19 research outputs found
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.Comment: 24 pages, 10 figures, submitted to Mechanics of Time-dependent
Material
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).Comment: 18 pages, 5 figure
A three-dimensional non-linear constitutive law for magnetorheological fluids, with applications
In this paper we first summarize the magnetic and mechanical balance equations for magnetorheological fluids undergoing steady motion in the presence of a magnetic field. A general three-dimensional non-linear constitutive law for such a fluid is given for the case in which the magnetic induction vector is used as the independent magnetic variable. The equations are needed for the analysis of boundary-value problems involving fluids with dispersed micron-sized ferrous particles subjected to a time-independent magnetic field. For illustration, the equations are applied, in the case of an incompressible fluid, to the solution of some basic problems. We consider unidirectional flow in a region confined by two infinite parallel plates with a magnetic field applied perpendicular to the plates. Next, we examine two problems involving a circular cylindrical geometry with the fluid occupying the region between two concentric cylinders: axial flow subjected to an axial magnetic field and circumferential flow with a circumferential field. After making some simplifying assumptions on the constitutive law and choosing material parameters, numerical solutions for the velocity profiles are illustrated