Numerical simulations of crystal defects are necessarily restricted to finite computational
domains, supplying artificial boundary conditions that emulate the effect of embedding the …

This paper aims at building a variational approach to the dynamics of discrete topological
singularities in two dimensions, based on Γ-convergence. We consider discrete systems …

In this paper we derive a line tension model for dislocations in 3D starting from a
geometrically nonlinear elastic energy with quadratic growth. In the asymptotic analysis, as …

We develop a rigorous framework for modeling the geometry equilibration of crystalline
defects. We formulate the equilibration of crystal defects as a variational problem on a …

We present a comprehensive error analysis of two prototypical atomistic-to-continuum
coupling methods of blending type: the energy-based and the force-based quasicontinuum …

This work introduces a model for large-strain, geometrically nonlinear elasto-plastic
dynamics in single crystals. The key feature of our model is that the plastic dynamics are …

In linearized continuum elasticity, the elastic strain due to a straight dislocation line decays
as O(r^-1), where r denotes the distance to the defect core. It is shown in V. Ehrlacher, C …

We consider crack propagation in a crystalline material in terms of bifurcation analysis. We
provide evidence that the stress intensity factor is a natural bifurcation parameter, and that …

The elastic field around a crack opening is known to be described by continuum linearised
elasticity in leading order. In this work, we explicitly develop the next term in the atomistic …

We consider a simple discrete model for screw dislocations in crystals. Using a variational
discrete scheme we study the motion of a configuration of dislocations toward low energy …