In this article, we develop a new implicit constitutive relation, which is based on thermodynamic foundation that relates the Hencky strain to Cauchy stress, by assuming structure for Gibbs potential stress. We study tension/compression of cylinder, biaxial stretching thin plate and simple shear within context our relation. then compare predictions relation Ogden’s with experiments Treloar conc...

in this study we consider pcf (plane couette flow) which is introduced by two parallel planes which have same velocity in opposite direction and the distance between them is filled by viscoelastic fluid. by this way we have modeled viscoelastic damper. the constitutive equation of js (johnson-segalman) has been used for dynamic analysis of viscoelastic damper’s behavior. by using this equation ...

where T is the stress tensor, p the hydrostatic pressure, S the extra-stress tensor, A the first RivlinEricksen tensor and μ the dynamic viscosity. Many common fluids show this “Newtonian” behavior and in fact the whole discipline of classical fluid mechanics is based upon this equation. However, the constitutive equation (1) does not show any of the normal stress effects or relaxation phenomen...

The paper deals with a scalar diffusion equation c ut = (F [ux])x+f, where F is a Prandtl-Ishlinskii operator and c, f are given functions. In the diffusion or heat conduction equation the linear constitutive relation is replaced by a scalar Prandtl-Ishlinskii hysteresis spatially dependent operator. We prove existence, uniqueness and regularity of solution to the corresponding initial-boundary...

First order traffic flow models have been studied for long time, since they represent the simplest way to begin with the understanding of such a complex system. To our knowledge the Lighthill-Whitham-Richards (LWR) model was the first model to describe unidirectional, one-dimensional traffic flow in a highway [1], [2]. This model considers the continuity equation for the density of vehicles (nu...

In this paper, Forchheimer equation is used as the constitutive equation for flow through rockfill, and the non-linear two-dimensional governing equation with free surface is solved by a new finite element method in a fixed grid. The model is verified by applying it to different flow conditions. The first scenario, which is assumed to be one-dimensional with analytical solution available for it...