The diffuse Nitsche method: Dirichlet constraints on phase-field boundaries

We explore diffuse formulations of Nitsche's method for consistently imposing Dirichlet boundary conditions on phase-field approximations of sharp domains. Leveraging the properties of the phase-field gradient, we derive the variational formulation of the diffuse Nitsche method by transferring all integrals associated with the Dirichlet boundary from a geometrically sharp surface format in the standard Nitsche method to a geometrically diffuse volumetric format. We also derive conditions for the stability of the discrete system and formulate a diffuse local eigenvalue problem, from which the stabilization parameter can be estimated automatically in each element. We advertise metastable phase-field solutions of the Allen-Cahn problem for transferring complex imaging data into diffuse geometric models. In particular, we discuss the use of mixed meshes, that is, an adaptively refined mesh for the phase-field in the diffuse boundary region and a uniform mesh for the representation of the physics-based solution fields. We illustrate accuracy and convergence properties of the diffuse Nitsche method and demonstrate its advantages over diffuse penalty-type methods. In the context of imaging based analysis, we show that the diffuse Nitsche method achieves the same accuracy as the standard Nitsche method with sharp surfaces, if the inherent length scales, i.e., the interface width of the phase-field, the voxel spacing and the mesh size, are properly related. We demonstrate the flexibility of the new method by analyzing stresses in a human vertebral body

SOLID-SHELL FINITE ELEMENT MODELS FOR EXPLICIT SIMULATIONS OF CRACK PROPAGATION IN THIN STRUCTURES

Crack propagation in thin shell structures due to cutting is conveniently simulated using explicit finite element approaches, in view of the high nonlinearity of the problem. Solidshell elements are usually preferred for the discretization in the presence of complex material behavior and degradation phenomena such as delamination, since they allow for a correct representation of the thickness geometry. However, in solid-shell elements the small thickness leads to a very high maximum eigenfrequency, which imply very small stable time-steps. A new selective mass scaling technique is proposed to increase the time-step size without affecting accuracy. New ”directional” cohesive interface elements are used in conjunction with selective mass scaling to account for the interaction with a sharp blade in cutting processes of thin ductile shells

The Secret Lives of Battery Materials: Core-Level Spectroscopy as a Probe of Compositional and Electronic Structure Inhomogeneities

The invention of rechargeable batteries has dramatically changed our landscapes and lives, underpinning the explosive worldwide growth of consumer electronics, ushering in an unprecedented era of electric vehicles, and potentially paving the way for a much greener energy future. Unfortunately, current battery technologies suffer from a number of challenges, e.g., capacity loss and failure upon prolonged cycling, limited ion diffusion kinetics, and a rather sparse palette of high-performing electrode materials. This dissertation will focus on elucidation of the influence of electronic structure on intercalation phenomena. Mechanistic understanding of compositional and electronic structure heterogeneities spanning from atomistic to mesoscale dimensions is imperative to facilitate the rational design of novel electrode chemistries and architectures. First, this dissertation provides an introduction to the fundamental science challenges involved in electrode design utilizing Vv2Ov5 as a model system to review means of defining ionic and electronic conduction pathways. Subsequently, the oxidative chemistry of graphite, a canonical anode material, is evaluated with the purpose of understanding the spatial localization and connectivity of functional groups in graphene oxide, which is of utmost relevance to the design of high-performing electrode composites. Furthermore, scanning transmission X-ray microscopy (STXM) observations indicate the formation of lithiation gradients in individual nanowires of layered orthorhombic Vv2Ov5 that arise from electron localization and local structural distortions. Electrons localized in the Vv2Ov5 framework couple to a local structural distortion, giving rise to small polarons, which are observed to be trap Li-ions and are found to represent a major impediment to Li-ion diffusion. In addition, this dissertation presents the first direct visualization of patterns of compositional inhomogeneities within cathode materials during electrochemical discharge. Two distinct patterns are evidenced: core—shell separation and striping modulations of Li-rich and Li-poor domains within individual particles. 3D compositional maps have been developed and translated to stress and strain maps, providing a hitherto unprecedented direct visualization of stress and strain inhomogeneities. Finally, a cluster of interlaced LivxVv2Ov5 nanoparticles is evaluated by scanning transmission X-ray microscopy. Increased heterogeneity at the interface between particles suggests the exchange of Li-ions, implying a “winner-takes-all” behavior (corresponding to particle-by-particle lithiation of an ensemble of particles). Such behavior portends the creation of localized hot-spots and provides insight into a possible origin of failure of Li-ion batteries