The Experts below are selected from a list of 315 Experts worldwide ranked by ideXlab platform
Morton E. Gurtin - One of the best experts on this subject based on the ideXlab platform.
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a gradient theory of Small Deformation single crystal plasticity that accounts for gnd induced interactions between slip systems
Journal of The Mechanics and Physics of Solids, 2011Co-Authors: Morton E. Gurtin, Nobutada OhnoAbstract:Abstract This paper develops a gradient theory of single-crystal plasticity based on a system of microscopic force balances, one balance for each slip system, derived from the principle of virtual power, and a mechanical version of the second law that includes, via the microscopic forces, work performed during plastic flow. When combined with thermodynamically consistent constitutive relations the microscopic force balances become nonlocal flow rules for the individual slip systems in the form of partial differential equations requiring boundary conditions. Central ingredients in the theory are densities of (geometrically necessary) edge and screw dislocations, densities that describe the accumulation of dislocations, and densities that characterize forest hardening. The form of the forest densities is based on an explicit kinematical expression for the normal Burgers vector on a slip plane.
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Boundary conditions in Small-Deformation, single-crystal plasticity that account for the Burgers vector
Journal of the Mechanics and Physics of Solids, 2005Co-Authors: Morton E. Gurtin, Alan NeedlemanAbstract:This paper discusses boundary conditions appropriate to a theory of single-crystal plasticity (Gurtin, J. Mech. Phys. Solids 50 (2002) 5) that includes an accounting for the Burgers vector through energetic and dissipative dependences on the tensor G=curlHp, with Hp the plastic part in the additive decomposition of the displacement gradient into elastic and plastic parts. This theory results in a flow rule in the form of N coupled second-order partial differential equations for the slip-rates γ˙α(α=1,2…,N), and, consequently, requires higher-order boundary conditions. Motivated by the virtual-power principle in which the external power contains a boundary-integral linear in the slip-rates, hard-slip conditions in which (A) γ˙α=0 on a subsurface Shard of the boundary for all slip systems α are proposed. In this paper we develop a theory that is consistent with that of (Gurtin, 2002), but that leads to an external power containing a boundary-integral linear in the tensor H˙ijpɛjrlnr, a result that motivates replacing (A) with the microhard condition (B) H˙ijpɛjrlnr=0 on the subsurface Shard. We show that, interestingly, (B) may be interpreted as the requirement that there be no flow of the Burgers vector across Shard. What is most important, we establish uniqueness for the underlying initial/boundary-value problem associated with (B); since the conditions (A) are generally stronger than the conditions (B), this result indicates lack of existence for problems based on (A). For that reason, the hard-slip conditions (A) would seem inappropriate as boundary conditions. Finally, we discuss conditions at a grain boundary based on the flow of the Burgers vector at and across the boundary surface.
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a gradient theory of Small Deformation isotropic plasticity that accounts for the burgers vector and for dissipation due to plastic spin
Journal of The Mechanics and Physics of Solids, 2004Co-Authors: Morton E. GurtinAbstract:Abstract This study develops a gradient theory of Small-Deformation viscoplasticity based on: a system of microforces consistent with its peculiar balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that accounts for the Burgers vector through a free energy dependent on curl H p , with Hp the plastic part of the elastic–plastic decomposition of the displacement gradient. The microforce balance and the constitutive equations, restricted by the second law, are shown to be together equivalent to a nonlocal flow rule in the form of a coupled pair of second-order partial differential equations. The first of these is an equation for the plastic strain-rate E p in which the stress T plays a basic role; the second, which is independent of T, is an equation for the plastic spin W p . A consequence of this second equation is that the plastic spin vanishes identically when the free energy is independent of curl H p , but not generally otherwise. A formal discussion based on experience with other gradient theories suggests that sufficiently far from boundaries solutions should not differ appreciably from classical solutions, but close to microscopically hard boundaries, boundary layers characterized by a large Burgers vector and large plastic spin should form. Because of the nonlocal nature of the flow rule, the classical macroscopic boundary conditions need be supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a variational formulation of the flow rule is derived. Finally, we sketch a generalization of the theory that allows for isotropic hardening resulting from dissipative constitutive dependences on ∇ E p .
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On a framework for Small-Deformation viscoplasticity: free energy, microforces, strain gradients
International Journal of Plasticity, 2003Co-Authors: Morton E. GurtinAbstract:Abstract This study develops a general theory for Small-Deformation viscoplasticity based on a system of microforces consistent with its own balance; a mechanical version of the second law that includes, via the microforces, work performed during viscoplastic flow; a constitutive theory that allows for dependences on plastic strain-gradients. The microforce balance and the constitutive equations—suitably restricted by the second law—are shown to be together equivalent to a flow rule that accounts for variations in free energy due to flow. When this energy is the sum of an elastic strain energy and a defect energy quadratic, isotropic, and positive definite in the plastic-strain gradients, the flow rule takes the form of a second-order parabolic PDE for the plastic strain coupled to the usual PDE arising from the standard macroscopic force balance and the elastic stress-strain relation. The classical macroscopic boundary conditions are supplemented by nonstandard boundary conditions associated with viscoplastic flow. As an aid to solution, a weak (virtual power) formulation of the nonlocal flow rule is derived.
David Saintillan - One of the best experts on this subject based on the ideXlab platform.
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A three-dimensional Small-Deformation theory for electrohydrodynamics of dielectric drops
Journal of Fluid Mechanics, 2021Co-Authors: Debasish Das, David SaintillanAbstract:Electrohydrodynamics of drops is a classic fluid mechanical problem where Deformations and microscale flows are generated by application of an external electric field. In weak fields, electric stresses acting on the drop surface drive quadrupolar flows inside and outside and cause the drop to adopt a steady axisymmetric shape. This phenomenon is best explained by the leaky-dielectric model under the premise that a net surface charge is present at the interface while the bulk fluids are electroneutral. In the case of dielectric drops, increasing the electric field beyond a critical value can cause the drop to start rotating spontaneously and assume a steady tilted shape. This symmetry-breaking phenomenon, called Quincke rotation, arises due to the action of the interfacial electric torque countering the viscous torque on the drop, giving rise to steady rotation in sufficiently strong fields. Here, we present a Small-Deformation theory for the electrohydrodynamics of dielectric drops for the complete Melcher–Taylor leaky-dielectric model in three dimensions. Our theory is valid in the limits of strong capillary forces and highly viscous drops and is able to capture the transition to Quincke rotation. A coupled set of nonlinear ordinary differential equations for the induced dipole moments and shape functions are derived whose solution matches well with experimental results in the appropriate Small-Deformation regime. Retention of both the straining and rotational components of the flow in the governing equation for charge transport enables us to perform a linear stability analysis and derive a criterion for the applied electric field strength that must be overcome for the onset of Quincke rotation of a viscous drop.
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A nonlinear Small-Deformation theory for transient droplet electrohydrodynamics
Journal of Fluid Mechanics, 2016Co-Authors: Debasish Das, David SaintillanAbstract:The Deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher–Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of Taylor (Proc. R. Soc. Lond. A, vol. 291, 1966, pp. 159–166), there have been numerous computational and theoretical studies to predict the Deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel Small-Deformation theory accurate to second order in electric capillary number for the complete Melcher–Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape Deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the Deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary element formulation and with existing experimental data in the Small-Deformation regime.
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a nonlinear Small Deformation theory for transient droplet electrohydrodynamics
arXiv: Fluid Dynamics, 2016Co-Authors: Debasish Das, David SaintillanAbstract:The Deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of \cite{taylor1966}, there have been numerous computational and theoretical studies to predict the Deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel Small-Deformation theory accurate to second order in electric capillary number ${O}(Ca_E^2)$ for the complete Melcher-Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape Deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the Deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary-element formulation and with existing experimental data in the Small-Deformation regime.
Debasish Das - One of the best experts on this subject based on the ideXlab platform.
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A three-dimensional Small-Deformation theory for electrohydrodynamics of dielectric drops
Journal of Fluid Mechanics, 2021Co-Authors: Debasish Das, David SaintillanAbstract:Electrohydrodynamics of drops is a classic fluid mechanical problem where Deformations and microscale flows are generated by application of an external electric field. In weak fields, electric stresses acting on the drop surface drive quadrupolar flows inside and outside and cause the drop to adopt a steady axisymmetric shape. This phenomenon is best explained by the leaky-dielectric model under the premise that a net surface charge is present at the interface while the bulk fluids are electroneutral. In the case of dielectric drops, increasing the electric field beyond a critical value can cause the drop to start rotating spontaneously and assume a steady tilted shape. This symmetry-breaking phenomenon, called Quincke rotation, arises due to the action of the interfacial electric torque countering the viscous torque on the drop, giving rise to steady rotation in sufficiently strong fields. Here, we present a Small-Deformation theory for the electrohydrodynamics of dielectric drops for the complete Melcher–Taylor leaky-dielectric model in three dimensions. Our theory is valid in the limits of strong capillary forces and highly viscous drops and is able to capture the transition to Quincke rotation. A coupled set of nonlinear ordinary differential equations for the induced dipole moments and shape functions are derived whose solution matches well with experimental results in the appropriate Small-Deformation regime. Retention of both the straining and rotational components of the flow in the governing equation for charge transport enables us to perform a linear stability analysis and derive a criterion for the applied electric field strength that must be overcome for the onset of Quincke rotation of a viscous drop.
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A nonlinear Small-Deformation theory for transient droplet electrohydrodynamics
Journal of Fluid Mechanics, 2016Co-Authors: Debasish Das, David SaintillanAbstract:The Deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher–Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of Taylor (Proc. R. Soc. Lond. A, vol. 291, 1966, pp. 159–166), there have been numerous computational and theoretical studies to predict the Deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel Small-Deformation theory accurate to second order in electric capillary number for the complete Melcher–Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape Deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the Deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary element formulation and with existing experimental data in the Small-Deformation regime.
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a nonlinear Small Deformation theory for transient droplet electrohydrodynamics
arXiv: Fluid Dynamics, 2016Co-Authors: Debasish Das, David SaintillanAbstract:The Deformation of a viscous liquid droplet suspended in another liquid and subject to an applied electric field is a classic multiphase flow problem best described by the Melcher-Taylor leaky dielectric model. The main assumption of the model is that any net charge in the system is concentrated on the interface between the two liquids as a result of the jump in Ohmic currents from the bulk. Upon application of the field, the drop can either attain a steady prolate or oblate shape with toroidal circulating flows both inside and outside arising from tangential stresses on the interface due to action of the field on the surface charge distribution. Since the pioneering work of \cite{taylor1966}, there have been numerous computational and theoretical studies to predict the Deformations measured in experiments. Most existing theoretical models, however, have either neglected transient charge relaxation or nonlinear charge convection by the interfacial flow. In this work, we develop a novel Small-Deformation theory accurate to second order in electric capillary number ${O}(Ca_E^2)$ for the complete Melcher-Taylor model that includes transient charge relaxation, charge convection by the flow, as well as transient shape Deformation. The main result of the paper is the derivation of coupled evolution equations for the induced electric multipoles and for the shape functions describing the Deformations on the basis of spherical harmonics. Our results, which are consistent with previous models in the appropriate limits, show excellent agreement with fully nonlinear numerical simulations based on an axisymmetric boundary-element formulation and with existing experimental data in the Small-Deformation regime.
Pavel Horvath - One of the best experts on this subject based on the ideXlab platform.
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Full theory of speckle displacement and decorrelation in the image field by wave and geometrical descriptions and its application in mechanics
Journal of Modern Optics, 2004Co-Authors: Pavel Horvath, Miroslav Hrabovský, Petr ŠmídAbstract:The paper describes the possibility of using the speckle pattern decorrelation for determination of Small Deformation tensor components of an elementary object surface area in an optical image field. The relationship between the Small-Deformation tensor and the speckle field displacement is analysed in detail. The studied problem is presented from the approximation viewpoint of both wave and geometrical optics.
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Theory of speckle displacement and decorrelation with electronic correlation
Czechoslovak Journal of Physics, 2001Co-Authors: Miroslav Hrabovský, Zdenek Baca, Pavel HorvathAbstract:The paper deals with the determination of Small Deformation tensor components by means of an optical experimental method, which utilizes statistical properties of the speckle field in optically free space. The term “Deformation tensor” is introduced and the relationship between the Small Deformation tensor components and the cross-correlation function of two intensity speckle patterns in free-space is analyzed. Furthermore, experimental arrangements for measurement of rotation, Deformation, and translation, and their sensitivity and accuracy analyses are also presented.
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Theory of speckle displacement and decorrelation in free-space geometry
11th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics, 1999Co-Authors: Zdenek Baca, Miroslav Hrabovský, Pavel HorvathAbstract:This paper deals with a determination of so called Small Deformation tensor of the elementary area of an object surface by means of an optical experimental method, availing of statistical properties of the speckle field in an optically free space geometry. The Small Deformation tensor and a correlation function are briefly mentioned, and the main emphasis is aimed at the theoretical derivation of the relationship between the correlation function of two speckle intensities, being recorded before and after Deformation. This results in the relationship theoretically enabling a determination of all components of a Small Deformation tensor by means of a relatively simple optical arrangement in connection with computer and linear CCD detector.
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Theory of speckle displacement and decorrelation and its application in mechanics
Optics and Lasers in Engineering, 1999Co-Authors: Miroslav Hrabovský, Zdenek Baca, Pavel HorvathAbstract:Abstract The paper deals with the determination of tensor of the so-called Small Deformation of an elementary area of an object surface by means of an optical experimental method, which makes use of properties of the speckle field in an optically free space or in an image field. The term “Small Deformation tensor” is introduced and a relationship between a Small Deformation tensor of surface and a speckle field in free space or image field is analyzed.
Rochish M Thaokar - One of the best experts on this subject based on the ideXlab platform.
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Time-dependent electrohydrodynamics of a compressible viscoelastic capsule in the Small-Deformation limit.
Physical review. E, 2016Co-Authors: Rochish M ThaokarAbstract:A theoretical analysis of the time-dependent electrohydrodynamics of a viscoelastic compressible capsule, characterized by the two-dimensional Young's modulus and surface viscosity, is studied in the Small-Deformation limit. A systematic ac electrohydrodynamics analysis is conducted, and time-independent and time-periodic Deformations are related to the electric capillary number and the membrane properties. Additionally, the relaxation of a capsule stretched by a dc electric field is also presented. This necessitates an accurate estimation of the initial strain field in the stretched capsule. Both an oscillatory analysis and an analysis of the relaxation of a stretched capsule are presented for a capsule containing an aqueous phase, modeled as a perfect conductor, and suspended in a perfect dielectric with an infinitesimally thin viscoelastic membrane separating the two. The membrane is assumed to be a perfect dielectric with no electrical contrast with the suspending fluid.
