Mesoscale Dzyaloshinskii-Moriya interaction: Geometrical tailoring of the magnetochirality

Crystals with broken inversion symmetry can host fundamentally appealing and technologically relevant periodical or localized chiral magnetic textures. The type of the texture as well as its magnetochiral properties are determined by the intrinsic Dzyaloshinskii-Moriya interaction (DMI), which is a material property and can hardly be changed. Here we put forth a method to create new artificial chiral nanoscale objects with tunable magnetochiral properties from standard magnetic materials by using geometrical manipulations. We introduce a mesoscale Dzyaloshinskii-Moriya interaction that combines the intrinsic spin-orbit and extrinsic curvature-driven DMI terms and depends both on the material and geometrical parameters. The vector of the mesoscale DMI determines magnetochiral properties of any curved magnetic system with broken inversion symmetry. The strength and orientation of this vector can be changed by properly choosing the geometry. For a specific example of nanosized magnetic helix, the same material system with different geometrical parameters can acquire one of three zero-temperature magnetic phases, namely, phase with a quasitangential magnetization state, phase with a periodical state and one intermediate phase with a periodical domain wall state. Our approach paves the way towards the realization of a new class of nanoscale spintronic and spinorbitronic devices with the geometrically tunable magnetochirality

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

Methods in Modelling of Composite Materials with Microstructure

Composite material properties are dependent on their microstructure. To adequately model these materials, a revised formulation of elasticity that accounts for microstructural effects must be considered. Size dependent behaviour is an inherent property of such materials, resulting in a need for non-classical continuum theories for adequate characterization. The modelling of bi-material composites is investigated, with emphasis on how material microstructure impacts the overall behaviour of continua. The work aims to provide mathematical models capable of predicting the homogenized material response under specified loads given known constituent properties, for eventual use in creating design provisions, integration into numerical simulations, and further applications in materials research. Specifically, this thesis considers Cosserat (micropolar) elasticity to model microstructural effects. Fiber reinforced composites with unidirectional fibers are modelled as transversely isotropic materials under the framework of Cosserat elasticity. The model assumes a periodic microstructure and develops a boundary condition to account for the periodicity. The governing equations for plane strain are developed, with the conditions for existence and uniqueness of the solution established. A three-dimensional model for an exponentially graded composite with microstructural effects is developed under the framework of Cosserat elasticity. The mixed boundary value problem is formulated and existence and uniqueness of a weak solution is established for use in accordance with the finite element method. The finite element formulation is developed and integrated into the commercial software Abaqus through a user developed element, with an associated post processing code for output visualization. Given a lack of elastic constants from experiments, validation is partially obtained through recovery of the classical limit. Following this, a conceptual extension to demonstrate a proof of concept is applied, with conclusions drawn based on the results. Recommendations for future extensions of the model are provided

An isogeometric boundary element formulation for stress concentration problems in couple stress elasticity

An isogeometric boundary element method (IGABEM) is developed for the analysis of two-dimensional linear and isotropic elastic bodies governed by the couple stress theory. This theory is the simplest generalised continuum theory that can eectively model size eects in solids. The couple stress fundamental solutions are explicitly derived and used to construct the boundary integral equations. A new boundary integral equation arises to obtain the moments and rotations introduced by the couple stress formulation. A new analytical solution is also derived in the present work for an elliptical opening in an innite sheet under uniaxial far-eld stress. Several stress concentration problems are examined to illustrate and validate the application of the IGABEM in couple stress elasticity. It is shown that the IGABEM scheme exhibits advantageous convergence properties in comparison with the conventional BEM for boundary value problems within the framework of couple stress elasticity

Multi-scale Modelling and Design of Composite Structures

L'abstract è presente nell'allegato / the abstract is in the attachmen

From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.Comment: Version 1.1, 50 pages, 6 figures. To appear in "Open Problems in Mathematics", Editors John Nash and Michael Th. Rassias. arXiv admin note: text overlap with arXiv:0909.491

A review of nonlinear FFT-based computational homogenization methods

Since their inception, computational homogenization methods based on the fast Fourier transform (FFT) have grown in popularity, establishing themselves as a powerful tool applicable to complex, digitized microstructures. At the same time, the understanding of the underlying principles has grown, in terms of both discretization schemes and solution methods, leading to improvements of the original approach and extending the applications. This article provides a condensed overview of results scattered throughout the literature and guides the reader to the current state of the art in nonlinear computational homogenization methods using the fast Fourier transform