Finally, to get the expression of total

stress tensor of fiber polymer composites, the following Equation has been used [28, 29].

The NE-SW

stress tensor formed the northwest trending and southwest verging open to close F1-folds and southwest directed D1-faults.

He studies the flow of a simple fluid for which the

stress tensor T can be express as a function of the first two Rivlin-Eriksen tenors.

Then under the conditions of plane deformation, the wave process at the interior points of the rectangular strip is described as a system of equations for the velocities of displacements [v.sub.1], [v.sub.2] and three linear combinations of the

stress tensor components p, q, r[8]:

In a reference frame [summation]'(x', y'), which is rotated against [summation](x, y) by -45[degrees] the

stress tensor reads [[sigma].sub.x'x'] = ([[sigma].sub.xx] + [[sigma].sub.yy])/2 - [[sigma].sub.xy], [[sigma].sub.y'y'] = ([[sigma].sub.xx] + [[sigma].sub.yy])/2 + - [[sigma].sub.xy], [[sigma].sub.y'y'] = ([[sigma].sub.xx] + [[sigma].sub.yy])/2 + [[sigma].sub.xy], and [[sigma].sub.x'y'] = ([[sigma].sub.xx] - [[sigma].sub.yy])/2.

The Lagrangian formulation from continuum mechanics is exploited using the Green-Lagrange strain tensor E along with the first Piola-Kirchhoff

stress tensor [T.sub.1] and second Piola-Kirchhoff

stress tensor [T.sub.2].

where [C.sub.p] is the specific heat, T is the temperature, Q is the heat flux, [sigma] is the Cauchy

stress tensor, [H.sub.T] is the material parameter, and their expressions are

The definition of the rock

stress tensor sigma, strain tensor for, based on the assumption of small deformation, equilibrium equations and geometric equations of rock mass are as follows:

The initial charge's shape, temperature,

stress tensor and anisotropic material property are first computed by LS-Dyna; then, carrying those physical properties, the deformed charge is exported to Moldex3D to continue the compression molding analysis.

The key to enhancing the stability concerning the coupling of the velocity ([U.sub.i]) and Reynolds-stress [??] fields is an appropriately blended Reynolds

stress tensor entering the divergence operator on the right-hand-side of the momentum equation (Eq.

[summation] and [summation]' are obtained by applying different linear transformations onto deviatoric

stress tensor S, reads, respectively

where T is the

stress tensor, D is the electric displacement vector, C is the elastic modulus tensor measured in a constant electric field, [??] is the piezoelectric tensor, and [??] is the dielectric tensor measured at constant strains.