The eigenvalues of steady flow in Mohr space
1986; Elsevier BV; Volume: 122; Issue: 1-2 Linguagem: Inglês
10.1016/0040-1951(86)90157-5
ISSN1879-3266
Autores Tópico(s)Geological formations and processes
ResumoThe eigenvalues of the velocity gradients tensor and of the position gradients tensor describing instantaneous flow or incremental deformations are easily determined in Mohr space as the points of intersection between a Mohr circle and the horizontal Mohr axis. Intersections occur only if the tensor has real eigenvalues. Eigenvectors associated with the eigenvalues are directions of no rotation. A line of material particles under an eigenvector does not rotate during steady flow, although the line is instantaneously stretching at a rate equal to its corresponding eigenvalue. For non-spinning steady sub-simple shearing there will always be two eigenvectors. The angle between the eigenvectors is dependent on the ratio of pure to simple shearing rates. This angle decreases as the pure shearing component decreases relative to the simple shearing component. Superimposed increments of pure shear and simple shear produce an equivalent set of non-rotated material lines but the deformation histories of these lines are rotational. The influence of eigendirections on geological structures is constrained by the rheology of a rock during deformation. In homogenous steady flow no influence may be obvious. Spatially periodic material softening along eigenvectors during bulk hardening may result in a complex fabric of intersecting shear zones. The geometry of the fabric elements provides important information on the bulk deformation of the rock, particularly on the bulk shear sense.
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