Showing papers by "Kumbakonam R. Rajagopal published in 1996"

On the oberbeck-boussinesq approximation

Abstract: This paper deals with a derivation (using a perturbation technique) of an approximation, due to Oberbeck8,9 and Boussinesq,1 to describe the thermal response of linearly viscous fluids that are mechanically incompressible but thermally compressible. The present approach uses a nondimensionalization suggested by Chandrasekhar2 and utilizing the ratio of two characteristic velocities as a measure of smallness, systematically derives the Oberbeck-Boussinesq approximation as a third-order perturbation. In the present approach, the material is subjected to the constraint that the volume change is determined solely by the temperature change in the body and uses a novel approach in deriving the thermodynamical restrictions. Consequently, it is free from the additional assumptions usually added on in earlier works in order to obtain the correct equations.

A Single Integral Finite Strain Viscoelastic Model of Ligaments and Tendons

Abstract: A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

Chemorheological Relaxation, Residual Stress, and Permanent Set Arising in Radial Deformation of Elastomeric Hollow Spheres

Abstract: Recently, a constitutive theory for rubber-like materials has been developed by which stress arises from different micromechanisms at different levels of deformation. For small deformations, the stress is given by the usual theory of rubber elasticity. As the deformation increases, there is scission of some junctions of the macromolecular microstructure. Junctions then reform to generate a new microstructure. The constitutive equation allows for continuous scission of the original junctions and formation of new ones as deformation increases. The macromolecular scission causes stress reduction, termed chemorheological relaxation. The new macromolecular structure results in permanent set on release of external load.The present work considers a hollow sphere composed of such a material, also assumed to be incom-pressible and isotropic, which undergoes axisymmetric deformation under radial traction. There develops an outer zone of material with the original microstructure and an inner zone of material having ...

On a Generalized Nonlinear K-∊ Model for Turbulence that Models Relaxation Effects

Abstract: In this paper, based on a similarity that exists between the constitutive relations for turbulent mean flow of a Newtonian fluid and that for the laminar flow of a non-Newtonian fluid, and making use of extended thermodynamics, we develop a generalized nonlinearK-ɛ model, whose approximate form includes the standardK-ɛ model and the nonlinearK-ɛ model of Speziale (1987) as special cases. Our nonlinearK-ɛ model, which is frame indifferent, can predict relaxation of the Reynolds stress, unlike most standardK-ɛ models. Also, our model is in keeping with that of Yakhotet al. (1992). Most interestingly, the linearized form of our model bears a striking resemblance to the model due to Yoshizawa and Nisizima (1993); however, it has been obtained from a totally different perspective.

Deformations of Nonlinear Elastic Solids in Unbounded Domains

Abstract: A boundary layer approximation for nonlinearly elastic solids is advocated, with the full nonlinear equations assumed to hold in a narrow region adjacent to a boundary, whereas in the rest of the domain the equations of linearized elasticity are supposed to hold.

Buoyancy-induced deformations in a compressible elastic solid

Abstract: Given a rectangular slab of a purely elastic material (neo-Hookean) with different temperatures imposed on the lateral surfaces, it is shown, within the context of a linearized theory, that the resulting deformation field is, under suitable boundary conditions, virtually identical to its fluid-mechanical counterpart given by a rectangular trench filled with a Newtonian liquid. A second, more general analogy between problems involving buoyancy induced deformations and the classical theory of thin plates is also presented.