BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

Bul. Inst. Polit. Iaşi, t. LVIII (LXII), f. 3, 2012 101
where Gdl (G – integration constant) represents the mechanical work needed to
the deformation in the elastic field (ξ) for the elementary front dl. If between the
deformation and the force is kept (in the elastic field) the same linear
dependence like in (19), then the deformation, when achieving the ratio A, is
A/B, so the constant G is
AB / 2
A
G= ∫ Bξξ d = . (21)
2B
0
If the impact zone width L is equally divided in n intervals, and the
deformation is measured in the (n+1) demarcating points of the intervals, then,
according to (20) and substituting the deformation with the function
fi
(), l i= 1, non the intervals, it can be written
L L 2 L
f () l
Ed
= ∫Af ()d l l + ∫B + Gdl
dl
∫
. (22)
0 0 0
2
A
Confronting the Eq. (22) with the form Ed
= K1+ AK2
+ BK 3
and
B
after the integrals processing, the following values for the coefficients
L
K
1
= ,
2
n
2 n
L ⎡
L
K = ⎢ ( ξ + ξ ) − ( m + m
⎣
2 i+ 1 i 2 i i−
2n
i= 1 12n
i=
1
⎤
⎥
⎦
∑ ∑ 1 ) ,
K
3
n
=
3L
n
∑
i=
1
n
∑
i=
1
3 3
( ξi+
1
− ξi
)
.
( m + m )
i
i−1
(23)
The deformation function was integrated in the form (9). The average
deformation was calculated like an integral average on the length L of the
deformed front
and finally
L
i i=
n
1 1
ξ = med
ξ()d
l l ξi
()d l l
L∫
= ∑ L
∫
0
l
li−1
i=
1
,
(24)
n
2
1 ⎡ 1 ⎛ L ⎞ ⎤
ξmed = ∑ ⎢( ξi+ 1
+ ξi) − ( mi + mi−
1
2n
i=
1
12
⎜
n
⎟ )⎥ . (25)
⎢⎣
⎝ ⎠ ⎥⎦
3. The Calibration of the Model
The calculus model will be calibrated on the calculus presented in (***,
1980), considering that for the Ford vehicle (frontal damaged) the deformation