Benchmark solution
=====================

The imposed loads allow us to obtain a homogeneous solution. Since the main directions are the directions specific to the strain tensor, the elastic energy is deduced from the loads defined above in the following way:

:math:`{W}_{\mathrm{el}}=\frac{({U}_{1}^{2}+{U}_{2}^{2}+{U}_{3}^{2})}{2{L}^{2}}`

The associated damage values are analytically extracted from it:

:math:`d=1-(\frac{2{W}_{y}{L}^{2}}{{U}_{1}^{2}+{U}_{2}^{2}+{U}_{3}^{2}})`

We then consider that the test is verified if Newton returns the same damage values to us, at a precision of :math:`{10}^{-6}`.