Page 19 - Mechanics Analysis Composite Materials

4 Mechanics and analysis of composite materials

where o =F/A, E = A/L0, and el = Al/Lo. Integral

is a specific elastic energy (energy accumulated in the unit volume of the bar) that is
referred to as an elastic potential. It is important that U does not depend on the
history of loading. This means that irrespective of the way we reach point 1 of the
curve in Fig 1.2 (e.g., by means of continuous loading, increasing force F step by
step, or using any other loading program), the final value of U will be the same and
will depend only on the value of final strain el for the given material.
A very important particular case of the elastic model is the linear elastic model
described by the well-known Hooke’s law (see Fig. 1.3)

Here, E is the modulus of elasticity. As follows from Eqs. (1.3) and (1.6), E = o
if E = 1, Le. if A =LO. Thus, modulus can be interpreted as the stress causing
elongation of the bar in Fig. 1.1 as high as the initial length. Because the majority of
structural materials fails before such a high elongation can occur, modulus is usually
much higher then the ultimate stress 8.
Similar to specific strength k, in Eq. (1.2), we can introduce the corresponding
specific modulus

E
kE -
P
determining material stiffness with respect to material density.

Fig. 1.3. Stress-strain diagram for a linear elastic material.