Related papers: A Three-Dimensional Continuum Simulation Method fo…
Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
This paper discusses the free energy of complex dislocation microstructures, which is a fundamental property of continuum plasticity. In the past, multiple models of the self energy of dislocations have been proposed in the literature that…
To study the nanoscopic interaction between edge dislocations and a phase boundary within a two-phase microstructure the effect of the phase contrast on the internal stress field due to the dislocations needs to be taken into account. For…
Grain boundaries affect properties of polycrystalline materials. The influence of a boundary is largely determined by its energy. Grain boundary energy is often portrayed as a function of macroscopic boundary parameters representing grain…
Grain boundary migration governs microstructural evolution in crystalline materials, directly influencing mechanical properties such as strength and thermal stability. Disconnections, which are line defects formed at grain boundaries in…
We give a Dirichlet form approach for the construction of distorted Brownian motion in a bounded domain $\Omega$ of $\mathbb{R}^d$, $d \geq 1$, with boundary $\Gamma$, where the behavior at the boundary is sticky. The construction covers…
Pore-scale simulations accurately describe transport properties of fluids in the subsurface. These simulations enhance our understanding of applications such as assessing hydrogen storage efficiency and forecasting CO$_2$ sequestration…
Three-dimensional dislocation dynamics simulations are used to study micro-crack interaction with the first micro-structural barrier in face-centred cubic bi-crystals loaded in high cycle fatigue conditions. In the examined configuration,…
We aim at deriving an equation of motion for specific sums of momentum mode occupation numbers from models for electrons in periodic lattices experiencing elastic scattering, electron-phonon scattering or electron-electron scattering. These…
Grain boundary complexions have been observed to affect the mechanical behavior of nanocrystalline metals, improving both strength and ductility. While an explanation for the improved ductility exists, the observed effect on strength…
Thermomechanical processing such as annealing is one of the main methods to tailor the mechanical properties of materials, however, much is unknown about the reorganization of dislocation structures deep inside macroscopic crystals that…
We consider a continuum mathematical model of biological tissue formation inspired by recent experiments describing thin tissue growth in 3D-printed bioscaffolds. The continuum model involves a partial differential equation describing the…
We study kinetic theories for isotropic, two-dimensional grain boundary networks which evolve by curvature flow. The number densities $f_s(x,t)$ for $s$-sided grains, $s =1,2,\ldots$, of area $x$ at time $t$, are modeled by kinetic…
Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play an essential role in defining the materials properties across…
Solids with spatial variations in the crystalline axes naturally evolve into cells or grains separated by sharp walls. Such variations are mathematically described using the Nye dislocation density tensor. At high temperatures,…
This paper presents a novel formula for the transition density of the Brownian motion on a sphere of any dimension and discusses an algorithm for the simulation of the increments of the spherical Brownian motion based on this formula. The…
We develop an irreversible thermodynamics framework for the description of creep deformation in crystalline solids by mechanisms that involve vacancy diffusion and lattice site generation and annihilation. The material undergoing the creep…
The aim of this paper is to propose a novel methodology to deal with micro-structural boundary conditions for the analysis of granular materials. The response of the granular assembly is modelled through the discrete element method (DEM),…
The simulation of certain flow problems requires a means for modeling a free fluid surface; examples being viscoelastic die swell or fluid sloshing in tanks. In a finite-element context, this type of problem can, among many other options,…