Related papers: Mechanical Analyses using Discrete Harmonic Expans…
The application of harmonic expansions to estimate intra-grain stress distributions from grain-averaged stress data is presented that extends the capabilities of the open source code, MechMonics. The method is based on using an optimization…
A rigorous methodology is developed for computing elastic fields generated by experimentally observed defect structures within grains in a polycrystal that has undergone tensile extension. An example application is made using a near-field…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
Wide-area synchrophasor ambient measurements provide a valuable data source for real-time oscillation mode monitoring and analysis. This paper introduces a novel method for identifying inter-area oscillation modes using wide-area ambient…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…
The spatial variability of stress fields resulting from polycrystalline aggregate calculations involving random grain geometry and crystal orientations is investigated. A periodogram-based method is proposed to identify the properties of…
We present a novel formalism to characterize elastic heterogeneities in amorphous solids. In particular, we derive high-order strain-energy expansions for pairwise energies under athermal quasistatic dynamics. We then use the presented…
To develop, calibrate and/or validate continuum models from experimental or numerical data, micro-macro transition methods are required. These methods are used to obtain the continuum fields (such as density, momentum, stress) from the…
A method for the evaluation of the epsilon expansion of multi-loop massless Feynman integrals is introduced. This method is based on the Gegenbauer polynomial technique and the expansion of the Gamma function in terms of harmonic sums.…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
A simple micromechanical model of polycrystalline materials is proposed, which enables us to swiftly produce grain-boundary-stress distributions induced by the uniform external loading (in the elastic strain regime). Such statistical…
The specificity of modal-expansion formalisms is their capabilities to model the physical properties in the natural resonance-state basis of the system in question, leading to a transparent interpretation of the numerical results. In…
The study of polycrystalline materials requires theoretical and computational techniques enabling multiscale investigations. The amplitude expansion of the phase field crystal model (APFC) allows for describing crystal lattice properties on…
We present the applications of methods from nonlinear local harmonic analysis in variational framework to calculations of nonlinear motions in polynomial/rational approximations (up to any order) of arbitrary n-pole fields. Our approach is…
We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities:…
Effective harmonic methods allow for calculating temperature dependent phonon frequencies by incorporating the anharmonic contributions into an effective harmonic Hamiltonian. The systematic errors arising from such an approximation are…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
A mesoscopic grain-envelope model applying a phase-field front-propagation method is developed to simulate grain growth under additive manufacturing process conditions. The envelope represents the outer surface of dendritic grains through a…
The traditional techniques for extracting polycrystalline grain structures from microscopy images, such as transmission electron microscopy (TEM) and scanning electron microscopy (SEM), are labour-intensive, subjective, and time-consuming,…
FFT-based solvers are increasingly used by many researcher groups interested in modelling the mechanical behavior associated to a heterogeneous microstructure. A development is reported here that concerns the viscoelastic behavior of…