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:
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
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.