Conventional battery models (e.g., Pseudo-2D model) were developed especially for particle-based battery electrodes and have limitations in addressing the newly-emerging fiber-based ones. This thesis proposes numerical tools for efficient property evaluation of fiber-based electrodes and for multiscale simulation of battery electrochemical behavior. 
An efficient computational model is first developed to evaluate percolation threshold, effective electronic conductivity, and capacity of fiber-based electrodes. The electrode is composed of conductive and active fibers mixed in an electrolyte matrix. This model rests with generation of randomly-distributed fibers by Monte Carlo method. The connection between conductive fibers is used to determine percolation threshold and electronic conductivity, while the connection between conductive and active fibers defines the active material utilization and capacity. An optimal active-conductive material ratio is identified to maximize the electrode capacity, and the study of fiber orientation effect reveals that the isotropic distribution leads to the highest utilization of active fibers. 
For more accurate estimation, a FE² multiscale framework is further proposed to solve physics-based governing equations. The first part extends the conventional FE² method suited to a one-equation model to transient diffusion in a two-phase medium described by a two-equation model. The new features include the macroscale equations derived by the volume-averaging method and separate treatment of the two phases in terms of information exchange between macro- and micro-scales and boundary conditions of the microscale problem. The differentiation of the two phases results in additional macroscale source terms upscaled from the microscale interfacial flux. Unlike effective material properties, the tangents of the interfacial flux depend on the microscopic length scale. 
The second part of the FE² framework addresses the ionic transport in the pore-filling electrolyte of separators, ignoring the interfacial flux between the electrolyte and the active material. The FE² method features a macroscale constitutive relation numerically obtained, rather than assumed as in Pseudo-2D model and many of the existing models, from microscale simulation results. This unique feature enables the FE² method to allow for nonlinear (concentration-dependent) transport properties at the microscale and reflect them at the macroscale without postulation. The well-defined microscale problem setting results in effective transport properties expressed in a tensor format that is indispensable for an anisotropic microstructure. 

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.

The emergence of new kinds of micro-technologies, e.g., MEMS (microelectromechanical systems) devices, biomedical microma- chines, remote sensors, etc., has given rise to new approaches in battery development. The additional thesis contributes part of Finite Element Analysis of microbatteries, to be specific, the trenched mirobatteries architecture. The project aims to perform a parametric study of micro-battery, including a python script implemented and an example of asymmetric trench model simulation. The python executable allows to run the parametric study in an automatic way. The asymmetric working example provides a generic trench model template.

The python executable consists of six functional blocks, namely: reading the input data from users, generating meshes with multiple parameters, splitting the interface nodes, refining the mesh files, running the simulations, and collecting the generic output parameter. Generating meshes allows users to create 2D triangle mesh with two parameters for a given geometry. Splitting the interface nodes uses a generic manner to split interfaces for an arbitrary structure. Once splitting interface is done, the executable is able to seek the new nodes on the interface and compile them in a prescribed fashion before simulation. Coming into the last part, the executable makes use of a set of external programs to run Jem-Jive carrying out the relative outcome. A simple case will go through every step how this script works, after which a more complicated model will be illustrated.

Generally, though taking the advantage of symmetry of trench makes the parametric study easier and straightforward to handle with, which only the half of trench is considered, an asymmetric trench model is more probable and realistic. An example is provided afterwards with five pillars which not only their length may vary, but imperfection is introduced here: pillars can be slightly inclined as well until they touch each other. An important property worth noticing is the top and bottom of the trench stay smoothie although inclination occurs and the neutral layer of pillar still remains the same length. The example gives a detailed universal geometric derivation and formulas with respect to heights and inclined angles, which are regarded as two relative variables implemented by the python executable mentioned above.