Defects such as gas pores can be formed and trapped in the fusion zone during laser welding. These defects can significantly affect the mechanical reliability of the welded joint. Current nondestructive inspection technologies are able to detect micro-voids in a mass production context. Finite element analysis can therefore be used to assess the lifetime of an observed component via image-based modeling. Unfortunately, running a simulation per component entails a huge and generally unaffordable computational cost. In addition, voids do not admit a parametric modeling. In this paper, a numerical method is proposed to study the impact of defects on the mechanical response of a welded joint. It is based on model order reduction techniques that decrease the computational cost of each simulation related to an image-based modeling. To tackle the reduction of nonparametric defects, a multiscale construction of the reduced basis is proposed, although no scale separation is assumed when computing the mechanical response of the structure. Some empirical modes are representing the structure behavior and other empirical modes are related to the defect-induced local fluctuations. They are then assembled to simulate a defective joint. Assets and limitations of the proposed method are explored through a simplified two-dimensional (2D) problem. For the sake of reproducibility, this 2D problem is fully parametric. Finally, a realistic three-dimensional (3D) industrial case is presented, where voids geometries have been measured via computed tomography. This 3D problem being nonparametric, fluctuation modes must be computed on the fly, once the computed tomography has been performed. K E Y W O R D Scombinatorial model order reduction, elasto-plasticity, impossible sampling, material health monitoring, reduced order model INTRODUCTIONDirect numerical simulations (DNSs) have been introduced in fluid mechanics to account for the wide range of scales in turbulent flows, 1 without using a simplified modeling of motions at small scales. In mechanics of heterogeneous Int J Numer Methods Eng. 2020;121:2581-2599. wileyonlinelibrary.com/journal/nme
In continuum mechanics, the prediction of defect harmfulness requires to solve approximately partial differential equations with given boundary conditions. In this contribution boundary conditions are learnt for tight local volumes (TLV) surrounding cracks in three-dimensional volumes. A nonparametric data-driven approach is used to define the space of defects, by considering defects observed via X-Ray computed tomography. The dimension of the ambient space for the observed images of defects is huge. A nonlinear dimensionality reduction scheme is proposed in order to train a reduced latent space for both the morphology of defects and their local mechanical effects in the TLV. A multimodal autoencoder enables to mix morphological and mechanical data. It contains a single latent space, termed mechanical latent space. But this latent space is fed by two encoders. One is related to the images of defects and the other to mechanical fields in the TLV. The latent variables are input variables for a geometrical decoder and for a mechanical decoder. In this work, mechanical variables are displacement fields. The autoencoder on mechanical variables enables projection-based model order reduction as proposed in the study of Lee and Carlberg. The main novelty of this paper is a submodeling approach assisted by artificial intelligence. Here, for defect images in the test set, Dirichlet boundary conditions are applied to TLV. These boundary conditions are forecasted by the mechanical decoder with a latent vector predicted by the morphological encoder. For that purpose, a mapping is trained to convert morphological latent variables into mechanical latent variables, denoted "direct mapping." An "inverse mapping" is also trained for error estimation with respect to morphological predictions. Errors on mechanical predictions are close to 5% with simulation speed-up ranging for 3 to 120. We show that latent variables forecasted by the images of defects are prone to a better understanding of the predictions.
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