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and<br />

Ψ ′ = GV 0 2<br />

2σ0AL εr<br />

(9.10)<br />

where, G is the impacted mass, V0 is initial velocity of the projector and L is the initial<br />

length of absorber. As an engineering approach, L can be replaced by 4/3f in order to<br />

reflect the axial length of an energy absorber participating to energy absorption (Jones<br />

In Press). The energy absorption of foam filler in the case of filled tube is added to the<br />

denominator of Equations 9.9 and 9.10. The energy absorption in a simple compression<br />

then becomes,<br />

E f = σ pA fδ f 4 3<br />

ε r (9.11)<br />

Equations 9.9 and 9.10 are rearranged with the above for static loading as<br />

and for dynamic loading as<br />

Ψ =<br />

Ψ ′ =<br />

3Pm<br />

4εr σ0A0+σp A f (9.12)<br />

GV 0 2<br />

8δ fεr σ0A0+σp A f (9.13)<br />

By substituting Equations 9.1 and 9.2 into Equation 9.12, energy-absorbing<br />

effectiveness factor becomes,<br />

184

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