Lamé's Ellipsoid and Mohr's Circles (Part 4: Spheres)
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Given a continuum body, the stress tensor is a symmetric matrix that contains the stresses at a point. The traction vector on a plane defined by its perpendicular unitary vector, , is obtained multiplying the stress tensor by . The stress tensor has three real eigenvalues (the principal stresses: , , and ) and three associated eigenvectors (the principal directions). On the coordinate system defined by these eigenvectors Lamé's ellipsoid represents where the heads of the traction vectors lie.
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Contributed by: Luis Martín Yagüe, Agustín Lacort Echeverría, and Antonio Sánchez Parandiet (March 2011)
After work by: Eugenio Bravo Sevilla
Open content licensed under CC BY-NC-SA
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"Lamé's Ellipsoid and Mohr's Circles (Part 4: Spheres)"
http://demonstrations.wolfram.com/LamesEllipsoidAndMohrsCirclesPart4Spheres/
Wolfram Demonstrations Project
Published: March 7 2011