112

N. Chari et al.

Here, Young’s modulus (E) is given by

E =

Tensile Stress

Extensional Strain ^{= σ}

ε ⁼

F/Ao

L/Lo

=

FLo

AoL

(8.2)

where

F

is the force exerted on an object (resilin) under tension.

Ao

is the original cross-sectional area at the side where force is applied on the

resilin.

L

is the change of length in resilin.

Lo

is the original length of resilin.

Force exerted by stretching or contracting the resilin is given by using Young’s

modulus of material under specific strain conditions as follows:

F = ^{E AoL}

Lo

(8.3)

However, Hooke’s Law describes the stiffness of a spring material, and from

Eq. 7.3, we can derive the parameters of Hooke’s law as follows:

F =

 E Ao

Lo



L = kx

(8.4)

Here, Hooke considered



E Ao

Lo



as k and L as x.

From the above equations, it is possible to calculate the elastic potential energy

stored in chitin by taking the integral of Eq. 7.3 with respect to its length, L, as

follows:

Ue =



E AoL

Lo

dL = ^{E Ao}

Lo



L dL = ^{E AoL2}

2Lo

Ue = ^{E AoL2}

2Lo

(8.5)

where

Ue is considered as elastic potential energy.

Here, it is also possible to calculate the elastic potential energy per/unit volume

as follows:

U =

Ue

AoLo

= ^EL2

2L²o

= ¹

2 ^Eε2

(8.6)