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International audience; Solving mechanical problems in large structures with rich localized behaviors remains a challenging issue despite the enormous advances in numerical procedures and computational performance. In particular, these localized behaviors need for extremely fine descriptions, and this has an associated impact in the number of degrees of freedom from one side, and the decrease of the time step employed in usual explicit time integrations, whose stability scales with the size of the smallest element involved in the mesh. In the present work we propose a data-driven technique for learning the rich behavior of a local patch and integrate it into a standard coarser description at the structure level. Thus, localized behaviors impact the global structural response without needing an explicit description of that fine scale behaviors.

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Efficient and optimal design of radar-based Advanced Driver Assistant Systems (ADAS) needs the evaluation of many different electromagnetic solutions for evaluating the impact of the radome on the electromagnetic wave propagation. Because of the very high frequency at which these devices operate, with the associated extremely small wavelength, very fine meshes are needed to accurately discretize the electromagnetic equations. Thus, the computational cost of each numerical solution for a given choice of the design or operation parameters, is high (CPU time consuming and needing significant computational resources) compromising the efficiency of standard optimization algorithms. In order to alleviate the just referred difficulties the present paper proposes an approach based on the use of reduced order modeling, in particular the construction of a parametric solution by employing a non-intrusive formulation of the Proper Generalized Decomposition, combined with a powerful phase-angle unwrapping strategy for accurately addressing the electric and magnetic fields interpolation, contributing to improve the design, the calibration and the operational use of those systems.

International audience; Industrials have an intensive use of numerical simulations in order to avoid physical testing and to speed up the design stages of their products. The numerical testing is indeed quicker to set-up, less expensive, and supplies a lot of information about the system under study. Moreover, it can be much closer to the physical tests as the computation power increases. Despite the rise of this power, time consuming simulations remain challenging to be used in design process, especially in an optimization study. Crash simulations belong to this category. These rapid dynamic computations are used by RENAULT during the sizing of the vehicle structure in order to ensure that it meets specifications set up to reach safety criteria in case of accidents. They are completed using finite element software such as VPS (Virtual Performance Solver) developed by ESI group that will be used in this study. For car manufacturers, the goal of the optimization study is to minimize the mass of the vehicle (and thus its consumption) by modifying the thicknesses of some parts (from 20 to 100 variables). Industrials such as RENAULT currently perform optimization studies based on numerical design of experiments. The number of computations required by this technique is from 3 to 10 times the number of variables. This is too much in order to be intensively used in a design process.In order to decrease the time-to-market and to explore alternative technical solutions, we explore the potential of using a parametrized reduced order model in the optimization studies. The parametrized reduced order model gives an estimation of the high-fidelity result for a new set of parameters without using the solver, by analysing the existing results of previous computations with various sets of parameters. The developed reduced order model is called ReCUR. It is partly based on a CUR approach embedded in a regression analysis. The regression statistical model uses the data of a few calculations made with the solver. Other tools such as clustering and linear programming are used to get the regression analysis more efficient.It is hoped to drastically reduce the number of required simulations of a standard optimization study. In this paper, the construction of the reduced order model will be presented. Then, the relevancy of using the reduced order model into a design process will be exhibited through the treatment of two industrial test-cases. Some improvements of the method as well as several potential uses will then be outlined. The applications will highlights the promising power of the method to shorten design process using optimisation and long-run simulations.

Most of mechanical systems and complex structures exhibit plate and shell components. Therefore, 2D simulation, based on plate and shell theory, appears as an appealing choice in structural analysis as it allows reducing the computational complexity. Nevertheless, this 2D framework fails for capturing rich physics compromising the usual hypotheses considered when deriving standard plate and shell theories. To circumvent, or at least alleviate this issue, authors proposed in their former works an in-plane-out-of-plane separated representation able to capture rich 3D behaviors while keeping the computational complexity of 2D simulations. However, that procedure it was revealed to be too intrusive for being introduced into existing commercial softwares. Moreover, experience indicated that such enriched descriptions are only compulsory locally, in some regions or structure components. In the present paper we propose an enrichment procedure able to address 3D local behaviors, preserving the direct minimally-invasive coupling with existing plate and shell discretizations. The proposed strategy will be extended to inelastic behaviors and structural dynamics.

This paper proposes a general framework for expressing parametrically quantities of interest related to the solution of complex structural mechanics models, in particular the ones involved in crash analyses where strongly coupled nonlinear and dynamic behaviors coexist with space-time localized mechanisms. Advanced nonlinear regressions able to proceed in the low-data limit, enabling to accommodate heterogeneous parameters, will be proposed and their performances evaluated in the case of crash simulations. As soon as these parametric expressions will be determined, they can be used for generating large amounts of realizations of the quantity of interest for different choices of the parameters, for supporting data-analytics. On the other hand, such parametric representations allow the use advanced optimization techniques, evaluate sensitivities and propagate uncertainty all them under the stringent real-time constraint.

International audience; Description of complex materials, in particular complex fluids, involves numerous computational challenges. Today, atomistic descriptions are too expensive from the computational point of view, motivating that this kind of analysis is restricted to extremely small systems. The next scale introduces some simplificative hypotheses, leading to coarse grained descriptions. At this level, Brownian dynamics simulations are usually employed. However, this level of description requires intensive computation resources with significant unfavorable impact on the simulation performances (CPU time). For these reasons sometimes kinetic theory descriptions are preferred. In those de- scriptions, the molecular conformation is described from a probability distribution function (PDF) whose evolution is governed by the Fokker-Planck equation. This approach, despite its mathematical simplicity introduces some computational challenges. First, the distribution function is defined in a multidimensional space, and then the associated partial differential equations must be solved in a multidimensional domain (some times involving thousands dimensions). Secondly, the analysis of transient models needs intensive computation, in particular when the system response under small amplitude oscillations (of high and very high frequency) is concerned. In some of our former works we proposed a technique based on the separated representation of the unknown field able to circumvent the curse of dimensionality. In this paper, we are addressing the second chal- lenging point, the one related to the transient behavior. For this purpose we propose a separated representation of transient models leading to a non-incremental strategy, allowing impressive CPU time savings.