Classical Constitutive equations like the Navier-Stokes model for fluids and the linearized elastic model for solids are explicit models in that they provide explicit expressions for the stress in terms of kinematical quantities. Similarly, the constitutive equation for a Simple Material is also an explicit equation for the stress in terms of the histories of the deformation gradient and the de...

We study the global existence of solutions of initial-boundary-value problems for a quasilinear hyperbolic-parabolic equation describing the longitudinal motion of a one-dimensional viscoelastic rod. We treat a variety of nonhomogeneous boundary conditions, requiring separate analyses, because they lead to distinctive physical eeects. We employ a constitutive equation giving the stress as a gen...

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive eq...

Constitutive equations for electrorheological (ER) fluids have been based on experimental results for steady shearing flows and constant electric fields. The fluids have been modeled as being rigid until a yield stress is reached. Additional stress is then proportional to the shear rate. Recent experimental results indicate that ER materials have a regime of solid-like response when deformed fr...

Rubbery materials can undergo deformation induced microstructural changes leading to softening of response and permanent set. In this work, these materials are modeled by a constitutive equation that incorporates the following micromechanism : when the deformation becomes large enough, network junctions break during further increments of deformation and then heal. New networks are formed by thi...

In previous work it was shown that a class of axisymmetric viscoelastic membrane problems can be reduced to the numerical solution of a system of partial differential-Volterra integral equations. This general method has the disadvantage that a change in constitutive equation requires rederivation of specific details of the governing system. In this paper, a revised method is presented in which ...

In this article we analyse a fully discrete approximation to the time dependent viscoelasticity equations allowing for multicomponent fluid flow. The Oldroyd B constitutive equation is used to model the viscoelastic stress. For the discretization, time derivatives are replaced by backward difference quotients, and the non-linear terms are linearized by lagging appropriate factors. The modeling ...