Stress Free Solvent Vol Frac#

```Stress Free Solvent Vol Frac = CONSTANT <float> []
```

Description / Usage#

This required card is used to specify the model for the stress-free solvent volume fraction, which is the volume fraction of solvents in the solid material in its stress-free state. This card is used exclusively in materials of LAGRANGIAN or TOTAL_ALE Mesh Motion types (see Mesh Motion card) which are being modeled as gelled solids laden with solvent. At the gel-point, the solid is considered to be stress free, after which a reduction of solvent leads to volume shrinkage and hence a rising stress state. Definitions of the input parameters are as follows:

 CONSTANT Name of the model for the stress-free solvent volume fraction. The value of the stress-free solvent volume fraction; this value is unitless.

Examples#

The following is a sample card:

```Stress Free Solvent Vol Frac = CONSTANT 0.5
```

This specification sets the volume fraction of solvent in the material to 50 per cent. That volume fraction is tantamount to the gel point of the material.

Technical Discussion#

The stress free state volume fraction of solvent is basically the solvent fraction at which a material gels, viz., the state at which the material solidifies from a liquid state. This quantity is used in the continuity equation for incompressible solid materials, through which is transported by a variety of diffusion models (see Diffusivity card). The continuity equation, viz., EQ = continuity, is applied as follows:

where the dependent variable is the solid phase pressure (see Solid Constitutive Equation card). Here det F is the determinant of the deformation gradient tensor, yi is the volume fraction of component i (specified by the EQ = species_bulk card), and y0 is the volume fraction of total solvents at the stress free state. Clearly, as the solvent concentration decreases the local volume of solid decreases, creating a rising stress.

References#

GT-001.4: GOMA and SEAMS tutorial for new users, February 18, 2002, P. R. Schunk and D. A. Labreche

GT-019.1: Elastoviscoplastic (EVP) Constitutive Model in GOMA: Theory, Testing, and Tutorial, P. R. Schunk, A. Sun, S. Y. Tam (Imation Corp.) and K. S. Chen, January 11, 2001

SAND96-2149: Drying in Deformable Partially-Saturated Porous Media: Sol-Gel Coatings, Cairncross, R. A., P. R. Schunk, K. S. Chen, S. S. Prakash, J. Samuel, A. J. Hurd and C. Brinker (September 1996)