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_CONF_GRADV

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.