Showing papers by "Kumbakonam R. Rajagopal published in 2017"
TL;DR: The concept of a non-smooth viscosity solution is introduced which is described by generalized variational inequalities and coincides with the weak solution in the smooth case and is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.
Abstract: A major drawback of the study of cracks within the context of the linearized theory of elasticity is the inconsistency that one obtains with regard to the strain at a crack tip, namely it becoming infinite. In this paper we consider the problem within the context of an elastic body that exhibits limiting small strain wherein we are not faced with such an inconsistency. We introduce the concept of a non-smooth viscosity solution which is described by generalized variational inequalities and coincides with the weak solution in the smooth case. The well-posedness is proved by the construction of an approximation problem using elliptic regularization and penalization techniques.
38 citations
TL;DR: In this article, the authors propose a non-linear constitutive relation between the linearized strain and the stress that can be properly justified to describe the response of such alloys.
31 citations
TL;DR: A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed in this article.
Abstract: A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed. Using this methodology, a general constitutive representation for a subclass of implicit models relating the Cauchy stress and the Hencky strain is obtained for an isotropic material with no internal constraints. It is shown that even for this subclass, unlike classical Green elasticity, one has to specify three potentials to relate the Cauchy stress and the Hencky strain. Then, a procedure to obtain implicit constitutive representations for isotropic materials with internal constraints is presented. As an illustration, it is shown that for incompressible materials the Cauchy stress and the Hencky strain could be related through a single potential. Finally, constitutive approximations are obtained when the displacement gradient is small.
25 citations
TL;DR: In this paper, a power-law relationship was proposed to describe the uniaxial response of several metallic alloys, and the model that is being considered fits experimental data exceedingly well.
Abstract: Many titanium alloys and even materials such as concrete exhibit a nonlinear relationship between strain and stress, when the strain is small enough that the square of the norm of the displacement gradient can be ignored in comparison to the norm of the displacement gradient. Such response cannot be described within the classical theory of Cauchy elasticity wherein a linearization of the nonlinear strain leads to the classical linearized elastic response. A new framework for elasticity has been put into place in which one can justify rigorously a nonlinear relationship between the linearized strain and stress. Here, we consider one such model based on a power-law relationship. Previous attempts at describing such response have been either limited to the response of one particular material, e.g. Gum Metal, or involved a model with more material moduli, than the model considered in this work. For the uniaxial response of several metallic alloys, the model that is being considered fits experimental data exceedingly well.
22 citations
TL;DR: In this paper, the development of a method for the determination of the material properties of rubber and rubber-like materials within the context of a novel constitutive framework was discussed, and the method was applied to a novel class of rubber materials.
Abstract: We discuss the development of a method for the determination of the material properties of rubber and rubberlike materials within the context of a novel constitutive framework that has bee...
22 citations
TL;DR: An overview of the developments in modelling of blood rheology and clot formation/lysis in the last 10 to 15 years is given.
Abstract: Several advances have taken place since the early 2000s in the field of blood flow modelling. These advances have been driven by the development of assist devices such as Left Ventricular Assist Devices (LVADs), etc., and by the acceptance of in silico tests for the generation of hypotheses concerning clot formation and lysis. We give an overview of the developments in modelling of blood rheology and clot formation/lysis in the last 10 to 15 years. In blood rheology, advances are increasingly supplemented by flow simulation studies. In clot formation (or coagulation), advances have taken place in both single-scale modeling under quiescent conditions as well as in multi-scale modeling in the presence of flow. The future will possibly see more blood flow simulations in complex geometries and, simultaneously, development and simulation of multi-scale models for clot formation and lysis.
19 citations
TL;DR: In this article, the authors developed a rigorous mathematical approach for deriving a pressure field from experimental data for a velocity field that can be obtained by direct measurement, and computed dissipation, kinetic energy and pressure are then presented in an idealized geometry, but relevant to a realistic geometry, with a symmetric stenosis.
15 citations
TL;DR: In this article, a generalization of the incompressible Oldroyd-B model based on a thermodynamic framework is presented, where the response of the fluid is viewed as a combination of an elastic component and a dissipative component.
Abstract: Summary
This paper presents a generalization of the incompressible Oldroyd-B model based on a thermodynamic framework within which the fluid can be viewed to exist in multiple natural configurations. The response of the fluid is viewed as a combination of an elastic component and a dissipative component. The dissipative component leads to the evolution of the underlying natural configurations, while the response from the natural configuration to the current configuration is considered elastic and therefore non-dissipative. For an incompressible fluid, it is necessary that both the elastic behavior as well as the dissipative behavior is isochoric. This is achieved by ensuring that the determinant of the stretch tensor associated with the elastic response meets the constraint that its determinant is unity.
A new stabilized mixed method is developed for the velocity, pressure and the kinematic tensor fields. Analytical models for fine scale fields are derived via the solution of the fine-scale equations facilitated by the Variational Multiscale framework that are then variationally embedded in the coarse-scale variational equations. The resulting method inherits the attributes of the classical SUPG and GLS methods, while a significant new contribution is that the form of the stabilization tensors is explicitly derived. A family of linear and quadratic tetrahedral and hexahedral elements is developed with equal-order interpolations for the various fields. Numerical tests are presented that validate the incompressibility of the elastic stretch tensor, show optimal L2 convergence for the conformation tensor field, and present stable response for high Weissenberg number flows. Copyright © 2016 John Wiley & Sons, Ltd.
14 citations
TL;DR: In this article, the authors generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature.
Abstract: In this paper we generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play. The implicit constitutive relations for thermoelastic response presented here provide a very natural way to overcome a serious problem associated with the celebrated model due to Fourier, namely infinite speed of the propagation of temperature. We also study some boundary value problems within the context of the implicit equations that we have developed. We carry out a linearization based on the classical assumption that the displacement gradient is small and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature.
14 citations
TL;DR: In this article, the authors model the mechanical behavior of light-activated shape memory polymers with a view toward determining the effect of the viscoelasticity of the polymers in terms of their shape.
Abstract: In this article, we model the mechanical behavior of light-activated shape memory polymers with a view toward determining the effect of the viscoelasticity of the polymers with regard to their shap...
13 citations
TL;DR: In this paper, the macroscopic response of light-activated shape memory polymers (LASMPs) subject to mechanical loadings and exposure to light at certain wavelengths and frequenc...
Abstract: The aim of this paper is to model the macroscopic response of light-activated shape memory polymers (LASMPs) subject to mechanical loadings and exposure to light at certain wavelengths and frequenc...
TL;DR: In this paper, a study of the temperature dependence of the mechanical behavior of asphalt binders was conducted, and the results were used to characterise the binders using a nonlinear viscoelastic model.
Abstract: This is a study of the temperature dependence of the mechanical behaviour of asphalt binders. Creep-recovery and steady-shear experiments were conducted on selected modified and unmodified binders at 60, 70 and 80 C, and the results were used to characterise the binders using a nonlinear viscoelastic model. Experimental and model parameters obtained in this manner were all found to follow Arrhenius relationship with temperature. Rutting parameters such as zero shear viscosity, non-recoverable creep compliance, Superpave criterion and apparent viscosity were predicted using the model, and were also found to follow an Arrhenius relationship with temperature. However, it was found that the temperature sensitivity of the binders can vary considerably. Issues with ‘failure temperature’-based grading systems, such as the Superpave high temperature specification, were analysed in the light of the Arrhenius-like temperature dependence and varying temperature sensitivities. Possible ways to consider varying temper...
TL;DR: In this article, all wave patterns for non-classic nonlinearly elastic materials under Riemann data are established completely by separating the phase plane into twelve disjoint regions and by using a nonnegative dissipation rate assumption and the maximally dissipative kinetics at any stress discontinuity.
Abstract: Recently there has been interest in studying a new class of elastic materials, which is described by implicit constitutive relations. Under some basic assumption for elasticity constants, the system of governing equations of motion for this elastic material is strictly hyperbolic but without the convexity property. In this paper, all wave patterns for the nonclassic nonlinearly elastic materials under Riemann data are established completely by separating the phase plane into twelve disjoint regions and by using a nonnegative dissipation rate assumption and the maximally dissipative kinetics at any stress discontinuity. Depending on the initial data, a variety of wave patterns can arise, and in particular there exist composite waves composed of a rarefaction wave and a shock wave. The solutions for a physically realizable case are presented in detail, which may be used to test whether the material belongs to the class of classical elastic bodies or the one wherein the stretch is expressed as a function of the stress.
TL;DR: In this paper, the authors studied the state of stress and strain close to sharp cracks in elastic solids subjected to an antiplane states of stress, and proposed a non-monotonic strain-stress relation within the context of a generalization of the Cauchy theory of elasticity.
TL;DR: In this article, an extension to a thermodynamically consistent finite deformation, fully three dimensional approach based on a two-network theory is presented. But the authors focus on the attenuation of blast by different layered polymeric structures in a fully 3D setting.
TL;DR: In this article, the authors provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing, and show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter.
Abstract: We provide numerical simulations of an incompressible pressure-thickening and shear-thinning lubricant flowing in a plane slider bearing. We study the influence of several parameters, namely the ratio of the characteristic lengths $\varepsilon>0$ (with $\varepsilon\searrow0$ representing the Reynolds lubrication approximation); the coefficient of the exponential pressure--viscosity relation $\alpha^*\geq0$; the parameter $G^*\geq0$ related to the Carreau--Yasuda shear-thinning model and the modified Reynolds number $\mathrm{Re}_\varepsilon\geq0$. The finite element approximations to the steady isothermal flows are computed without resorting to the lubrication approximation. We obtain the numerical solutions as long as the variation of the viscous stress $\mathbf{S}=2\eta(p,\mathrm{tr}\mathbf{D}^2)\mathbf{D}$ with the pressure is limited, say $|\partial\mathbf{S}/\partial p|\leq1$. We show conclusively that the existing practice of avoiding the numerical difficulties by cutting the viscosity off for large pressures leads to results that depend sorely on the artificial cut-off parameter. We observe that the piezoviscous rheology generates pressure differences across the fluid film.
TL;DR: In this paper, two boundary value problems within the context of the above model, namely the stress relaxation of a right circular annular cylinder subject to twisting, and the inflation of a sphere are studied.
Abstract: Recently, a thermodynamically consistent non-linear constitutive equation has been developed to describe the large deformation cyclic response of viscoelastic polyamides (see [ 17 ]). In this paper, two boundary value problems within the context of the above model, namely the stress relaxation of a right circular annular cylinder subject to twisting, and the inflation of a sphere are studied. In addition to solving the above problems numerically, investigation of the merits and pitfalls of studying the same boundary value problem for a special class of inhomogeneous body and its homogenized counterpart is undertaken. This study finds that for moderate strains the differences in relaxation time between the actual inhomogeneous body and its homogenized counterparts may be significant.