.
x
m
x
m
y
m
y
m
x
m
x
m
y
m
y
m
xy
τ
xy
τ
yx
τ
yx
τ
xy
τ
xy
τ
yx
τ
yx
τ
z
θ
z
x
x
θ
χ
∂
= ∂
x
m
x
m
z
θ
z
z
x
x
θ
θ
δ
∂
+ ∂
y
m
y
m
z
z
y
y
θ
θ
δ
∂
+ ∂
z
θ
z
y
y
θ
χ
∂
= ∂
3
3a
3b
3c
3d
y
m
y
m
x
m
x
m
xy
σ
xy
σ
yx
σ
yx
σ
yy
σ
yy
σ
xx
σ
xx
σ
yy
σ
yy
σ
xx
σ
xx
σ
yy
σ
yy
σ
s
xy
σ
s
xy
σ
s
yx
σ
s
yx
σ
xx
σ
xx
σ
x
m
x
m
y
m
y
m
xy
τ
yx
τ
yx
τ
xy
τ
s
yx
σ
s
xy
σ
s
yx
σ
s
xy
σ
xy
γ
1
2
3
4
5
Fig. 5.15 Reduced Cosserat continuum stress point
5.6 Thermo-mechanical Analysis of Cosserat Continuum: Length-Scale Effects
247