Bridging CAD, Image Data and Mechanics for Digital Twins of Additively Manufactured TPMS Lattice Metamaterials

Lightweight load-bearing structures are a cornerstone of the sustainable transition in aeronautics and space, where every gram saved reduces fuel consumption and emissions. Architected lattice metamaterials, in particular shell-based Triply Periodic Minimal Surface (TPMS) lattices produced by metal additive manufacturing, offer outstanding stiffness-to-weight ratios and are prime candidates to lighten engine and structural components such as turbine blades. However, the manufacturing process introduces geometric defects (wall-thickness variations, shape distortion, surface bias) that make the manufactured part deviate from its idealized CAD design, which today limits the adoption of such parts for demanding aerospace use. This PhD tackles this challenge by building 'digital image-to-mechanical twins' of as-manufactured lattices. The latter are sought to be compact, accurate and CAD-compatible numerical replicas, reconstructed directly from X-ray computed-tomography images. Such twins are built to predict the real mechanical response of the printed structure together with its uncertainty. The project sits at the crossroads of three exciting fields: computer-aided geometric design, computational mechanics and experimental mechanics; and mobilizes cutting-edge tools including isogeometric analysis, image data assimilation and machine learning. More precisely, the work is organized around three goals. (a) From image to geometry: reconstruct a smooth, analysis-suitable shell model of the defected lattice using recent multi-sided 'General Bézier' patches together with a novel virtual image-correlation method that fits the volume image data. (b) From geometry to uncertainties: exploit the massive redundancy of cells in lattice structures (a single specimen contains thousands of nominally identical cells) to let machine learning discover a compact probabilistic model of the defects while staying explicitly linked to the original CAD. (c) From uncertain geometries to reliable prediction: implement an efficient isogeometric shell solver to compute the mechanical behavior of lattices made of many cells and quantify how defect variability affects the effective stiffness. As a longer-term perspective, the developed pipeline could also be used to pre-compensate the CAD so that the printed part matches the intended geometry. Beyond simulation, the project has a strong real-data component: the candidate will work with actual tomographic images of printed lattices and will take part in the experimental tasks (printing lattice specimens and imaging them by tomography) to generate the data needed to validate the methods. Overall, this is a genuinely interdisciplinary project on timely topics at the interface of applied mathematics, mechanical engineering and data science. It benefits from an appealing research environment: an international co-supervision between the Clément Ader Institute (INSA Toulouse, France) and the Basque Center for Applied Mathematics (BCAM, Bilbao, Spain), a co-supervision with a socio-economic partner, IRT Saint Exupéry, a planned research mobility between the two laboratories, and full access to the fabrication, imaging and computing resources needed to carry the work through from design to experimental validation. École doctorale : MEGEP - Mécanique, Energétique, Génie civil, Procédés Direction : Robin BOUCLIER Financement : MSCA COFUND BEST