Discrete fiber models beyond classical applications: Rigid line inclusions, fiber-based batteries, challenges

Reinforced composites are used in many industrial and multi-functional applications. The efficiency of the reinforcements depends mainly on the aspect ratio, material properties, and the adhesion between matrix and reinforcement. Particularly, high aspect ratio fillers and inclusions have gained popularity due to their unique material and geometrical features, where a fundamental understanding of composites hierarchical structure and behavior is crucial for the optimal design and performance. There is however a lack of robust numerical modeling frameworks that are able to accurately represent composites with high aspect ratio reinforcements. Ideally the expensive mesh generation of the standard finite element method or the simplifying assumptions adopted by smeared type or mean-field approaches should be avoided.
A group of numerical techniques here referred to as "embedded methods" eliminate mesh conformity restrictions and significantly reduce the computational cost of the standard finite element method, while still benefiting from the advantages of a direct numerical analysis. In formulating the embedded models, enrichment techniques and different element technologies are considered, and physical assumptions are investigated. Limitations of the classical embedded models are highlighted through numerical examples, on the basis of which possible enhancements are discussed. We specifically highlight the important roles of field gradients continuity/discontinuity and the element size, order, and regularity extensions on the smoothness of the solutions.
A computationally efficient embedded model is then applied to the study of failure and inclusion orientation effects in planar composites. A detailed study is also performed for dense fiber-reinforced composites, where homogenized mechanical properties are extracted and various forms of neutrality of thin fibers are demonstrated. In this context, a part of this thesis is dedicated to one-to-one comparisons between results obtained using the standard finite element method and embedded techniques. This led to a range of model and geometry parameters under which predictions of embedded technique are reliable. Comparisons are reported in terms of homogenized properties and local field variables, namely relative displacement between inclusions and matrix (slips).
Finally as a preliminary step towards multi-functional fiber-based structural batteries, an electro-chemical system characterized by composite cathode in a half cell configuration is considered. The main point of difference with common composite batteries is that active material particles are cast in form of high aspect ratio fibers, which are efficiently discretized by use of the embedded technique. A discrete definition of fibers, unlike the case of mean-field approaches, allows to define local fields and interfacial conditions between fibers and electrolyte and is crucial for the accurate modelling of a battery cell with fiber-based electrodes.