Stretching energy (${\mathcal{E}}_s=\frac{1}{2}\int C(\alpha -1{)}^{2}dS$)

The part of elastic energy associated with a change of material length. A simple quadratic constitutive equation assigns energy density $C(\alpha -1{)}^2/2$ per reference arc length, where $C>0$ is stretching stiffness and $\alpha$ is the stretch ratio. Such a small-strain model need not remain realistic as $\alpha \to 0$.