Additive Manufacturing (AM) and digital imaging are currently revolutionising the area of mechanics of materials. AM now allows the fabrication of industrially-relevant cellular architected structures called lattices. However, AM generates non-negligible strut-level defects compared to the initial Computer-Aided Design (CAD). Volume imaging such as X-ray Computed Tomography opens the door for finely analysing such defects and, by means of data assimilation between measured fields obtained by Digital Volume Correlation (DVC) and simulated fields obtained by image-based modelling, for truly characterizing the behaviour of the lattice.
Yet, three challenges need to be addressed:
- the geometric description of the defect must be compatible with CAD to characterize the geometric variability;
- it is requested to measure kinematic fields at the sub-cellular scale while the texture is very weak at this scale;
- the need of high-fidelity descriptions and the explosion of camera sensor definition require developing HPC tools at each step of the workflow.
The goal of this project is to answer these issues to build a mechanical virtual twin of the lattice at the architecture scale by benefiting of the today massive image data. The proposed methodology relies on the construction and HPC of a dedicated spline-parametrized model. More precisely, we will:
- consider spline composition for the geometrical modelling which allows an explicit description of the geometric variability (inspired from [1]);
- assist DVC with a physically-sound weak regularization using a simple linear-elastic image-based model (inspired from [2]);
- develop specific procedures in the field of IsoGeometric Analysis (IGA) for fast assembly as well as for scalable matrix-free solutions based on domain decomposition (inspired from [3,4,5]), that benefit from the repetitiveness of the cell pattern.
The consortium is composed of the Institute of Mathematics of Toulouse (IMT, UMR 5219), the laboratory of computer sciences LIP6 from Sorbonne University (LIP6, UMR 7606), the Clément Ader Institute (i.e., the laboratory of mechanics of Toulouse, ICA, UMR 5312), and the chair of numerical modeling and Simulation at EPFL, Switzerland. It thus covers the interdisciplinary skills required for a successful completion of this project, namely applied mathematics, computer sciences and mechanics through different fields like IGA, HPC, (image) data assimilation, material science and experimental mechanics.
Main references upon which the project is based:
[1] T. Hirschler, P. Antolin, and A. Buffa. Fast and multiscale formation of isogeometric matrices of microstructured geometric models.
Computational Mechanics, 69, 439-466. 2022
[DOI]
[ARXIV]
[2] A. Rouwane, R. Bouclier, J.C. Passieux and J.N. Périé. Architecture-Driven Digital Image Correlation Technique (ADDICT) for the measurement of sub-cellular kinematic fields in speckle-free cellular materials.
International Journal of Solids and Structures, 234-235, 111223. 2022
[DOI]
[HAL]
[3] P. Jolivet, M.A. Badri and Y. Favennec. Deterministic radiative transfer equation solver on unstructured tetrahedral meshes: efficient assembly and preconditioning.
Journal of Computational Physics, 437. 2021
[DOI]
[HAL]
[4] T. Hirschler, R. Bouclier, D. Dureisseix, A. Duval, T. Elguedj, and J. Morlier. A dual domain decomposition algorithm for the analysis of non-conforming isogeometric Kirchhoff–Love shells.
Computer Methods in Applied Mechanics and Engineering, 357, 112578. 2019
[DOI]
[HAL]
[5] R. Bouclier and J.C. Passieux. A domain coupling method for finite element digital image correlation with mechanical regularization: Application to multiscale measurements and parallel computing.
International Journal for Numerical Methods in Engineering, 111, 123-143. 2017
[DOI]
[HAL]
