stress tensor


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stress tensor

[′stres ‚ten·sər]
(mechanics)
A second-rank tensor whose components are stresses exerted across surfaces perpendicular to the coordinate directions.
References in periodicals archive ?
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.