From identifying constituents to simulating the longitudinal strength of fiber-reinforced composites and microstructure optimization

Abstract: Carbon fibre-reinforced composites offer exceptional specific strength, but predicting their behaviour along the fibre axis remains a fundamental challenge. Existing models rely on simplifying assumptions about load transfer and fibre defect statistics, and require microscale characterization data that is rarely accessible in practice. This thesis addresses both difficulties: constituent properties are inferred from composite-scale measurements, and the resulting models are used directly for strength prediction and microstructure design.

The first part develops an inverse homogenization approach in which simple laminate tensile tests replace microscale or bulk experiments. Anisotropic elastic fibre properties and viscoelastic matrix properties are identified in situ, with uncertainty quantification confirming the robustness of the fibre identification. Experimental validation reveals differences between bulk and in situ matrix behaviour, underscoring the importance of scale-consistent characterization.

The second part introduces a strength prediction framework built entirely on full-field FFT computations, avoiding prescribed assumptions on load transfer by solving local equilibrium directly under progressive fibre failure. GPU acceleration and discrete damage modelling manage the associated computational cost. Comparison with benchmark data shows improved predictions, yet residual discrepancies point to a deeper issue: fibre strength cannot be treated as an intrinsic material property independent of scale. This observation motivates an inverse use of the framework, in which temperature-dependent strength tests are used to infer the in situ fibre defect distribution, in a logic that mirrors the matrix identification in Part 1.

The final part combines the sensitivity tools from Part 1 with the FFT solvers from Part 2 to address microstructure design. The resulting method, Kairotop, optimizes disordered microstructures toward target mechanical or transport properties, without prescribing a geometry. By exploiting rather than suppressing the initial randomness of the microstructure, it produces architectures that are both optimized and morphologically disordered.

Jury

Yentl Swolfs, reviewer, Research Professor, Department of Materials Engineering, KU Leuven
Renald Brenner, reviewer, Directeur de recherche CNRS, Institut Jean le Rond d’Alembert, Sorbonne Université
Nicolas Carrere, examiner, Professeur, ENSTA Bretagne
Julie Diani, examiner, Directrice de recherche CNRS, Laboratoire de mécanique des solides (LMS), École Polytechnique
Sébastien Joannès, examiner, Chargé de recherche CNRS, Centre des matériaux, Mines ParisTech
Lionel Gélébart, examiner, Ingénieur de recherche, CEA Saclay
Noël Lahellec, examiner (co-supervisor), Professeur, LMA, Aix-Marseille Université
Cédric Bellis, examiner (co-supervisor), Chargé de recherche CNRS, LMA
Christian Hochard, invited (co-supervisor), Professeur, LMA, Aix-Marseille Université

La soutenance de thèse de Robin Valmalette est prévue le 3 juin à 14h00 - amphithéâtre du LMA