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Dorin Ieşan - One of the best experts on this subject based on the ideXlab platform.
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Thermal Stresses in Chiral Elastic Beams
Journal of Thermal Stresses, 2011Co-Authors: Dorin IeşanAbstract:The chiral effects cannot be described by means of the classical thermoelasticity. In the context of the linear theory of Cosserat thermoelasticity we study the deformation of a chiral beam subjected to a prescribed thermal field. This paper points out the importance of the generalized Plane Strain Problem in the analysis of thermal stresses in chiral elastic beams. First, we investigate the effects of a thermal field which is linear in the axial coordinate. It is shown that this temperature variation produces extension, bending, torsion, flexure and a Plane deformation. Then, we study the deformation of the beam when the thermal field is a polynomial of degree m (m > 1) in the axial coordinate. The solution is reduced to the solving of some two-dimensional Problems. The method is used to solve the Problem of a circular cylinder subjected to a temperature that is independent of the axial coordinate.
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Torsion of chiral Cosserat elastic rods
European Journal of Mechanics - A Solids, 2010Co-Authors: Dorin IeşanAbstract:This paper is concerned with the torsion of isotropic chiral Cosserat elastic cylin-ders. First, the generalized Plane Strain Problem is defined and an existence result is presented. Then, the three-dimensional Problem is reduced to the study of some generalized Plane Strain Problems. In general, the torsion of the cylinder is accom-panied by bending and extension. The method is applied to study the torsion of a circular cylinder.
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Classical and Generalized Models of Elastic Rods
2008Co-Authors: Dorin IeşanAbstract:Preface Saint-Venant's Problem Preliminaries Formulation of Saint-Venant's Problem Saint-Venant's Solutions Unified Treatment Plane Deformation Properties of the Solutions to Saint-Venant's Problem New Method of Solving Saint-Venant's Problem Minimum Energy Characterizations of Solutions Truesdell's Problem Saint-Venant's Principle Theory of Loaded Cylinders Problems of Almansi and Michell Almansi-Michell Problem Almansi Problem Characterization of Solutions Direct Method Applications Deformation of Nonhomogeneous Cylinders Preliminaries Plane Strain Problem: Auxiliary Plane Strain Problems Extension and Bending of Nonhomogeneous Cylinders Torsion Flexure Elastic Cylinders Composed of Different Nonhomogeneous and Isotropic Materials Piecewise Homogeneous Cylinders Applications Anisotropic Bodies Preliminaries Generalized Plane Strain Problem Extension, Bending, and Torsion Flexure of Anisotropic Cylinders Minimum Energy Characterizations of Solutions Global Strain Measures Problem of Loaded Cylinders Orthotropic Bodies Plane Strain Problem of Orthotropic Bodies Deformation of Elastic Cylinders Composed of Nonhomogeneous and Anisotropic Materials Cylinders Composed of Different Orthotropic Materials Cosserat Elastic Continua Basic Equations Plane Strain Saint-Venant's Problem for Cosserat Cylinders Minimum Principles Global Strain Measures Theory of Loaded Cosserat Cylinders Nonhomogeneous Cosserat Cylinders Plain Strain Problems Saint-Venant's Problem Problems of Almansi and Michell Anisotropic Cosserat Cylinders Cylinders Composed of Different Elastic Materials Porous Elastic Bodies Basic Equations Plane Strain Extension, Bending, and Torsion of Porous Elastic Cylinders Cylinders Composed of Different Porous Materials Applications Answers to Selected Problems Bibliography Index Exercises appear at the end of each chapter.
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On the Deformation of Functionally Graded Porous Elastic Cylinders
Journal of Elasticity, 2007Co-Authors: Dorin Ieşan, Antonio ScaliaAbstract:This paper is concerned with the linear theory of inhomogeneous and orthotropic elastic materials with voids. We study the Problem of extension and bending of right cylinders when the constitutive coefficients are independent of the axial coordinate. First, the Plane Strain Problem for inhomogeneous and orthotropic elastic materials with voids is investigated. Then, the solution of the Problem of extension and bending is expressed in terms of solutions of three Plane Strain Problems. The results are used to study the extension of a circular cylinder with a special kind of inhomogeneity. The influence of the material inhomogeneity on the axial Strain is established.
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On the Plane Strain of thermo-microstretch elastic solids
International Journal of Engineering Science, 2004Co-Authors: Dorin Ieşan, Ramón QuintanillaAbstract:This paper is concerned with the linear theory of thermo-microstretch elastic solids. We present a method to reduce the thermoelastic Plane Strain Problem to an isothermal one with zero body loads and with certain boundary data. The result is used to study the thermoelastic deformation of a tube and the Problem of thermal stresses in a cylinder subjected to a uniform temperature gradient.
J. Bai - One of the best experts on this subject based on the ideXlab platform.
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Equilibrium equations and boundary conditions of Strain gradient theory in arbitrary curvilinear coordinates
Journal of the Mechanical Behavior of Materials, 2014Co-Authors: Mikhail A. Guzev, J. BaiAbstract:Abstract: Equilibrium equations and boundary condi-tions of the Strain gradient theory in arbitrary curvilinear coordinates have been obtained. Their special form for an axisymmetric Plane Strain Problem is also given. Keywords: arbitrary curvilinear coordinates; boundary conditions; equilibrium equations; Strain gradient model. DOI 10.1515/jmbm-2014-0018 1 Introduction In the early 1960s, Toupin [1, 2] and Mindlin [3, 4] pro-posed a Strain gradient theory, which suggests that energy depends not only on deformations, but also on gradient of deformations. Since then, various exten-sions or versions of the theory have been developed and applied to different Problems [5–8]. In the past 20 years there has been a growing interest in various versions of this theory in the field of mechanics due to its successful application to a number of Problems pertaining to current technologies including nanotechnology. Classical contin-uum theories are not capable of addressing Problems for which the size effect due to the underlying microstructure is important to include in a phenomenological descrip-tion. Moreover localization of Strain due to material sof-tening cannot be captured. Both these issues have been considered successfully within internal length or Strain gradient theories, as has been demonstrated by Aifantis et al. for plasticity [9–12] and elasticity [13–16], as well as by other authors including Fleck and Hutchinson [17–19], Chambon et al. [20], Lurie and co-workers [21, 22], and Zhao et al. [23, 24]. Possible application of this theory to the macrodescription of materials was given by Qi et al. [25], and the relation of kinematical parameters with internal geometrical material characteristics was demon-strated by Guzev [26, 27].The Strain gradient theory developed by Toupin [1] and Mindlin [3] was formulated in Cartesian rectangular coordinates. For Problems which require curvilinear coor-dinates, the corresponding equilibrium equations and boundary conditions cannot be obtained automatically from the theory. Therefore, an appropriate form of equilib-rium equations and boundary conditions of Strain gradient theories in curvilinear coordinates would be desirable to obtain. An effort in this direction has been made by Zhao and Pedroso [28], who adopted the approach proposed by Eringen [29] suggesting that the transition from rectangular coordinates to any of the curvilinear coordinates follows two rules: (a) the partial differentiation symbol (,) must be replaced by the covariant differentiation symbol (;); and (b) the repeated indices must be on diagonal positions. However, a systematic derivation following this approach was not explicitly provided in Eringen’s book [29].This task was undertaken during our study where equilibrium equations and boundary conditions of the Strain gradient theory in arbitrary curvilinear coordinates are provided. The axisymmetric Plane Strain Problem for long cylinder was also considered in detail as a special case. The structure of the present article is as follows. Section 2 summarizes the principle of virtual work used for derivation of equilibrium equations and boundary conditions of Strain gradient theory. Section 3 provides the form of equilibrium equations in curvilinear coordinates, while Section 4 lists the corresponding curvilinear coordi-nate form of associated boundary conditions. Finally, in Section 5, the formalism is specialized for a Plane Strain Problem of a pressurized long cylinder.
George Z. Voyiadjis - One of the best experts on this subject based on the ideXlab platform.
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Strain gradient finite element model for finite deformation theory: size effects and shear bands
Computational Mechanics, 2020Co-Authors: Yooseob Song, George Z. VoyiadjisAbstract:In this work, a thermodynamically consistent constitutive formulation for the coupled thermomechanical Strain gradient plasticity theory is developed in the context of the finite deformation framework. A corresponding finite element solution is presented to investigate the microstructural features of metallic volumes. The developed model is established based on an extra Helmholtz-type partial differential equation, and the nonlocal quantity is calculated in a coupled method based on the equilibrium conditions. This approach is well known for its computational strength, however, it is also commonly accepted that it cannot capture the size effect phenomenon observed in the micro-/nanoscale experiments during hardening. In order to resolve this issue, a modified Strain gradient approach which can capture the size effects under the finite deformation is constructed in this work. The shear Problem is then solved to carry out the feasibility study of the developed model on the size effect phenomenon. Lastly, a Plane Strain Problem under uniaxial tensile loading with shear bands is examined to perform the mesh sensitivity tests of the model during softening.
Ares J. Rosakis - One of the best experts on this subject based on the ideXlab platform.
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A finite element analysis of small-scale yielding near a stationary crack under Plane stress
Journal of The Mechanics and Physics of Solids, 2002Co-Authors: R Narasimhan, Ares J. RosakisAbstract:Abstract A detailed finite element analysis of the monotonic loading of a stationary crack is performed under Mode I Plane stress, small-scale yielding conditions. A small Strain, J 2 incremental plasticity theory is employed and both elastic-perfectly plastic and power law hardening materials are considered. Some issues such as the range of dominance of the asymptotic stress and deformation fields and the amount of non-proportional loading near the crack tip, which have received wide attention in the analogous Plane Strain Problem, are examined. Special attention is devoted to the perfectly plastic idealization by performing a separate singular finite element analysis to clarify some details about the asymptotic stress and deformation fields. The full-field numerical solution is used to simulate synthetic (optical) caustic patterns at different distances from the tip, which are compared with experimental observations and with asymptotic analytical results.
Fazil Erdogan - One of the best experts on this subject based on the ideXlab platform.
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Fracture mechanics of orthotropic laminated plates—II. The Plane Strain crack Problem for two bonded orthotropic layers
International Journal of Solids and Structures, 1993Co-Authors: Binghua Wu, Fazil ErdoganAbstract:Abstract In this paper the Plane Strain Problem for two bonded orthotropic layers containing a crack perpendicular to the laminate surfaces is considered. After deriving the integral equation for the general Problem, the solution is obtained for three main crack geometries, namely an embedded crack, a surface crack and a crack terminating at the interface under a remotely applied membrane load or bending moment. For the crack terminating at the interface the necessary asymptotic analysis is carried out, the characteristic equation to determine the power of stress singularity β is obtained, and the influence of the material parameters on β is examined. The main results given in the paper consist of the stress intensity factors obtained for various crack geometries, material combinations and loading conditions.
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fracture mechanics of orthotropic laminated plates ii the Plane Strain crack Problem for two bonded orthotropic layers
International Journal of Solids and Structures, 1993Co-Authors: Fazil ErdoganAbstract:Abstract In this paper the Plane Strain Problem for two bonded orthotropic layers containing a crack perpendicular to the laminate surfaces is considered. After deriving the integral equation for the general Problem, the solution is obtained for three main crack geometries, namely an embedded crack, a surface crack and a crack terminating at the interface under a remotely applied membrane load or bending moment. For the crack terminating at the interface the necessary asymptotic analysis is carried out, the characteristic equation to determine the power of stress singularity β is obtained, and the influence of the material parameters on β is examined. The main results given in the paper consist of the stress intensity factors obtained for various crack geometries, material combinations and loading conditions.