Showing papers by "Kumbakonam R. Rajagopal published in 2022"
TL;DR: In this paper , the effects of the material moduli, the angle between the plane walls, and the inertial term on the velocity of the Jeffery-Hamel flow were analyzed.
Abstract: The flow between two divergent plane walls with a source at the vertex (Jeffery–Hamel flow) of a shear-thinning fluid, that mimics the response of a class of seemingly viscoplastic materials, is studied. The semi-inverse approach is used to obtain the governing equations for the velocity profile. The third-order non-linear ordinary differential equation governing the flow is solved numerically, and the effects of the material moduli that characterize the fluid, the angle between plane walls, and the inertial term, on the velocity are reported and discussed. Results show that there is a critical angle beyond which flow reversal occurs, and the number and angular extent of inflow regions varies based on the material moduli and the inertial term. • The Jeffery–Hamel flow of a shear-thinning fluid that mimics viscoplastic materials is studied. • Governing equations for the velocity profile are obtained using the semi-inverse approach and solved numerically. • Effects of the material moduli, the angle between the plane walls, and the inertial term on the velocity are analyzed. • Variation of material moduli led to the appearance of flow reversal regions whose number and angular extent changed. • Variation of angle showed a critical angle at which flow reversal takes place.
10 citations
TL;DR: In this paper , the pure bending of an elastic prismatic beam was investigated in the presence of density-dependent material parameters, and a semi-analytical solution to the boundary value problem was derived.
Abstract: We investigate the pure bending of an elastic prismatic beam, but unlike in the classical setting we assume that the material parameters are density-dependent. The corresponding boundary value problem admits a semi-analytical solution, and the derived formulae allow one to quickly assess the impact of density-dependent material parameters on the predicted deformation across various parameter regimes, and consequently make a decision on the importance of the density-dependent material parameters in the given setting.
6 citations
TL;DR: The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the "simple model" and Papanastasiou model as mentioned in this paper.
Abstract: The linear stability of channel flows driven by pressure drops is carried out for fluids that exhibit a yield stress, the mechanical response of which is prescribed by the Bingham constitutive relation or two of its regularizations: the model due to Allouche and co-workers that is usually referred to as the “simple model”, and Papanastasiou model. Despite the fact that these two regularized models provide a good approximation of the steady Poiseuille flow of a Bingham fluid, they fail to predict the stability characteristics of the exact Bingham model. The critical thresholds for the onset of turbulence predicted by using the simple and Papanastasiou models are essentially the same, but they differ significantly from that of the exact Bingham model. This discrepancy is shown to be due to the absence of energy dissipation in the rigid core of a Bingham fluid.
5 citations
TL;DR: It is shown how the material parameters derived from the uniaxial tests on circumferential and longitudinal specimens are insufficient to characterize the response of off-axis specimens.
4 citations
TL;DR: A review of the evolution of constitutive relations that have been developed to describe the response of arterial tissues, their inadequacies, and the various quintessential aspects of the response that need to be taken into consideration can be found in this article .
Abstract: Despite the tremendous impact that a good constitutive relation for the response of arterial tissues can have with regard to advances in cardiovascular science and medicine, and notwithstanding the intense effort to put a felicitous constitutive relation into place, no reliable constitutive relation is available in the literature. In this review article, we provide a brief survey and assessment of the evolution of constitutive relations that have been developed to describe the response of arterial tissues, their inadequacies, and the various quintessential aspects of the response that need to be taken into consideration. We then fashion a nonlinear constitutive relation to describe an inhomogeneous anisotropic compressible viscoelastic solid, which while being grossly inadequate to describe the tissue in its entirety, makes it evident that what one ought to strive for is not in capturing the complexity of tissues, but rather the development of a simple global measure that can be a reliable predictor of the onset of tissue disease, and tissue damage and failure.
4 citations
TL;DR: In this paper, an implicit constitutive relation between the stress and the left Cauchy-Green strain with the material moduli depending nonlinearly on the deformation gradient is developed.
3 citations
TL;DR: In this paper , the formation of vortices and other flow characteristics associated with the three-dimensional motions of an incompressible Navier-Stokes fluid in tubes containing a sinusoidal extension were investigated.
3 citations
TL;DR: In this article , the authors studied the stress and strain in a square plate containing an elliptic hole in the case of a porous elastic solid undergoing small strain, using a constitutive relation that has been put into place recently to describe the response of such solids undergoing small strains.
Abstract: We study the state of stress and strain in a square plate containing an elliptic hole in the case of a porous elastic solid undergoing small strain, using a constitutive relation that has been put into place recently to describe the response of such solids undergoing small strains. We carry out the study by solving the problem numerically. We verify that our numerical solutions agree with those for the classical linearized elastic solid when certain appropriate material parameters are set to zero. We show that the stress concentration factor in the case of the porous elastic solid can be much higher, as much as 300% of the stress concentration in the case of the classical linearized elastic solid, when the aspect ratio is sufficiently small, depending on the values of certain material parameters. The difference between the stress concentration for the porous solid increases as the aspect ratio (the ratio of the major axis to the minor axis) decreases. By allowing the aspect ratio of the ellipse to go to zero, we can obtain the state of stress and strain adjacent to a crack in the square plate; however, in this limit, the strains would greatly exceed the assumption under which the constitutive theory is derived.
3 citations
TL;DR: In this paper , a thermodynamically consistent model for thermo-chemo-mechanical processes in open systems comprised of nonlinear elastic solids that are infused with reactive fluids and are undergoing large local strains is presented.
3 citations
TL;DR: In this article , the authors explored the barriers to the entry of gig workers in gig platforms pertaining to the food delivery sector and proposed strategies to reduce the entry barriers in gig sector which would help to enhance productivity and generate employment opportunities.
Abstract: PurposeThe alternative arrangements to traditional employment have become a promising area in the gig economy with the technological advancements dominating every work. The purpose of this paper is to explore the barriers to the entry of gig workers in gig platforms pertaining to the food delivery sector. It proposes a framework using interpretive structural modelling (ISM) for which systematic literature review is done to extract the variables. This analysis helps to examine the relationship between the entry barriers to gig platforms. The study further proposes strategies to reduce the entry barriers in gig sector which would help to enhance productivity and generate employment opportunities.Design/methodology/approachThe study uses interpretive structural model (ISM) to ascertain the relationship between various entry barriers of the gig workers to the gig platforms. It also validates the relationship and understand the reasons of their association along with MICMAC analysis. The model was designed by consulting the gig workers and the experts allied to food delivery gig platforms namely Zomato and Swiggy.FindingsIt was observed that high competition, longer login hours and late-night deliveries are the significant barriers with high driving power and low dependence power. Poor payment structures and strict terms and conditions for receiving the incentives are interdependent on each other and have moderate driving and dependence power. The expenses borne by the gig workers, such as Internet, fuel and vehicle maintenance expenses have high dependence power and low driving power. Hence, they are relatively less significant than other barriers.Research limitations/implicationsThe study is confined to food delivery sector of India, without considering other important sectors of gig economy for generalizing the framework. As the study is based on forming an ISM framework through literature review only, it does not consider other research methods for analysing the entry barriers to the gig platforms.Practical implicationsThe study attempts to dig out the low entry barriers for gig workers in food delivery platforms as there is a dearth of analysis of these factors. This study would weave them using ISM framework to help the gig platforms overcome these barriers at various levels, thus adding to the body of literature.Originality/valueThe study discusses the need for understanding relationship between the entry barriers in the form of ISM model to identify the dependent and driving factors of the same.
2 citations
TL;DR: In this paper , it was shown that the dynamic equations describing quasistatic motion of an Eulerian strut, an infinite dimensional dynamical system, are globally well-posed.
Abstract: We formulate and consider the problem of an inextensible, unshearable, viscoelastic rod, with evolving natural configuration, moving on a plane. We prove that the dynamic equations describing quasistatic motion of an Eulerian strut, an infinite dimensional dynamical system, are globally well-posed. For every value of the terminal thrust, these equations contain a smooth embedded curve of static solutions (equilibrium points). We characterize the spectrum of the linearized equations about an arbitrary equilibrium point, and using this information and a convergence result for dynamical systems due to Brunovský and Polácik, we prove that every solution to the quasistatic equations of motion converges to an equilibrium point as time goes to infinity.
TL;DR: The intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the components of the contact force and contact couple are introduced, describing a uniform, hyperelastic, strain-limiting special Cosserat rod.
Abstract: . Motivated by recent strain-limiting models for solids and biological fibers, we introduce the first intrinsic set of nonlinear constitutive relations, between the geometrically exact strains and the components of the contact force and contact couple, describing a uniform, hyperelastic, strain-limiting special Cosserat rod. After discussing some attractive features of the constitutive relations (orientation preservation, transverse symmetry, and monotonic- ity), we exhibit several explicit equilibrium states under either an isolated end thrust or an isolated end couple. In particular, certain equilibrium states ex- hibit Poynting like effects, and we show that under mild assumptions on the material parameters, the model predicts an explicit tensile shearing bifurca- tion : a straight rod under a large enough tensile end thrust parallel to its center line can shear.
TL;DR: In this article, the authors study a start-up shear flow of a recently proposed model of a shear-thinning fluid that mimics the response of a class of viscoplastic materials.
TL;DR: In this article , the authors investigate the flow of a stress power-law fluid in an orthogonal rheometer and solve the corresponding nonlinear problem numerically via collocation method.
Abstract: The orthogonal rheometer, an instrument developed by Maxwell and Chartoff (1965) that has been used to measure the properties of non-Newtonian fluids, is essentially two parallel disks rotating about non-coincident axes with the same angular speed. By measuring the forces due to the flow of the fluid, and corroborating the constitutive relation with the same, one can determine the material moduli that characterize the fluid. In this paper, we discuss the flow of a novel constitutive relation that has been developed to describe the response of colloids. We find that pronounced boundary layers adjacent to the rotating plates can develop even at moderate Reynolds. These boundary layers are not necessarily restricted to inertial boundary layers. The flow patterns are also markedly different from those for the classical Navier–Stokes or power-law fluids. • We investigate the flow of a Stress Power-Law fluid in an orthogonal rheometer. • We write the governing equations and we look for a pseudo-planar solution. • We solve the corresponding nonlinear problem numerically via collocation method. • We perform numerical simulations to investigate the flow patterns. • We discuss the formation of boundary layers due to the shear-thinning (or shear thickening) nature of the fluid.
DOI•
26 Feb 2022
TL;DR: In this article , the authors derived constitutive relations for the response of elastic solids, which are transversely isotropic and those that have two preferred directions of symmetry wherein the material moduli of the body depend on its density, undergoing small deformations.
Abstract: In this short note we derive constitutive relations for the response of elastic solids, which are transversely isotropic and those that have two preferred directions of symmetry wherein the material moduli of the body depend on its density, undergoing small deformations. Such constitutive relations have relevance to the response of rocks, concrete, ceramics, bones, and porous metals. The constitutive relations that we develop reduce appropriately to the classical linearized elastic constitutive relation, when appropriate material moduli are set to zero. The new constitutive relations, when restricted to those that are linear in both the stress and the linearized strain, have terms in addition to those for a classical linearized elastic body, and it would be interesting to investigate the consequence of these additional terms with regard to the response of the body.
TL;DR: In this article , the authors studied the mechanical behavior of a slightly compressible neo-Hookean fiber, which is subjected to an axial pullout displacement, embedded in a slightly compressed generalized neo-hookean matrix, and found an interesting result that the maximum shear stress occurs in the interior of the matrix when the shear modulus of the fiber is comparable to the matrix.
Abstract: In this paper, we study the mechanical behavior of a slightly compressible neo-Hookean fiber, which is subjected to an axial pullout displacement, embedded in a slightly compressible generalized neo-Hookean matrix. We study three different boundary value problems containing both fully and partially embedded fibers. We study the effect of material and geometric parameters on the force required to axially displace the fiber, the shear stress at the interface and in the interior of the fiber–matrix system, and the norm of the Green–St. Venant strain. We found an interesting result in that the maximum shear stress occurs in the interior of the matrix when the shear modulus of the fiber is comparable to that of the matrix. Furthermore, as the fiber and matrix becomes more compressible, the maximum shear stress decreases.
TL;DR: In this article , the authors studied the stress concentration around a circular rigid inclusion in an incompressible anisotropic homogeneous nonlinearly elastic thin sheet subjected to in-plane finite deformation uniaxial extension.
Abstract: In this paper, we study the stress concentration around a circular rigid inclusion in an incompressible anisotropic homogeneous nonlinearly elastic thin sheet subjected to in-plane finite deformation uniaxial extension. Two classes of material symmetry are considered: transverse isotropy and orthotropy. For the case of transverse isotropy, a three-parameter constitutive relation that under infinitesimal deformations reduces appropriately to the classical incompressible linearized elastic transversely isotropic constitutive relation is studied. Similarly, a six-parameter constitutive relation is considered for the case of orthotropic material symmetry. These constitutive relations may be suitable to describe the response of transversely isotropic and orthotropic bodies subjected to moderate deformations.
TL;DR: In this paper , the authors describe the logarithmic convexity argument for third order in time partial differential equations and prove a uniqueness result whenever certain conditions on the parameters are satisfied.
Abstract: In this short note, we want to describe the logarithmic convexity argument for third order in time partial differential equations. As a consequence, we first prove a uniqueness result whenever certain conditions on the parameters are satisfied. Later, we show the instability of the solutions if the initial energy is less or equal than zero.
04 Dec 2022-Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology
TL;DR: In this article , a lower-dimensional model for thin-film flow of fluids with pressure-dependent viscosity was presented, where the authors also incorporated the energy equation and derived a simplified model of the flow.
Abstract: This paper constitutes the third part of a series of works on lower-dimensional models in lubrication. In Part A, it was shown that implicit constitutive theory must be used in the modelling of incompressible fluids with pressure-dependent viscosity and that it is not possible to obtain a lower-dimensional model for the pressure just by letting the film thickness go to zero, as in the proof of the classical Reynolds equation. In Part B, a new method for deriving lower-dimensional models of thin-film flow of fluids with pressure-dependent viscosity was presented. Here, in Part C, we also incorporate the energy equation so as to include fluids with both temperature and pressure dependent viscosity. By asymptotic analysis of this system, as the film thickness goes to zero, we derive a simplified model of the flow. We also carry out an asymptotic analysis of the boundary condition, in the case where the normal stress is specified on one part of the boundary and the velocity on the remaining part.