5.1 Introduction
127
Fig. 5.2 Examples of practical plane strain problems
⎧
⎨
⎩
σ x
σ y
τ xy
⎫
⎬
⎭
=
E
(1 + ν) (1 − 2ν)
⎡
⎣
(1 − ν)
ν
0
ν
(1 − ν) 0
0
0
1−2ν
2
⎤
⎦
⎧
⎨
⎩
ε x
ε y
γ xy
⎫
⎬
⎭
(5.7)
5.2 Relationship Between Plane Stress and Plane Strain
5.2.1 Plane Stress Case
From the stress–strain relationship (Eq. 4.22), we have
σ x = (2G + λ)ε x + λ
ε y + ε z
or
127
Fig. 5.2 Examples of practical plane strain problems
⎧
⎨
⎩
σ x
σ y
τ xy
⎫
⎬
⎭
=
E
(1 + ν) (1 − 2ν)
⎡
⎣
(1 − ν)
ν
0
ν
(1 − ν) 0
0
0
1−2ν
2
⎤
⎦
⎧
⎨
⎩
ε x
ε y
γ xy
⎫
⎬
⎭
(5.7)
5.2 Relationship Between Plane Stress and Plane Strain
5.2.1 Plane Stress Case
From the stress–strain relationship (Eq. 4.22), we have
σ x = (2G + λ)ε x + λ
ε y + ε z
or