Une vision faiblement intrusive de la méthode LATIN-PGD en non-linéaire

Driven by a high digitalization context with Digital Twins, reduced-order modeling (ROM) methods are becoming increasingly coveted by the industrial sector, keen to benefit from new tools and robust techniques that allow faster computations.However, the spread of these ROM methods within commercial finite element software is currently hindered by two main obstacles: non-intrusiveness and robustness. This arises directly from the nature of the associated algorithms involving many unconventional operations and thus preventing from getting robust and reliable tools all integrated into one certified product. This thesis introduces a weakly-invasive reformulation of the LATIN-PGD method designed to compute and improve reduced-order models directly into any general-purpose industrial finite element software.Under the quasi-static assumption, we assume any time-dependent non-linear parametrized problems in solid mechanics. The guiding thought we propose to pursue is to combine PGD with all facilities offered by such software, implying emph{de facto} the ability to handle any non-linearities -- materials, contacts, large transformations. This way of proceeding provides unified tools -- for the construction of reduced-order models in non-linear context -- all integrated into one certified product in consistency to have end-to-end processes. Thanks to the first implementation conducted within Simcenter Samcef pilot software owned by Siemens Digital Industries Software, we emphasize the assets of this approach without ever redeveloping any non-linear part of the software. Finally, attractive performance gains are achieved on some non-linear time-dependent industrial test-cases involving some parameters.