# Polymer Stress Formulation#

Polymer Constitutive Equation = {model_name}


## Description / Usage#

This card specifies which formulation of the polymer constitutive equation should be used. Valid options are

EVSS_G

Uses the classic elastic-viscous stress splitting of Rajagopalan (1990) where the stress is the elastic stress only without a Newtonian component. This option is the default if this Polymer Stress Formulation card is not supplied. This formulation is almost never used. Prefer EVSS_F

EVSS_F

Uses the EVSS formulation of Guenette and Fortin (1995) that solves the standard stress equation with the addition of a new term to the momentum equation. This formulation is used most often.

EVSS_L

Uses a research formulation for viscoelasticity that includes a level set discretization that switches the equations from solid to fluid. This option is not currently in production usage. Partial level set support is included in EVSS_F formulation

LOG_CONF

Log-conformation tensor formulation from Fattal and Kupferman 2004, uses DEVSS-G

Log-conformation tensor formulation from Fattal and Kupferman 2004, uses DEVSS-G but all gradient terms in constitutive equation are the field variable $$\nabla v$$ instead of the projection $$G$$

SQRT_CONF

sqrt-conformation tensor formulation from Balci et al. 2011, uses DEVSS-G stabilization

## Examples#

The following is a sample card that sets the polymer stress formulation to EVSS_F:

Polymer Stress Formulation = EVSS_F


## Technical Discussion#

If using SQRT_CONF with no guess for the square root of stress tensor, $$b$$, recommended initial guess is the identity tensor for all modes.

Use post processing card Map Conf Stress to output the stress values, otherwise the usual S values are the given conformation tensor base form such as the SQRT being $$b$$ in $$b^Tb = c$$ or LOG being $$s = log c$$

## References#

Guenette, R. and M. Fortin, “A New Mixed Finite Element Method for Computing Viscoelastic Flow,” J. Non-Newtonian Fluid Mech., 60 (1995) 27-52.

Rajagopalan, D., R. C. Armstrong and R. A. Brown, “Finite Element Methods for Calculation of Viscoelastic Fluids with a Newtonian Viscosity”, J. Non-Newtonian Fluid Mech., 36 (1990) 159-192.