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Showing papers by "Kumbakonam R. Rajagopal published in 2019"


Journal ArticleDOI
TL;DR: This expository review differs from others in providing a review of underlying methodologies for design of AVFS and the impact ofAVFS on traffic mobility and safety.
Abstract: There has been considerable interest recently in the development of connected and autonomous vehicles (CAVs). Automatic vehicle following capability is central for CAVs; in this article, we provide a review of the critical issues in the longitudinal control design for automatic vehicle following systems (AVFS) employed by CAVs. This expository review differs from others in providing a review of underlying methodologies for design of AVFS and the impact of AVFS on traffic mobility and safety.

27 citations


Journal ArticleDOI
TL;DR: In this paper, the deformation of a body with a smoothened V-notch subject to an anti-plane state of stress was studied in the context of a new class of elastic models.
Abstract: In this paper we study the deformation of a body with a notch subject to an anti-plane state of stress within the context of a new class of elastic models. These models stem as approximations of constitutive response functions for an elastic body that is defined within the context of an implicit constitutive relation between the stress and the deformation gradient. Gum metal and many metallic alloys are described well by such constitutive relations. We consider the state of anti-plane stress of a body with a smoothened V-notch within the context of constitutive relations for the linearized strain in terms of a power-law for the stretch. The problem is solved numerically and the convergence and the stability of the solution is studied.

17 citations


Journal ArticleDOI
TL;DR: In this paper, a thermodynamic framework for describing the mechanical response of viscoelastic polymers undergoing microstructural changes within the framework of a body possessing multiple natural configurations is presented.

16 citations


Journal ArticleDOI
TL;DR: In this article, a quasi-linear viscoelastic relation that stems from an implicit visco-elastic constitutive body containing a crack is considered and the abstract form of the response function is given first in Lp, p, p...
Abstract: A quasi-linear viscoelastic relation that stems from an implicit viscoelastic constitutive body containing a crack is considered. The abstract form of the response function is given first in Lp, p ...

16 citations


Journal ArticleDOI
TL;DR: In this paper, the kinematics of an inelastic solid established in terms of Laplace stretch and its rate were decomposed into one stretch that described an elastic response, another stretch that describes an in-elastic response, and their rates.
Abstract: The kinematics of an inelastic solid established in terms of Laplace stretch and its rate are decomposed into one stretch that describes an elastic response, another stretch that describes an inelastic response, and their rates. These kinematics are a direct consequence of Laplace stretch belonging to the group of all real, $$3 \times 3$$ , upper-triangular matrices with positive diagonal elements. The Laplace stretch follows from a Gram–Schmidt decomposition of the deformation gradient.

16 citations


Journal ArticleDOI
TL;DR: In this paper, various disparate restrictions are assumed with regard to bodies undergoing thermodynamic processes, in addition to the second law, to cull the class of constitutive relations for describing their response.

14 citations


Journal ArticleDOI
TL;DR: The well-posedness of the problem of non-penetrating crack in an elastic body whose material moduli depends on the mean normal stress is studied in this article, where the type of models considered are based on a new implicit theory for the response of elastic bodies.

11 citations


Journal ArticleDOI
18 Feb 2019-Fluids
TL;DR: In this paper, the authors derived the constitutive response of this class of fluids using a thermodynamic framework put into place to describe the dissipative response of materials where the materials' stored energy depends on the gradient of the density.
Abstract: In this paper, we study the pressure-driven thin film flow of an inhomogeneous incompressible fluid in which its viscosity depends on the density. The constitutive response of this class of fluids can be derived using a thermodynamical framework put into place to describe the dissipative response of materials where the materials’ stored energy depends on the gradient of the density (Mechanics of Materials, 2006, 38, pp. 233–242). Assuming a small aspect ratio for the channel, we use the lubrication approximation and focus on the leading order problem. We show the mathematical problem reduce to a nonlinear first order partial differential equation (PDE) for the density in which the coefficients are integral operators. The problem is solved numerically and plots that describe the evolution of the density in the fluid domain are displayed. We also show that it was possible to determine an analytical solution of the problem when the boundary data are small perturbations of the homogeneous case. Finally, we use such an analytical solution to validate the numerical scheme.

9 citations


Journal ArticleDOI
TL;DR: The mechanical behavior of asphalt binder is highly sensitive to temperature, and the manner in which mechanical characteristics change with temperature can also vary significantly from one asp... as mentioned in this paper,.
Abstract: The mechanical behavior of asphalt binder is highly sensitive to temperature. The manner in which mechanical characteristics change with temperature can also vary significantly from one asp...

8 citations


Journal ArticleDOI
TL;DR: The flow of a fluid obeying a constitutive relation of the symmetric part of the velocity gradient in a tube of elliptic and other non-circular cross-sections is considered with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube.
Abstract: Fluids described by constitutive relations wherein the symmetric part of the velocity gradient is a function of the stress can be used to describe the flows of colloids and suspensions. In this paper, we consider the flow of a fluid obeying such a constitutive relation in a tube of elliptic and other non-circular cross-sections with the view towards determining the velocity field and the stresses that are generated at the boundary of the tube. As tubes are rarely perfectly circular, it is worthwhile to study the structure of the velocity field and the stresses in tubes of non-circular cross-section. After first proving that purely axial flows are possible, that is, there are no secondary flows as in the case of many viscoelastic fluids, we determine the velocity profile and the shear stresses at the boundaries. We find that the maximum shear stress is attained at the co-vertex of the ellipse. In general tubes of non-circular cross-section, the maximum shear stress occurs at the point on the boundary that is closest to the centroid of the cross-section. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and applied mathematics'.

4 citations


Journal ArticleDOI
TL;DR: The test method of ASTM C512 (ASTM. 2015) is described in this paper, which is the standard test method for creep of concrete in compression, and the use of a spring-loaded creep...
Abstract: The test method of ASTM C512 (ASTM. 2015. Standard test method for creep of concrete in compression. ASTM C512/C512M. West Conshohocken, PA: ASTM) dictates the use of a spring-loaded creep ...

Journal ArticleDOI
28 May 2019-Fluids
Abstract: We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing.


Journal ArticleDOI
TL;DR: In this article, the authors studied the motion of a finite composite cylindrical annulus made of generalized neo-Hookean solids that is subject to periodic shear loading on the inner boundary.
Abstract: In this paper we study the motion of a finite composite cylindrical annulus made of generalized neo-Hookean solids that is subject to periodic shear loading on the inner boundary. Such a problem has relevance to several problems of technological significance, for example blood vessels can be idealized as finite anisotropic composite cylinders. Here, we consider the annulus to be comprised of an isotropic material, namely a generalized neo-Hookean solid and study the effects of annular thickness on the stress distribution within the annulus. We solve the governing partial differential equations and examine the stress response for the strain hardening and strain softening cases of the generalized neo-Hookean model. We also solve the problem of the annular region being infinite in length, that reduces the problem to a partial differential equation in only time and one spatial dimension. When the thickness of the annulus is sufficiently large, the solutions to the problems exhibit very interesting boundary layer structure in that the norm of the strain has a large gradient in a narrow region adjacent to one of the boundaries, with the strain being relatively uniform outside the narrow region. We also find that beyond a distance of two times the annular wall thickness from the ends of the cylinder the solutions for the infinite length cylinder match solutions for the finite length cylinder implying that end effects are not felt in most of the length of a sufficiently long annulus.

01 Jun 2019
TL;DR: In this paper, the authors derived a governing equation for web tension in a span by employing a Neo-Hookean material model that is applicable for transport of web materials under both small and large strains.
Abstract: In this work, we derive a governing equation for web tension in a span by employing a Neo-Hookean material model that is applicable for transport of web materials under both small and large strains. This governing equation may be employed to study the evolution of tension within a span as well as propagation of tension variations from span to span as the web is transported in the machine. First, we find the stretch in a web span and relate it to web tension via a Neo-Hookean material model; the Neo-Hookean model is linear for small strain and nonlinear otherwise. Second, we conduct a dimensional analysis by defining several key coefficients that aid in grouping the machine and web material parameters separately in order to obtain a compact system of governing equations; this representation may be utilized to efficiently study the impact of web and roller properties on transport behavior.

Proceedings ArticleDOI
24 Jul 2019
TL;DR: In this paper, the deformation of a nonlinearly elastic wedge in the case of a stored energy function that is given by a power law is considered and numerical solutions that are not unidirectional, in that the displacement is towards the apex in certain regions of the wedge and away from the vertex in other regions, are obtained.
Abstract: We consider the deformation of a nonlinearly elastic wedge in the case of a stored energy function that is given by a power law. Numerical solutions that are not unidirectional, in that the displacement is towards the apex in certain regions of the wedge and away from the apex in other regions, are obtained. Boundary conditions describing the extension or contracting of the planes are considered, and also traction boundary conditions.