Dislocations in nanowire heterostructures: from discrete to continuum

We discuss an atomistic model for heterogeneous nanowires, allowing for dislocations at the interface. We study the limit as the atomic distance converges to zero, considering simultaneously a dimension reduction and the passage from discrete to continuum. Employing the notion of Gamma-convergence, we establish the minimal energies associated to defect-free configurations and configurations with dislocations at the interface, respectively. It turns out that dislocations are favoured if the thickness of the wire is sufficiently large

Rigidity of three-dimensional lattices and dimension reduction in heterogeneous nanowires

In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large

Chain-like ground states in three dimensions

Abstract We investigate the minimization of configurational energies of Brenner type. These include two- and three-body interaction terms, which favor the alignment of first neighbors. In particular, such configurational energies arise in connection with the molecular-mechanical modeling of covalent$sp$-bonding in carbon. Ground states in three dimensions are characterized and the stability of chains and rings is discussed. The interaction energy is then augmented with terms corresponding to weaker interactions favoring the stratification of configurations. This gives rise to stratified structures, which are reminiscent of nanoscrolls and multi-wall nanotubes. Optimal stratified configurations are identified and their geometry is discussed

Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish

The paper studies the asymptotic analysis of a model coupling elastoplasticity and damage depending on three parameters -- governing viscosity, plastic hardening, and convergence rate of plastic strain and displacement to equilibrium -- as they vanish in different orders. The notion of limit evolution obtained is proven to coincide in any case with a notion introduced by Crismale and Rossi in 2019; moreover, such solutions are closely related to those obtained in the vanishing-viscosity limit by Crismale and Lazzaroni in 2016, for the analogous model where only the viscosity parameter was present

On the visco-plastic approximation of a rate-independent coupled elastoplastic damage model

In this paper we study a rate-independent system for the propagation of damage and plasticity. To construct solutions we resort to approximation in terms of viscous evolutions, where viscosity affects both damage and plasticity with the same rate. The main difficulty arises from the fact that the available estimates do not provide sufficient regularity on the limiting evolutions to guarantee that forces and velocities are in a duality pairing, hence we cannot use a chain rule for the driving energy. Nonetheless, via careful techniques we can characterize the limiting rate-independent evolution by means of an energy-dissipation balance, which encodes the onset of viscous effects in the behavior of the system at jumps