Lamé's Ellipsoid and Mohr's Circles (Part 2: Parallels)

σ

1

(x axis)

-2

σ

2

(y axis)

2

σ

3

(z axis)

4

cutting planes

x = D

y = D

z = D

constant D

0

σ

i

≠ 0

We plot the ellipses (that we call parallels) obtained by intersecting Lamé's ellipsoid with planes parallel to the principal planes. The points of these ellipses are the extremes of traction vectors whose intrinsic components (normal and tangential) are shown by a geometric construction using Mohr's circles.