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Strain and Strain Analysis |
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| When strain is homogeneous it transforms an imaginary sphere into an ellipsoid (3 perpendicular axes λ1≥λ2≥λ3) called the Finite Strain Ellipsoid from which it is easy to characterize the style of strain and its intensity. When strain is heterogeneous it transforms an imaginary sphere in a "potatoid", the characterization of which is extremely difficult. Fortunately it is always possible to define a scale at which strain is, in first approximation, homogeneous. |
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The strain, as geometrically characterized by an ellipsoid, is so easy to assess that only two parameters K and D completely define the style of strain (shape of ellipsoid) and the amount of strain (ellipsoidicity, i.e. how far it is from a perfect sphere) respectively. As shown on the right these two parameters are both function of the ratio λ1/λ2 and λ2/λ3. K and D do not request knowledge of the radius of the initial sphere only knowledge of the principal axes of the finite strain ellipsoid. |
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The Flinn diagram allows the representation of every type of ellipsoid. In this diagram, the ratio λ1/λ2 is the ordinate axis whereas the ratio λ2/λ3 is the abscissa axis. The parameter D is the distance between the origin of the graph (that represent the initial sphere) and the ellipsoid (in red on the diagram). The parameter K is the slope between the abscissa axis and the line joining the ellipsoid and the origin of the diagram.
Cigar shaped ellipsoids locate along the ordinate axis (K is infinite) where the strain is said to be constrictional. Pancake shaped ellipsoids locate along the abscissa axis (K=0) where the strain is said to be flattening. Plane strain (K=1) characterises the ellipsoids for which λ2 axis remains constant despite strain. Rocks strain-related fabric depends on the shape of the finite strain ellipsoid. Pancake shaped ellipsoid leads to S tectonites (strong schistosity, no lineation), cigar shaped ellipsoid leads to L tectonites (strong lineation, no schistosity). L=S tectonites are produced by plane strain. |
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