THEORETICAL BACKGROUND OF MASONRY MODEL

1
ε = σ −νσ −νσ
E
( )
xxi xxi i yyi i zzi
i
1
ε = σ −νσ −νσ
E
( )
yyi yyi i xxi i zzi
i
1
ε = σ −νσ −νσ
E
γ
γ
γ
( )
zzi zzi i xxi i yyi
i
xyi
yzi
xzi
τ
=
G
τ
=
G
τ
=
G
xyi
xyi
yzi
yzi
xzi
xzi
A.5
Now the strain energy for each component and 1 layer prism can be denoted as
U
U
2
1
= + + + + +
∑ ∫
( σ ε σ ε σ ε τ γ τ γ τ γ )
re xxi xxi yyi yyi zzi zzi xyi xyi yzi yzi xzi xzi i
1 2
Vi
i=
1
=
2
∫ + + + + +
V
( σ ε σ ε σ ε τ γ τ γ τ γ )
e xx xx yy yy zz zz xy xy yz yz xz xz
dV
dV
A6
where ‘re’ and ‘e’ represent the component and layer prism, respectively, and it is
obvious that
U
re
= U
A7
e
Introduce auxiliary stresses/strains,
σ
σ
σ
τ
τ
τ
xxi xx xxi
yyi
yy
zzi zz zzi
xyi
yzi
= σ + A
= σ
= σ + A
= τ
= τ
xy
yz
= τ + A
xzi xz xzi
A.8
and
THEORETICAL BACKGROUND OF MASONRY MODEL page 12 / 20