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


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


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.


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


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 \(s = log c\)


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.