MecaSequentialLinear

This use case aims to validate the methodology POD + ECM for uniform isotropic elactic material computations with Z-set, see Section Publications, article 1. In this linear case, the ECM should find a trivial quadrature formula, since the operators can be completely precomputed in the offline stage.

No optional prerequisite.

The data needed to execute the tutorials below can be loaded here: exampleMecaSequentialLinear.zip

Features: linear material

The physical setting, workflow and reduction strategy are the same as in the tutorial MecaSequential , hence we only point out the differences here. The difference is the use of a uniform isotropic elactic material. Even if the data is generated by Z-set, a constitutive law solver has been implemented in Containers/ConstitutiveLaws/MecaUniformLinearElasticity.py, hence Z-mat is not required to run the offline and online stages of this tutorial.

Results

The ECM selects 3 reduced integration points in this example (this can slightly vary due the probabilistic nature of our implementation for ECM)

In Fig. 6, the quality of the reduced model is illustrated by comparing it to the high-fidelity reference. The comparison is done on the displacement, since no internal variable is available with the simple considered material.

Fig. 6 Illustration of the ROM accuracy on the displacement U (left) HFM, (right) pointwise difference between the ROM and the HFM.