Related papers: Continuum model for dislocation structures of semi…
In this paper we consider the equilibrium problem in the relaxed linear model of micromorphic elastic materials. The basic kinematical fields of this extended continuum model are the displacement $u\in \mathbb{R}^3$ and the non-symmetric…
We find analytical solutions to the Cahn-Hilliard equation for the dynamics of an interface in a system with a conserved order parameter (Model B). We show that, although steady-state solutions of Model B are unphysical in the far-field,…
We focus on existence and rigidity problems of the vectorial Peierls-Nabarro (PN) model for dislocations. Under the assumption that the misfit potential on the slip plane only depends on the shear displacement along the Burgers vector, a…
This article concerns a systemic manifestation of small scale interfacial heterogeneities in large scale quantities of interest to a variety of diverse applications spanning the earth, biological and ecological sciences. Beginning with…
The Burgers distortion is a two-stage transition between body centered cubic (BCC) and hexagonal close-packed (HCP) structures. Refractory metal elements from the Sc and Ti columns of the periodic table (BCC/HCP elements) form BCC…
Interfaces such as grain boundaries in polycrystalline as well as heterointerfaces in multiphase solids are ubiquitous in materials science and engineering. Far from being featureless dividing surfaces between neighboring crystals,…
This work presents a finite element method for simulating dynamic processes that involve the coupled evolution of dislocation motion and crack propagation. The method numerically solves the Concurrent Atomistic-Continuum (CAC) formulation…
Persistence problems in weighted spaces have been studied for different dispersive models involving non-local operators. Generally, these models do not propagate polynomial weights of arbitrary magnitude, and the maximum decay rate is…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is also…
In recent years, the behavior of dislocations in random solid solutions has received renewed interest, and several models have been discussed where random alloys are treated as effective media containing random distributions of dilatation…
We propose an energy-stable parametric finite element method (ES-PFEM) for simulating solid-state dewetting of thin films in two dimensions via a sharp-interface model, which is governed by surface diffusion and contact line (point)…
Interface cracking is one of the most prominent failure modes in fibre reinforced polymer (FRP) composites. Recent trends in high-tech applications of FRP composites exploit the limits of the load bearing capacity, generally encompassing…
In Part I of this set of two papers, a model of mesoscopic plasticity is developed for studying initial-boundary value problems of small scale plasticity. Here we make qualitative, finite element method-based computational predictions of…
The present work provides fundamental quantities in generalized elasticity and dislocation theory of quasicrystals. In a clear and straightforward manner, the three-dimensional Green tensor of generalized elasticity theory and the extended…
High entropy alloys (HEAs) are single phase crystals that consist of random solid solutions of multiple elements in approximately equal proportions. This class of novel materials have exhibited superb mechanical properties, such as high…
The methods of non-equilibrium thermodynamics of systems with an interface have been applied to the study of transport processes in semiconductor junctions. A complete phenomenological model for drift-diffusion processes in a junction has…
We develop a novel nonlocal model of dislocations based on the framework of peridynamics. By embedding interior discontinuities into the nonlocal constitutive law, the displacement jump in the Volterra dislocation model is reproduced,…
A computational approach has been developed for the analysis of the properties of 3D dislocation substructures generated by the vector density continuum dislocation dynamics (CDD), within the framework of crystal plasticity. In the CDD…
Coarse grained, macroscale, spatial discretisations of nonlinear nonautonomous partial differential\difference equations are given novel support by centre manifold theory. Dividing the physical domain into overlapping macroscale elements…
We rigorously prove the bifurcation of slow-moving pattern interfaces with general direction in a two-dimensional Swift-Hohenberg-type model close to a Turing instability for a large class of nonlinearities. These interfaces describe the…