Related papers: A new level set-finite element formulation for ani…
Obtaining microscopic structure-property relationships for grain boundaries are challenging because of the complex atomic structures that underlie their behavior. This has led to recent efforts to obtain these relationships with machine…
Two main existence theorems are proved for two nonstandard systems of parabolic initial-boundary value problems. The systems are based on the "$ \phi $-$ \eta $-$ \theta $ model" proposed by Kobayashi [RIMS Kokyuroku, 1210 (2001), 68-77] as…
A finite element framework is presented for analyzing crack-tip phenomena in transversely isotropic, strain-limiting elastic materials. Mechanical response is characterized by an algebraically nonlinear constitutive model, relating stress…
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…
We modify a theory of flow stress introduced in [arXiv:1803.08247[cond-mat.mtrl-sci]], [arXiv:1809.03628[cond-mat.mes-hall]], [arXiv:1908.09338[cond-mat.mtrl-sci]] for a class of polycrystalline materials with equilibrium and…
This paper presents adaptive boundary element methods for positive, negative, as well as zero order operator equations, together with proofs that they converge at certain rates. The convergence rates are quasi-optimal in a certain sense…
The evolution of grain structures in materials is a complex and multiscale process that determines the material's final properties. Understanding the dynamics of grain growth is a key factor for controlling this process. We propose a…
We solve a coarsening system with small but arbitrary anisotropic surface tension and interface mobility. The resulting size-dependent growth shapes are significantly different from equilibrium microcrystallites, and have a distribution of…
We propose a new nonconforming \(P_1\) finite element method for elliptic interface problems. The method is constructed on a locally anisotropic mixed mesh, which is generated by fitting the interface through a simple connection of…
The bulk behaviour of granular materials is tied to its mesoscale and particle-scale features: strength properties arise from the buildup of various anisotropic structures at the particle-scale induced by grain connectivity (fabric), force…
A phase field theory of polycrystalline solidification is presented that is able to describe the nucleation and growth of anisotropic particles with different crystallographic orientation in three dimensions. As opposed with the…
In this paper, we investigate a variational polycrystalline model in finite crystal plasticity with one active slip system and rigid elasticity. The task is to determine inner and outer bounds on the domain of the constrained macroscopic…
Knowledge about grain boundary migration is a prerequisite for understanding and ultimately modulating the properties of polycrystalline materials. Evidence from experiments and molecular dynamics (MD) simulations suggests that the…
Many technologically useful materials are polycrystals composed of a myriad of small monocrystalline grains separated by grain boundaries. Dynamics of grain boundaries play a crucial role in determining the grain structure and defining the…
Nanocrystalline metals contain a large fraction of high-energy grain boundaries, which may be considered as glassy phases. Consequently, with decreasing grain size, a crossover in the deformation behaviour of nanocrystals to that of…
Matter agglomeration mesoscopic phenomena of irreversible type are well described by nonequilibrium thermodynamics formalism. The description assumes that the thermodynamic (internal) state variables are in local equilibrium, and uses the…
In this work we conduct a numerical search of non-trivial mechanisms, leading to new tendencies towards long-range ferromagnetic ordering in two-dimensional materials. For this purpose we employ an original variant of pairwise infinitesimal…
This work presents a modeling framework to represent the thermomechanical behavior of complex materials based on micromechanical dynamics. The framework is applied to nuclear fuel rod elements composed of Zircaloy-2 cladding tubes and…
Grain microstructures are crucial to the mechanical properties, performance, and often lifetime of metallic components. Hence, the prediction of grain microstructures emerging from solidification processes at relevant macroscopic scale is…
Grain boundary networks should play a dominant role in determining the mechanical properties of nanocrystalline metals. However, these networks are difficult to characterize and their response to deformation is incompletely understood. In…