2. 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:

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

The associated damage values are analytically extracted from it:

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

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