Related papers: An energy-consistent model of dislocation dynamics…
This note collects some results on the behaviour of screw dislocation in an elastic medium. By using a semi-discrete model, we are able to investigate two specific aspects of the dynamics, namely (i) the interaction with free boundaries and…
In this paper a geometric field theory of dislocation dynamics and finite plasticity in single crystals is formulated. Starting from the multiplicative decomposition of the deformation gradient into elastic and plastic parts, we use…
We formulate and study a stochastic model for the thermally-driven motion of interacting straight screw dislocations in a cylindrical domain with a convex polygonal cross-section. Motion is modelled as a Markov jump process, where waiting…
A non-isothermal phase field model that captures both displacive and diffusive phase transformations in a unified framework is presented. The model is developed in a formal thermodynamic setting, which provides guidance on admissible…
We propose nonlinear semi-discrete and discrete models for the elastic energy induced by a finite systems of edge dislocations in two dimensions. Within the dilute regime, we analyze the asymptotic behavior of the nonlinear elastic energy,…
A continuum model to study the influence of dislocations on the electronic properties of condensed matter systems is described and analyzed. The model is based on a geometrical formalism that associates a density of dislocations with the…
We consider the energetic description of a visco-plastic evolution and derive an existence result. The energies are convex, but not necessarily quadratic. Our model is a strain gradient model in which the curl of the plastic strain…
This paper focuses on an elastic dislocation problem that is motivated by applications in the geophysical and seismological communities. In our model, the displacement satisfies the Lam\'e system in a bounded domain with a mixed homogeneous…
In this paper we consider the dynamics of dislocations with the same Burgers vector, contained in the same glide plane, and moving in a material with periodic obstacles. We study two cases: i) the particular case of parallel straight…
We develop a model for the gliding of dislocations and plasticity in solid He-4. This model takes into account the Peierls barrier, multiplication and interaction of dislocations, as well as classical thermally and mechanically activated…
We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…
The elastodynamic Peach-Koehler force is computed for a fully-regularized straight dislocation with isotropic core in continuum isotropic elastic elasticity, in compact forms involving partial mass or impulsion functions relative to shear…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
Because of the enormous range of time and space scales involved in dislocation dynamics, plastic modeling at macroscale requires a continuous formulation. In this paper, we present a rigorous formulation of the transition between the…
We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated…
A theoretical framework for dislocation dynamics in quasicrystals is provided according to the continuum theory of dislocations. Firstly, we present the fundamental theory for moving dislocations in quasicrystals giving the dislocation…
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…
We give a complete and rigorous derivation of the mechanical energy for twisted 2D bilayer heterostructures without any approximation beyond the existence of an empirical many-body site energy. Our results apply to both the continuous and…
We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion,…
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…