Effect of Elastic Strains in Steady-State Elasto Visco-Plastic Flow
The effect of elastic strains in the steady state elasto visco-plastic flow (Maxwell fluid) under the rolling process is analyzed quantitively. As a simple model for treating an elastic effect, the Jauman derivative of stress is considered. Several schemes are found for analyzing the model by the finite element method (2’9). Shimazaki and Thompson (5) used the mixed method which decouples the momentum and continuity equations from the constitutive equation. Because the constitutive equation becomes nonlinear due to the elastic effect, an iterative procedure is incorporated between two sets of finite element equations until convergence is obtained. The decoupled formulation scheme requires a less storage area for the stiffness matrix, therefore, the amount of computer time is often decreased for higher nonlinear problems even if it incorporates the simple iterative procedure.
Although the above method appears to be stable at low elastic responses, oscillations in stress begin to appear as the elastic effect is increased. This can be attributed to the property of the standard Galerkin method which produces a central difference type of approximation in the constitutive equation.
In this paper we use the same algorithm as in (5), but the Petrov-Galerkin method is introduced into the finite element equation for the constitutive law. As a result, oscillations in stress are eliminated, the rate of convergence is improved and convergence is obtained even in the presence of a higher elastic response
KeywordsStress Deviator Viscoelastic Fluid Elastic Effect Finite Element Equation Maxwell Fluid
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