evacuation tunnel tube. Thus the two tunnels are connected by the evacuation passages, equipped with adjustable escape doors. By a combination of experimental and numerical work, the air flow-field and the performance of the ventilation sys- tem are investigated. The velocity field and its turbulence properties exiting the fans were determined experimentally using hot-wire anemometry. These data were further processed to be used in the tunnel flow computations by CFD. The efficiency of momentum transfer ( 𝜂 𝑖 , Kempf factor) of the longitu- dinal tunnel ventilation is determined. The effect that the imposed boundary conditions and the level of their detail, have within a CFD computation of tunnel airflow, with respect to accuracy, velocity distribution and computed 𝜂 𝑖 . Finally a traffic-loaded (traffic “jam”) case of flow is studied through ex- periment and CFD. The difficulty in assessing the required thrust of the plant in traffic-jam tunnel conditions is discussed, and the ventilation efficiency is estimated. Based on later results, the two limiting shapes of axial velocity distribution with respect to height above the road, in this type of tunnel and traffic, are estimated. The last result can be used as a realistic boundary condition (as inlet b.c. and/or initial condition) for numerical studies of flow and fire scenarios in such tunnels with the traffic load critical for design.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"10 1","pages":"151-165"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83463607","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. The results of the experimental investigations of the turbulent swirl flow in a straight conical diffuser with inlet diameter 0 . 4m and total divergence angle 8 . 6 ◦ are presented in this paper. The incompressible swirl flow field is generated by the axial fan with outer diameter 0 . 397m . The measurements were performed in one measuring section downstream the axial fan impeller in the conical diffuser in position ( z/R 0 = 1) with original classical probes and an one-component laser Doppler anemometry (LDA) system, for four flow regimes. The comparative measurements of axial and circumferential velocities are presented. The Reynolds number, calculated on the basis of the average velocity, ranges from 149857 to 216916. Integral parameters, such as volume flow rate, average circulation and swirl number, are determined. Statistical characteristics, such as level of turbulence, skewness and flatness factors, are calculated. The highest levels of turbulence for axial velocity are reached in region 0 . 4 < r/R < 0 . 6 , where D = 2 R . The highest levels of turbulence for circumferential velocity are reached for the regimes with lower circulation in r/R ≈ 0 . 4 , i.e., in the vortex core region for the cases with higher circulation.
{"title":"Integral and statistical characteristics of the turbulent swirl flow in a straight conical diffuser","authors":"B. Ilic, S. Cantrak, Z. Janković","doi":"10.2298/TAM171201012I","DOIUrl":"https://doi.org/10.2298/TAM171201012I","url":null,"abstract":". The results of the experimental investigations of the turbulent swirl flow in a straight conical diffuser with inlet diameter 0 . 4m and total divergence angle 8 . 6 ◦ are presented in this paper. The incompressible swirl flow field is generated by the axial fan with outer diameter 0 . 397m . The measurements were performed in one measuring section downstream the axial fan impeller in the conical diffuser in position ( z/R 0 = 1) with original classical probes and an one-component laser Doppler anemometry (LDA) system, for four flow regimes. The comparative measurements of axial and circumferential velocities are presented. The Reynolds number, calculated on the basis of the average velocity, ranges from 149857 to 216916. Integral parameters, such as volume flow rate, average circulation and swirl number, are determined. Statistical characteristics, such as level of turbulence, skewness and flatness factors, are calculated. The highest levels of turbulence for axial velocity are reached in region 0 . 4 < r/R < 0 . 6 , where D = 2 R . The highest levels of turbulence for circumferential velocity are reached for the regimes with lower circulation in r/R ≈ 0 . 4 , i.e., in the vortex core region for the cases with higher circulation.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"10 1","pages":"127-137"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86054598","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A physically based, finite deformation, rate and temperature dependent theory and model have been developed to simulate the deformation and failure of FRP composite materials and structures. Failure modes include: inter alia, fiber crushing and kinking as occurs during extreme compressive loading; fiber fracture as occurs in for example fragmentation; interlaminar shear as occurs at elevated temperatures and that leads to kinking; debonding and delamination including the coupling with laminate kinking; and debonding as occurs in cored FRP panels. The theory/model is capable of describing quasi-static (including creep) as occurs at elevated temperatures, and dynamic deformation and failure as occurs during shock, blast or impact. The model is implemented within LS DYNA and specific example simulations are described that illustrate the theory/model capabilities. In Part I, fragmentation is not covered in detail. Fiber fracture and fragmentation are to be covered to detail with specific examples in Part II.
{"title":"Constitutive modeling for FRP composite materials subject to extreme loading","authors":"J. Asaro, D. Benson","doi":"10.2298/TAM180415011A","DOIUrl":"https://doi.org/10.2298/TAM180415011A","url":null,"abstract":"A physically based, finite deformation, rate and temperature dependent theory and model have been developed to simulate the deformation and failure of FRP composite materials and structures. Failure modes include: inter alia, fiber crushing and kinking as occurs during extreme compressive loading; fiber fracture as occurs in for example fragmentation; interlaminar shear as occurs at elevated temperatures and that leads to kinking; debonding and delamination including the coupling with laminate kinking; and debonding as occurs in cored FRP panels. The theory/model is capable of describing quasi-static (including creep) as occurs at elevated temperatures, and dynamic deformation and failure as occurs during shock, blast or impact. The model is implemented within LS DYNA and specific example simulations are described that illustrate the theory/model capabilities. In Part I, fragmentation is not covered in detail. Fiber fracture and fragmentation are to be covered to detail with specific examples in Part II.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"6 1","pages":"205-230"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78648288","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Locomotion of multibody systems in resistive media can be based on periodic change of the system configuration. The following types of mobile robotic systems are examined in the paper: multilink snake-like systems; multibody systems in quasi-static motion; systems consisting of several interacting bodies; fish-like, frog-like, and boat-like systems swimming in fluids; systems containing moving internal masses. Dynamics of these systems subjected to various resistance forces, both isotropic and anisotropic, are investigated, including dry friction forces obeying Coulomb’s law and forces directed against the velocity of the moving body and proportional to the velocity value or its square. Possible modes of locomotion and control algorithms are discussed. Optimization for various types of mobile robots is considered. Optimal values of geometrical and mechanical parameters as well as optimal controls are obtained that provide the maximum locomotion speed or minimum energy consumption. Results of experiments and computer simulation are discussed.
{"title":"Locomotion of multibody robotic systems: Dynamics and optimization","authors":"L. F. Chernousko","doi":"10.2298/TAM171017001C","DOIUrl":"https://doi.org/10.2298/TAM171017001C","url":null,"abstract":"Locomotion of multibody systems in resistive media can be based on periodic change of the system configuration. The following types of mobile robotic systems are examined in the paper: multilink snake-like systems; multibody systems in quasi-static motion; systems consisting of several interacting bodies; fish-like, frog-like, and boat-like systems swimming in fluids; systems containing moving internal masses. Dynamics of these systems subjected to various resistance forces, both isotropic and anisotropic, are investigated, including dry friction forces obeying Coulomb’s law and forces directed against the velocity of the moving body and proportional to the velocity value or its square. Possible modes of locomotion and control algorithms are discussed. Optimization for various types of mobile robots is considered. Optimal values of geometrical and mechanical parameters as well as optimal controls are obtained that provide the maximum locomotion speed or minimum energy consumption. Results of experiments and computer simulation are discussed.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"281 1","pages":"1-1"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76805677","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the fluid flow and heat transfer in a helical pipe filled with a sparsely packed porous medium. Motivated by the engineering applications, pipe’s thickness and the distance between two coils of the helix have the same small order of magnitude, whereas the fluid inside the pipe is assumed to be cooled (or heated) by the exterior medium. After writing the dimensionless Darcy–Brinkman–Boussinesq system in curvilinear coordinates, we employ the multi-scale expansion technique to formally derive the effective model valid for small Brinkman–Darcy number. The obtained asymptotic solution is given in the explicit form which is important with regards to numerical simulations. Comparison with our previous results on the straight-pipe flow is also provided.
{"title":"Asymptotic solution for the Darcy-Brinkman- Boussinesq flow in a pipe with helicoidal shape","authors":"Igor Pažanin","doi":"10.2298/TAM180424008P","DOIUrl":"https://doi.org/10.2298/TAM180424008P","url":null,"abstract":"We study the fluid flow and heat transfer in a helical pipe filled with a sparsely packed porous medium. Motivated by the engineering applications, pipe’s thickness and the distance between two coils of the helix have the same small order of magnitude, whereas the fluid inside the pipe is assumed to be cooled (or heated) by the exterior medium. After writing the dimensionless Darcy–Brinkman–Boussinesq system in curvilinear coordinates, we employ the multi-scale expansion technique to formally derive the effective model valid for small Brinkman–Darcy number. The obtained asymptotic solution is given in the explicit form which is important with regards to numerical simulations. Comparison with our previous results on the straight-pipe flow is also provided.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"31 1","pages":"189-203"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87779242","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
. This article considers a plane strain gradient plasticity theory of the Gurtin–Anand model [M. Gurtin, L. Anand, A theory of strain gra- dient plasticity for isotropic, plastically irrotational materials Part I: Small deformations , J. Mech. Phys. Solids 53 (2005), 1624–1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin–Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.
{"title":"An effect of a purely dissipative process of microstresses on plane strain gradient plasticity problems","authors":"A. Borokinni, O. Fadodun, A. Akinola","doi":"10.2298/TAM171017002B","DOIUrl":"https://doi.org/10.2298/TAM171017002B","url":null,"abstract":". This article considers a plane strain gradient plasticity theory of the Gurtin–Anand model [M. Gurtin, L. Anand, A theory of strain gra- dient plasticity for isotropic, plastically irrotational materials Part I: Small deformations , J. Mech. Phys. Solids 53 (2005), 1624–1649] for an isotropic material undergoing small deformation in the absence of plastic spin. It is assumed that the system of microstresses is purely dissipative, so that the free energy reduces to a function of the elastic strain, while the microstresses are only related to the plastic strain rate and gradient of the plastic strain rate via the constitutive relations. The plane strain problem of the Gurtin–Anand model for a purely dissipative process gives rise to elastic incompressibility. A weak formulation of the flow rule is derived, making the plane strain problem suitable for finite element implementation.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":"8 3 1","pages":"177-188"},"PeriodicalIF":0.7,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78471210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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