Lamé's Ellipsoid and Mohr's Circles (Part 4: Spheres)

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

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.


This Demonstration shows the curves obtained by cutting Lamé's ellipsoid with spheres of different radius; the points of these curves are the extremes of the traction vectors with the same norm. Their intrinsic components (normal and tangential) are shown as the green locus over Mohr's circles.


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




Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.