First strain invariant
= First strain invariant
{title2=$I_1=\operatorname{tr}B$}
The first principal invariant of the <left Cauchy-Green deformation tensor> is the sum of the squares of the <principal stretches>. Since $B=FF^T$, it also equals $\sum_{i,I}F_{iI}^2$. Its derivative with respect to the <deformation gradient> is $2F$. For a <strain energy density> $W=w(I_1)$ with <incompressibility>, the <Cauchy stress tensor> is $T=2w'(I_1)B-pI$.