Flowing media in both industrial and natural processes are often characterized as assemblages of densely packed granular materials. Typically, the constitutive relations for the stress tensor and heat flux vector are fundamentally nonlinear. Moreover, these equations are coupled through the Clausius–Duhem inequality. However, the consequences of this coupling are rarely studied. Here we address...

We give a short survey of several results concerning mathematical analysis of models describing flows of incompressible rate type fluids. After recalling the system of governing equations, we first present the result of P.-L. Lions and N. Masmoudi [4] about global existence of solution to a special case of Oldroyd model. Then we present results of F.-H. Lin, C. Liu and P. Zhang [3] and Y. Chen ...

Deformation and strength behavior of geomaterials in the preand post-failure regimes are of significant interest in various geomechanics applications. To address the need for development of a realistic constitutive framework, which allows for an accurate simulation of pre-failure response as well as an objective and meaningful post-failure response, a strain gradient plasticity model is formula...

It is shown that expansion waves for the compressible Navier-Stokes equations are nonlinearly stable. The expansion waves are constructed for the compressible Euler equations based on the inviscid Burgers equation. Our result shows that Navier-Stokes equations and Euler equations are timeasymptotically equivalent on the level of expansion waves. The result is proved using the energy method, mak...

The Casimir attraction can significantly interfere the physical response of nanoactuators. The intensity of the Casimir force depends on the geometries of interacting bodies. The present paper is dedicated to model the influence of the Casimir attraction on the electrostatic stability of nanoactuators made of cylindrical conductive nanowire/nanotube. An asymptotic solution, based on path-integr...

By adopting the variational point of view, the constitutive equations of a non linear elastic plate are deduced under kinematical constraints on the admissible deformations.

Constitutive equations are derived for the time-dependent behavior of particlereinforced elastomers at isothermal loading with finite strains. A rubbery polymer is modelled as a network of macromolecules bridged by junctions which can slip with respect to the bulk material under straining. A filled elastomer is thought of as an ensemble of meso-regions where sliding occurs with different rates....

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 ...

A continuum theory is developed for a geophysical fluid consisting of two species. Balance laws are given for the individual components of the mixture, modeled as micropolar viscous fluids. The continua allow independent rotational degrees of freedom, so that the fluids can exhibit couple stresses and a non-symmetric stress tensor. The second law of thermodynamics is used to develop constitutiv...