2. Benchmark results

We do not have a reference solution.

As long as the solution of the local model remains homogeneous for the various Gauss points, that is to say for :math:`tmathrm{=}mathrm{0.93s}`, the results obtained with*Code_Aster for this model will be taken as a reference solution. For the results of the gradient model, we must find exactly the results obtained with the local version. At this moment, we will therefore test, for both models, the Cauchy stress \({\sigma }_{\mathit{yy}}\) in the direction \(y\), the Cauchy stress \({\sigma }_{\mathit{zz}}\) in the direction \(z\), the cumulative plastic deformation \(p\) and the porosity \(f\), calculated at the point of Gauss No. 1 of the mesh [1,2,3,4], calculated at the point of Gauss No. 1 of the mesh [].

• For the gradient model, the response must remain consistent in the Gauss points throughout the loading path. To test this result, the Cauchy constraint \({\sigma }_{\mathit{yy}}\) in the y direction at Gauss points No. 1, 2, 3 and 4 of the mesh [1,2,3,4] and at the final instant will be adopted as a reference solution.