arXiv subjects

Satish Karra

Publications and source records attributed to Satish Karra.

21 records · Page 2Linked to original sources

arXiv2010

A thermodynamic framework to develop rate-type models for fluids without instantaneous elasticity

In this paper, we apply the thermodynamic framework recently put into place by Rajagopal and co-workers, to develop rate-type models for viscoelastic fluids which do not possess instantaneous elasticity. To illustrate the capabilities of such models we make a specific choice for the specific Helmholtz potential and the rate of dissipation and consider the creep and stress relaxation response associated with the model. Given specific forms for the Helmholtz potential and the rate of dissipation, the rate of dissipation is maximized with the constraint that the difference between the stress power and the rate of change of Helmholtz potential is equal to the rate of dissipation and any other constraint that may be applicable such as incompressibility. We show that the model that is developed exhibits fluid-like characteristics and is incapable of instantaneous elastic response. It also includes Maxwell-like and Kelvin-Voigt-like viscoelastic materials (when certain material moduli take special values).

math.NA↗

arXiv2010

Development of three dimensional constitutive theories based on lower dimensional experimental data

Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate of entropy production, etc. In this paper we show different choices for the manner in which the body stores energy and dissipates energy and satisfies the requirement of maximization of the rate of entropy production that leads to many three dimensional models. All of these models, in one dimension, reduce to the model proposed by Burgers to describe the viscoelastic behavior of bodies.

math.NA↗

arXiv2010

Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid

The mechanical response and load bearing capacity of high performance polymer composites changes due to diffusion of a fluid, temperature, oxidation or the extent of the deformation. Hence, there is a need to study the response of bodies under such degradation mechanisms. In this paper, we study the effect of degradation and healing due to the diffusion of a fluid on the response of a solid which prior to the diffusion can be described by the generalized neo-Hookean model. We show that a generalized neo-Hookean solid - which behaves like an elastic body (i.e., it does not produce entropy) within a purely mechanical context - creeps and stress relaxes when infused with a fluid and behaves like a body whose material properties are time dependent. We specifically investigate the torsion of a generalized neo-Hookean circular cylindrical annulus infused with a fluid. The equations of equilibrium for a generalized neo-Hookean solid are solved together with the convection-diffusion equation for the fluid concentration. Different boundary conditions for the fluid concentration are also considered. We also solve the problem for the case when the diffusivity of the fluid depends on the deformation of the generalized neo-Hookean solid.

physics.class-ph↗