The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.
{"title":"Ut vis sic tensio","authors":"Giuseppe Saccomandi","doi":"10.2298/TAM170703011S","DOIUrl":"https://doi.org/10.2298/TAM170703011S","url":null,"abstract":"The mechanical properties of rubber-like materials have been offering an outstanding challenge to the solid mechanics community for a long time. The behaviour of such materials is quite difficult to predict because rubber self-organizes into mesoscopic physical structures that play a prominent role in determining their complex, history-dependent and strongly nonlinear response. In this framework one of the main problems is to find a functional form of the elastic strain-energy that best describes the experimental data in a mathematical feasible way. The aim of this paper is to give a survey of recent advances aimed at solving such a problem.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73659019","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}
{"title":"Stability of LevitronTM revisited","authors":"S. Simić","doi":"10.2298/tam171107017s","DOIUrl":"https://doi.org/10.2298/tam171107017s","url":null,"abstract":"","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73551151","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 pileup of edge dislocations against an arbitrarily inclined flat bimetallic interface is considered. Equilibrium positions of dislocations are determined for a given number of dislocations and specified material properties, assuming that the resolved shear stress along the pileup plane from a remotely applied loading is uniform and equal for all interface inclination angles. Numerical results are compared for pileups at 0°, 30°, 45°, and 60° relative to the interface normal. The overall dislocation distribution is mildly affected by the inclination of the interface, although there are some notable differences. While an inclined interface repels the first and last dislocation stronger than the orthogonal interface, for piled-up dislocations in-between this is not necessarily the case. Small differences in the pileup length and the proximity of the leading dislocation to differently inclined interfaces can considerably affect the interface stresses. The magnitude of interface stresses decreases with the increase of the shear moduli ratio G2/G1 due to stronger repulsion exerted on dislocations by stiffer interfaces. The disparity in Poisson’s ratio also affects the interface stresses. The back stress behind a trailing dislocation is evaluated and discussed.
{"title":"A pileup of screw dislocations against an inclined bimetallic interface","authors":"A. V. Lubarda","doi":"10.2298/TAM170504007L","DOIUrl":"https://doi.org/10.2298/TAM170504007L","url":null,"abstract":"A pileup of edge dislocations against an arbitrarily inclined flat bimetallic interface is considered. Equilibrium positions of dislocations are determined for a given number of dislocations and specified material properties, assuming that the resolved shear stress along the pileup plane from a remotely applied loading is uniform and equal for all interface inclination angles. Numerical results are compared for pileups at 0°, 30°, 45°, and 60° relative to the interface normal. The overall dislocation distribution is mildly affected by the inclination of the interface, although there are some notable differences. While an inclined interface repels the first and last dislocation stronger than the orthogonal interface, for piled-up dislocations in-between this is not necessarily the case. Small differences in the pileup length and the proximity of the leading dislocation to differently inclined interfaces can considerably affect the interface stresses. The magnitude of interface stresses decreases with the increase of the shear moduli ratio G2/G1 due to stronger repulsion exerted on dislocations by stiffer interfaces. The disparity in Poisson’s ratio also affects the interface stresses. The back stress behind a trailing dislocation is evaluated and discussed.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80700218","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}
In this note we consider mechanical systems with smooth linear nonholonomic constraints which do not depend on time. For a special case of Chaplygin systems, when the motion of the system can be described as a closed system of differential equations in local coordinates of the reduced space of the same dimension as the dimension of the constraint distribution, we define linear connections for which the equations of motion take the form of equations of geodesic lines. In the case of inertial motion, or motion under influence of potential forces, we give explicit expressions for coefficients of linear connections, in a form much simpler then those given for a general case in [4]. Let us consider mechanical system M with local coordinates q (i = 1, . . . , n). It is well known that the configuration space Vn of M is the Riemannian space with the metric defined by the expression
在这个笔记中，我们考虑具有不依赖于时间的光滑线性非完整约束的机械系统。对于Chaplygin系统的一种特殊情况，当系统的运动可以被描述为与约束分布维数相同维数的约化空间局部坐标中的封闭微分方程组时，我们定义了运动方程采用测地线方程形式的线性连接。对于惯性运动或受势能影响的运动，我们给出了线性连接系数的显式表达式，其形式比[4]中一般情况下给出的形式简单得多。我们考虑具有局部坐标q (i = 1，…)的机械系统M。， n)。众所周知，M的位形空间Vn是由表达式定义度规的黎曼空间
{"title":"On geometrization of motion of some nonholonomic systems","authors":"A. Bakša","doi":"10.2298/TAM171110013B","DOIUrl":"https://doi.org/10.2298/TAM171110013B","url":null,"abstract":"In this note we consider mechanical systems with smooth linear nonholonomic constraints which do not depend on time. For a special case of Chaplygin systems, when the motion of the system can be described as a closed system of differential equations in local coordinates of the reduced space of the same dimension as the dimension of the constraint distribution, we define linear connections for which the equations of motion take the form of equations of geodesic lines. In the case of inertial motion, or motion under influence of potential forces, we give explicit expressions for coefficients of linear connections, in a form much simpler then those given for a general case in [4]. Let us consider mechanical system M with local coordinates q (i = 1, . . . , n). It is well known that the configuration space Vn of M is the Riemannian space with the metric defined by the expression","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82919629","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 apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the oregonator model. Additionally, we investigate their Hamiltonian, Nambu-Poisson and metriplectic characters.
{"title":"On integrals, Hamiltonian and metriplectic formulations of polynomial systems in 3D","authors":"Ougul Esen, A. Choudhury, P. Guha","doi":"10.2298/TAM161118001E","DOIUrl":"https://doi.org/10.2298/TAM161118001E","url":null,"abstract":"We apply the Darboux integrability method to determine first integrals and Hamiltonian formulations of three dimensional polynomial systems; namely the reduced three-wave interaction problem, the Rabinovich system, the Hindmarsh-Rose model, and the oregonator model. Additionally, we investigate their Hamiltonian, Nambu-Poisson and metriplectic characters.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76050390","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}
Khairuzzaman Mamun, M. M. Rahman, M. Akhter, M. Ali
A numerical simulation to investigate the Non-Newtonian modeling effects on physiological flows in a three dimensional idealized artery with a single stenosis of 85% severity is given. The wall vessel is considered to be rigid. Oscillatory physiological and parabolic velocity profile has been imposed for inlet boundary condition. Determination of the physiological waveform is performed using a Fourier series with sixteen harmonics. The investigation has a Reynolds number range of 96 to 800. Low Reynolds number k ? w model is used as governing equation. The investigation has been carried out to characterize two Non-Newtonian constitutive equations of blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has also been investigated to study the physics of fluid. The results of Newtonian model are compared with the Non-Newtonian models. The numerical results are presented in terms of velocity, pressure, wall shear stress distributions and cross sectional velocities as well as the streamlines contour. At early systole pressure differences between Newtonian and Non-Newtonian models are observed at pre-stenotic, throat and immediately after throat regions. In the case of wall shear stress, some differences between Newtonian and Non-Newtonian models are observed when the flows are minimum such as at early systole or diastole. In general, the velocities at throat regions are highest at all-time phase. However, at pick systole higher velocities are observed at post-stenotic region. Downstream flow of all models creates some recirculation regions at diastole.
{"title":"Physiological non-Newtonian blood flow through single stenosed artery","authors":"Khairuzzaman Mamun, M. M. Rahman, M. Akhter, M. Ali","doi":"10.1063/1.4958361","DOIUrl":"https://doi.org/10.1063/1.4958361","url":null,"abstract":"A numerical simulation to investigate the Non-Newtonian modeling effects on\u0000 physiological flows in a three dimensional idealized artery with a single\u0000 stenosis of 85% severity is given. The wall vessel is considered to be\u0000 rigid. Oscillatory physiological and parabolic velocity profile has been\u0000 imposed for inlet boundary condition. Determination of the physiological\u0000 waveform is performed using a Fourier series with sixteen harmonics. The\u0000 investigation has a Reynolds number range of 96 to 800. Low Reynolds number\u0000 k ? w model is used as governing equation. The investigation has been\u0000 carried out to characterize two Non-Newtonian constitutive equations of\u0000 blood, namely, (i) Carreau and (ii) Cross models. The Newtonian model has\u0000 also been investigated to study the physics of fluid. The results of\u0000 Newtonian model are compared with the Non-Newtonian models. The numerical\u0000 results are presented in terms of velocity, pressure, wall shear stress\u0000 distributions and cross sectional velocities as well as the streamlines\u0000 contour. At early systole pressure differences between Newtonian and\u0000 Non-Newtonian models are observed at pre-stenotic, throat and immediately\u0000 after throat regions. In the case of wall shear stress, some differences\u0000 between Newtonian and Non-Newtonian models are observed when the flows are\u0000 minimum such as at early systole or diastole. In general, the velocities at\u0000 throat regions are highest at all-time phase. However, at pick systole\u0000 higher velocities are observed at post-stenotic region. Downstream flow of\u0000 all models creates some recirculation regions at diastole.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89932450","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 paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ‘pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin’s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.
{"title":"Analysis of the brachistochronic motion of a variable mass nonholonomic mechanical system","authors":"B. Jeremić, R. Radulović, A. Obradović","doi":"10.2298/TAM150723002J","DOIUrl":"https://doi.org/10.2298/TAM150723002J","url":null,"abstract":"The paper considers the brachistochronic motion of a variable mass nonholonomic mechanical system [3] in a horizontal plane, between two specified positions. Variable mass particles are interconnected by a lightweight mechanism of the ‘pitchfork’ type. The law of the time-rate of mass variation of the particles, as well as relative velocities of the expelled particles, as a function of time, are known. Differential equations of motion, where the reactions of nonholonomic constraints and control forces figure, are created based on the general theorems of dynamics of a variable mass mechanical system [5]. The formulated brachistochrone problem, with adequately chosen quantities of state, is solved, in this case, as the simplest task of optimal control by applying Pontryagin’s maximum principle [1]. A corresponding two-point boundary value problem (TPBVP) of the system of ordinary nonlinear differential equations is obtained, which, in a general case, has to be numerically solved [2]. On the basis of thus obtained brachistochronic motion, the active control forces, along with the reactions of nonholonomic constraints, are determined. The analysis of the brachistochronic motion for different values of the initial position of a variable mass particle B is presented. Also, the interval of values of the initial position of a variable mass particle B, for which there are the TPBVP solutions, is determined.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89494444","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 considers a boundary layer analysis on the effects of diffusion-thermo, heat absorption and homogeneous chemical reaction on mag- netohydrodynamic flow of an incompressible, laminar chemically reacting mi- cropolar fluid past a semi-infinite vertical porous plate is made numerically. The governing partial differential equations are solved numerically using the finite element method. The numerical results are compared and found to be in good agreement with previous results as special case of the present inves- tigation. The effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed and explained graphically. Also the effects of the pertinent parameters on the local Skin friction coefficient, wall Couple stress and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are presented numerically in tabular form.
{"title":"DIFFUSSION-THERMO AND CHEMICAL REACTION EFFECTS ON AN UNSTEADY MHD FREE CONVECTION FLOW IN A MICROPOLAR FLUID","authors":"SivaReddy Sheri, M. Shamshuddin","doi":"10.2298/TAM160223007S","DOIUrl":"https://doi.org/10.2298/TAM160223007S","url":null,"abstract":"This paper considers a boundary layer analysis on the effects of diffusion-thermo, heat absorption and homogeneous chemical reaction on mag- netohydrodynamic flow of an incompressible, laminar chemically reacting mi- cropolar fluid past a semi-infinite vertical porous plate is made numerically. The governing partial differential equations are solved numerically using the finite element method. The numerical results are compared and found to be in good agreement with previous results as special case of the present inves- tigation. The effects of the various important parameters entering into the problem on the velocity, microrotation, temperature and concentration fields within the boundary layer are discussed and explained graphically. Also the effects of the pertinent parameters on the local Skin friction coefficient, wall Couple stress and rates of heat and mass transfer in terms of the local Nusselt and Sherwood numbers are presented numerically in tabular form.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78382743","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}
R. R. Srinivasa, G. Aruna, N. Naidu, S. Varma, Mohammad Mehdi Rashidi
In this research paper, we found both numerical and analytical solutions for the effect of chemical reaction on unsteady, incompressible, viscous fluid flow past an exponentially accelerated vertical plate with heat absorption and variable temperature in a magnetic field. The flow problem is governed by a system of coupled non-linear partial differential equations with suitable boundary conditions. We have solved the governing equations by an efficient, accurate, powerful finite element method (FEM) as well as Laplace transform technique (LTT). The evaluation of the numerical results are performed and graphical results for the velocity, temperature and concentration profiles within the boundary layer are discussed. Also, the expressions for the skin-friction, Nusselt number and the Sherwood number coefficients have been derived and discussed through graphs and tabular forms for different values of the governing parameters.
{"title":"Chemically reacting fluid flow induced by an exponentially accelerated infinite vertical plate in a magnetic field and variable temperature via LTT and FEM","authors":"R. R. Srinivasa, G. Aruna, N. Naidu, S. Varma, Mohammad Mehdi Rashidi","doi":"10.2298/TAM151214003S","DOIUrl":"https://doi.org/10.2298/TAM151214003S","url":null,"abstract":"In this research paper, we found both numerical and analytical solutions for the effect of chemical reaction on unsteady, incompressible, viscous fluid flow past an exponentially accelerated vertical plate with heat absorption and variable temperature in a magnetic field. The flow problem is governed by a system of coupled non-linear partial differential equations with suitable boundary conditions. We have solved the governing equations by an efficient, accurate, powerful finite element method (FEM) as well as Laplace transform technique (LTT). The evaluation of the numerical results are performed and graphical results for the velocity, temperature and concentration profiles within the boundary layer are discussed. Also, the expressions for the skin-friction, Nusselt number and the Sherwood number coefficients have been derived and discussed through graphs and tabular forms for different values of the governing parameters.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89610051","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 full list of entire and finite valued solutions of the three body problem in the form of functions, depending on a time variable, is established. All the entire and finite valued solutions are among the solutions of Euler and Lagrange.
{"title":"On the entire and finite valued solutions of the three-body problem","authors":"A. Belyaev","doi":"10.2298/TAM160126010B","DOIUrl":"https://doi.org/10.2298/TAM160126010B","url":null,"abstract":"A full list of entire and finite valued solutions of the three body problem in the form of functions, depending on a time variable, is established. All the entire and finite valued solutions are among the solutions of Euler and Lagrange.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2016-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78661201","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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