Deformation of a continuum element

[Studious_stud]

Homework Statement

The continuum element shown in Figure (a) deforms to figure (b)

I'm looking to find the positions after deformation (x coordinates) by expressing them in terms of E coordinates.

Homework Equations

The Attempt at a Solution

x1 = E1 + E2
x2 = E1 + E2
x3 = E3

The first two equations for x I need help with, I'm not sure about the angles. I've done a previous question where the element deforms similarly (pure shear) but it stays within the same quadrant. The fact that this is flipped to the opposite quadrant is confusing me.

When the element deforms but stays in the same quadrant the answer is:

x1 = E1cosa + E2sina
x2 = E1sina + E2cosa
x3 = E3

 

[paisiello2]

What are E1, E2, and E3 supposed to be?

 

[Chestermiller]

In your first figure, it doesn't look like the deformation is pure shear. Those parameters m and n look like stretches.

Chet

 

[Chestermiller]

If the position vector between material points A and B is expressed as E₁i in the original configuration of the body (figure a), and this vector stretches by an amount m to obtain the deformed configuration (figure b), what is the equation for the position vector between material points A and B in the deformed configuration?

Chet