A Viscoelastic Constitutive Model with Nonlinear Evolutionary Internal Variables

Based on the internal variable theory, a viscoelastic constitutive model of a highly deformable continuous medium is proposed. A set of second rank tensorial internal state variables corresponding to Biot's strain is introduced, and a nonlinear evolution

A Pressure-Correction Method And Its Applications On An Unstructured Chimera Grid

In this paper, an unstructured Chimera mesh method is used to compute incompressible flow around a rotating body. To implement the pressure correction algorithm on unstructured overlapping sub-grids, a novel interpolation scheme for pressure correction is proposed. This indirect interpolation scheme can ensure a tight coupling of pressure between sub-domains. A moving-mesh finite volume approach is used to treat the rotating sub-domain and the governing equations are formulated in an inertial reference frame. Since the mesh that surrounds the rotating body undergoes only solid body rotation and the background mesh remains stationary, no mesh deformation is encountered in the computation. As a benefit from the utilization of an inertial frame, tensorial transformation for velocity is not needed. Three numerical simulations are successfully performed. They include flow over a fixed circular cylinder, flow over a rotating circular cylinder and flow over a rotating elliptic cylinder. These numerical examples demonstrate the capability of the current scheme in handling moving boundaries. The numerical results are in good agreement with experimental and computational data in literature. (C) 2007 Elsevier Ltd. All rights reserved.

Some theoretical aspects of the simplified Navier-Stokes(SNS) equations

This study deals with the formulation, mathematical property and physical meaning of the simplified Navier-Stokes (SNS) equations. The tensorial SNS equations proposed is the simplest in form and is applicable to flow fields with arbitrary body boundaries. The zones of influence and dependence of the SNS equations, which are of primary importance to numerical solutions, are expounded for the first time from the viewpoint of subcharacteristics. Besides, a detailed analysis of the diffusion process in flow fields shows that the diffusion effect has an influence zone globally windward and an upwind propagation greatly depressed by convection. The maximum upwind influential distance of the viscous effect and the relative importance of the viscous effect in the flow direction to that in the direction normal to the flow are represented by the Reynolds number, which illustrates the conversion of the complete Navier-Stokes (NS) equations to the SNS equations for flows with large Reynolds number.

On the invariant representation of spin tensors with applications

The invariant representation of the spin tensor defined as the rotation rate of a principal triad for a symmetric and non-degenerate tensor is derived on the basis of the general solution of a linear tensorial equation. The result can be naturally specified to study the. spin of the stretch tensors and to investigate the relations between various rotation rate tensors encountered frequently in modern continuum mechanics. A remarkable formula which relates the generalized stress conjugate to the generalized strain in Hill's sense. to Cauchy stress, is obtained in invariant form through the work conjugate principle. Particularly, a detailed discussion on the time rate of logarithmic strain and its conjugate stress is made as the principal axes of strain arc not fixed during deformation.