A linear viscoelastic, orthotropic lamina has principal creep compliances given in contracted notation by

\[S_{i j}(t)=E_{i j}=F_{i j} t, \quad i, j=1,2, \ldots, 6\]

where \(E_{i j}\) and \(F_{i j}\) are material constants and \(t\) is time. The lamina is subjected to plane stress with constant stresses

\[\sigma_{i}(t)=\sigma_{i}^{\prime} H(t), \quad i, j=1,2, \ldots, 6\]

where \(\sigma_{i}^{\prime}\) are constants and \(H(t)\) is the unit step function. If the failure strains for pure longitudinal, transverse, and shear loading of the lamina are \(e_{\mathrm{L}}, e_{\mathrm{T}}\), and \(e_{\mathrm{LT}}\), respectively, find the expressions for the time to failure for each of the three strains.