which together with the

incompressibility condition ([u.sub.i,i] = 0) constitutes the complete set of the PDEs system to solve the final deformation profiles.

Multiplying the first equation and the second equation in (1) by u, b, respectively, and integrating the resulting equations by parts over [R.sup.3], we obtain after adding them together from the

incompressibility condition [nabla] x u = 0 and [nabla] x b = 0

Let us impose the

incompressibility condition [nabla] x u = 0.

As mentioned before, the radial velocity [u.sup.b.sub.0] is determined from the

incompressibility condition (40):

p is a Lagrange multiplier associated to the global

incompressibility condition, and g is the multiplier associated to the incompressibility of the elastic part.

The

incompressibility condition is implemented in the functional integral, too.

If the desired eigenvector is written in terms of the velocity and pressure components x = [[x.sup.H.sub.u] [x.sup.H.sub.p]].sup.H], the

incompressibility condition [C.sup.H][x.sub.u] = 0 holds.

If we add in the equation (1.1) the

incompressibility condition div([??]) = 0, then we obtain the following convolution equation of Navier Stokes type:

For simplicity, the material is assumed to be incompressible, which allows for the thickness to be calculated from the original thickness by use of the

incompressibility condition:

[14] and Sagaseta [15] considered the problem as strain controlled and obtained strains by using only the

incompressibility condition. The presence of the top free surface was considered by means of a virtual image technique and some results for the elastic half-space.

The proposed damage model in crosslinked rubbers is based on two assumptions: (i) irreversibility of chain scission because of quick neutralization of free radicals formed in scission process (33), and (ii)

incompressibility condition common in damage models, because the volume concentration of microscopic voids formed by the scissions is negligible almost until the failure.

For simple tension condition, uniaxial state of stress is present, with a multiaxial stretch state with the longitudinal stretch value of [lambda] and two equal transverse stretch values of [[lambda].sup.-1/2] satisfy the

incompressibility condition. Planar tension specimen is under plane stress condition with longitudinal and transverse stresses.