The Experts below are selected from a list of 276 Experts worldwide ranked by ideXlab platform
G M Homsy - One of the best experts on this subject based on the ideXlab platform.
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Axisymmetric Deformation and stability of a viscous drop in a steady electric field
Journal of Fluid Mechanics, 2007Co-Authors: G M HomsyAbstract:We consider a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics. The jump in electrical properties creates an electric stress balanced by hydrodynamic and capillary stresses. Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically with boundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and λ (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, CaE .F orλ = 1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R, Q)-plane in which the drop either attains a steady shape under any field strength or reaches a fold-point instability past a critical CaE. We identify the latter with linear instability of the steady shape to Axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for λ =1 .
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Axisymmetric Deformation and stability of a viscous drop in a steady electric field
Journal of Fluid Mechanics, 2007Co-Authors: Etienne Lac, G M HomsyAbstract:We consider a neutrally buoyant and initially uncharged drop in a second liquid subjected to a uniform electric field. Both liquids are taken to be leaky dielectrics. The jump in electrical properties creates an electric stress balanced by hydrodynamic and capillary stresses. Assuming creeping flow conditions and axisymmetry of the problem, the electric and flow fields are solved numerically with boundary integral techniques. The system is characterized by the physical property ratios R (resistivities), Q (permitivities) and λ (dynamic viscosities). Depending on these parameters, the drop deforms into a prolate or an oblate spheroid. The relative importance of the electric stress and of the drop/medium interfacial tension is measured by the dimensionless electric capillary number, CaE .F orλ = 1, we present a survey of the various behaviours obtained for a wide range of R and Q. We delineate regions in the (R, Q)-plane in which the drop either attains a steady shape under any field strength or reaches a fold-point instability past a critical CaE. We identify the latter with linear instability of the steady shape to Axisymmetric disturbances. Various break-up modes are identified, as well as more complex behaviours such as bifurcations and transition from unstable to stable solution branches. We also show how the viscosity contrast can stabilize the drop or advance break-up in the different situations encountered for λ =1 .
Pin Tong - One of the best experts on this subject based on the ideXlab platform.
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on the elastic Axisymmetric Deformation of a rod containing a single cylindrical inclusion
International Journal of Solids and Structures, 2000Co-Authors: Zheng Zhong, Pin TongAbstract:This paper studies the Axisymmetric Deformation of a rod containing a single cylindrical transformation inclusion with uniform Axisymmetric eigenstrain. Elastic solutions of the problem are obtained by means of the principle of superposition. The original problem is divided into two sub-problems to derive the analytical expressions for the displacements, the stresses and the elastic strain energy of the whole rod. Quantitative pictures on the stress and strain jumps across the inclusion–matrix interface and on the evolution of the strain energy of the whole rod are illustrated. The results show that the normalized elastic strain energy depends on the relative length of the cylindrical inclusion for the length–radius ratio l/a<2. This strain energy increases very quickly at the initial growth and soon reaches the peak value, then decreases with the further increase of l/a and finally reaches its steady state value. Several Deformation features of this non-classical inclusion–matrix system are discussed. The work of this paper also provides a quantitative solution in the investigation of the propagation of strain discontinuity observed during thermoelastic phase transformation in solids such as TiNi shape memory alloy wires.
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On the elastic Axisymmetric Deformation of a rod containing a single cylindrical inclusion
International Journal of Solids and Structures, 2000Co-Authors: Zheng Zhong, Qingping Sun, Pin TongAbstract:This paper studies the Axisymmetric Deformation of a rod containing a single cylindrical transformation inclusion with uniform Axisymmetric eigenstrain. Elastic solutions of the problem are obtained by means of the principle of superposition. The original problem is divided into two sub-problems to derive the analytical expressions for the displacements, the stresses and the elastic strain energy of the whole rod. Quantitative pictures on the stress and strain jumps across the inclusion–matrix interface and on the evolution of the strain energy of the whole rod are illustrated. The results show that the normalized elastic strain energy depends on the relative length of the cylindrical inclusion for the length–radius ratio l/a
Mark E. Mear - One of the best experts on this subject based on the ideXlab platform.
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Effect of void shape on the macroscopic response of non-linear porous solids
International Journal of Plasticity, 1996Co-Authors: K. C. Yee, Mark E. MearAbstract:Abstract The macroscopic response of an incompressible power-law matrix containing aligned spheroidal voids is investigated. The voids are assumed to be arranged in a uniform array, and the response of the solid is evaluated by isolating a typical block of the material containing a single void. The requisite boundary value problem for this “unit cell” is solved using a spectral method which is an adaption of that used by Lee and Mear “Axisymmetric Deformation of Power-law Solids containing Elliptical Inhomogeneities. Part I: Rigid Inclusions”, J. Mech. Phys. Solids , (1992) 8 , 1805. Attention is restricted to Axisymmetric Deformation, and results for the macroscopic strain-rates (or strains) are presented for a range of void shape, void volume concentrations, hardening exponents and remote stress triaxilities.
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Axisymmetric Deformation of power-law solids containing a dilute concentration of aligned spheroidal voids
Journal of the Mechanics and Physics of Solids, 1992Co-Authors: B.j. Lee, Mark E. MearAbstract:Abstract T he macroscopic response of an incompressible power-law matrix containing a dispersion of aligned, spheroidal voids is investigated. Attention is restricted to dilute concentrations of voids and to Axisymmetric Deformation of the solid. The essential step in the analysis is the solution of a kernel problem for an isolated void, and this solution is obtained accurately and efficiently using a Ritz procedure developed for this purpose. Results for macroscopic strain-rates are presented for void shapes ranging from penny-shaped cracks to infinitely long circular cylinders and for a wide range of triaxialities and matrix hardening exponents. These results are used to assess the role of void shape on the overall response of porous solids.
James G. Simmonds - One of the best experts on this subject based on the ideXlab platform.
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Love's stress function for torsionless Axisymmetric Deformation of elastically isotropic bodies with body forces
Journal of Applied Mechanics, 2000Co-Authors: James G. SimmondsAbstract:This note shows that the Axisymmetric Deformation of an elastically isotropic solid of revolution, subject to both axial and radial body forces, may be described in terms of Love's stress function, provided certain simple terms are added to the displacement-stress function relations.
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An asymptotic analysis of end effects in the Axisymmetric Deformation of elastic tubes weak in shear: Higher-order shell theories are inadequate and unnecessary☆
International Journal of Solids and Structures, 1992Co-Authors: James G. SimmondsAbstract:Abstract This paper specializes to a semi-infinite tube Morgan's (Int. J. Solids Structures10, 837–852, 1974) two-stress-function formulation of the equations for the Axisymmetric Deformation of a linearly elastic transversely isotropic cylindrical body free of surface tractions. The ratio of the tube's shear modulus to its radial (transverse) extensional modulus is taken to be of the order of magnitude of the square root of its thickness to its mean radius. The equations are solved by formal asymptotic expansion in (fractional) powers of the thickness to radius ratio for four canonical sets of end conditions: (A) axisymmctric equilibrated tractions : (B) and (C). two different combinations of tractions and displacements: and (D) axisymmctric radial and axial displacements. The solutions exhibit interior (i.e. shell-like) parts and wide and narrow boundary (or edge) layers, the latter containing components that vary extremely rapidly through the thickness of the tube. The analysis focuses on computing the lowest-order correction, both in the interior and in the boundary layers, to classical shell theory. It is shown that in cases (A)- (C) the interior correction to classical shell theory—that is, those effects so-called higher-order shell theories attempt to capture—can (ultimately) be determined directly, in terms of the edge data, but that in case of prescribed displacements (D), the computation of (three-dimensional) boundary-layer effects is essential. These conclusions are consistent with those for elastically isotropic shells found by Gregory and Wan (1992) who used ingenious arguments based on the Betti Reciprocity Principle.
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simplifications under the kirchhoff hypothesis of taber s nonlinear theory for the Axisymmetric bending and torsion of elastic shells of revolution
International Journal of Solids and Structures, 1991Co-Authors: R. England, James G. SimmondsAbstract:Abstract We show that, under the Kirchhoff hypothesis, Taber's recent theory for the simultaneous Axisymmetric bending and torsion of shells of revolution undergoing large strains can be simplified considerably. In general, his 33 equations can be reduced to four first-order ordinary differential equations and two algebraic equations for six unknowns. For small strains, the equations can be reduced further to two coupled nonlinear equations for the meridional angle of rotation and a stress function, as in Reissner's theory of torsionless, Axisymmetric Deformation.
Larry A Taber - One of the best experts on this subject based on the ideXlab platform.
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Torsional boundary layer effects in shells of revolution undergoing large Axisymmetric Deformation
Computational Mechanics, 1992Co-Authors: F. -c. Su, Larry A TaberAbstract:Numerical and asymptotic solutions are developed to the equations governing large torsional, Axisymmetric Deformation of rubberlike shells of revolution. The shell equations include large-strain geometric and material nonlinearities, transverse shear Deformation, transverse normal stress and strain, and torsion. Both analyses allow ready incorporation of different strain-energy density functions. In the asymptotic analysis, the interior solution corresponds to that of nonlinear membrane theory and contains a primary boundary layer. The edge-zone solution gives a secondary boundary layer that, for large strain, divides into a bending-twisting moment component and a torsional-membrane component. The boundary layer behavior is illustrated for a clamped neo-Hookean cylinder subjected to internal pressure and axial torque.
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Axisymmetric Deformation of poroelastic shells of revolution
International Journal of Solids and Structures, 1992Co-Authors: Larry A TaberAbstract:Abstract A linear theory is developed for Axisymmetric Deformation of thin poroelastic shells of revolution. With fluid solid coupling included through Biot's consolidation theory, results are presented for cylindrical shells with an oscillating internal pressure and various surface boundary conditions on the fluid. First, the effects of fluid flow and shell inertia on the stretching behavior are studied through a separation of variables solution. Then, the bending behavior near a clamped edge is examined through an asymptotic solution of a matrix form of the governing equations. The results show that the asymptotic solution is accurate in the low frequency range, when the loading time is large compared to the consolidation time. In addition, for the examples studied, the fluid flow influences the membrane more than the bending behavior, but damping due to flow resistance is limited near resonance.