Lamé's Ellipsoid and Mohr's Circles (Part 3: Meridians)

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.

For a continuous body, the stress tensor is a symmetric matrix representing the stresses at a point. The traction vector on a plane defined by its unit normal vector is the matrix product of the stress tensor with . The stress tensor has three real eigenvalues (the principal stresses, , , and ) and three associated eigenvectors (the principal directions). In the coordinate system defined by these eigenvectors, the Lamé's ellipsoid represents the locus of the traction vector heads.


This Demonstration shows ellipses, called meridians, obtained by cutting Lamé's ellipsoid by sheaves of planes through the , , and axes, with equations




In the first two cases, is the angle between the plane and the - plane (); in the third case is the angle between the plane and the - plane ().

The points of the meridians are endpoints of the traction vectors, whose intrinsic components (normal and tangential) are represented by green loci within the Mohr 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.