Micromechanics- Matrix Formulae

Question 1

Specially orthotropic case

Answer 1

A lamina which is loaded along the principal material axes. Loaded in 0 and 90° directions and is the simplest case

Question 2

Compliance matrix for specially orthotropic lamina

Answer 2

S11 S12 0
S12 S22 0
0 0 S66

Question 3

Stress and strain matrices related by compliance matrix for specially orthotropic

Answer 3

(ε1, ε2, γ12)
(σ1, σ2, τ12)

Question 4

The compliance coefficients needed for the specially orthotropic system and their formulae

Answer 4

S11=1/E1
S12=-ν12/E1=-ν21/E2
S22=1/E2
S66=1/G12

Question 5

What did each of the compliance coefficients (and zeros) mean in the real world?

Answer 5

S11: extension in the 1 direction
S12: extension-extension coupling (Poisson’s effect)
S22: extension in the 2 direction
S66: shear in the 1-2 plane
0s: no shear-extension coupling

Question 6

Transformed compliance tensor

Answer 6

[Sbar]=[U]^-1[S][T]
[ε’]=[Sbar][σ’]
S11 S12 S16
S12 S22 S26
S16 S26 S66
All S are bar