We study the properties of strain bursts (dislocation avalanches) occurring in two-dimensional discrete dislocation dynamics models under quasistatic stress-controlled loading. Contrary to previous suggestions, the avalanche statistics differ fundamentally from predictions obtained for the depinning of elastic manifolds in quenched random media. Instead, we find an exponent $$\tau${}=1$ of the power-law distribution of slip or released energy, with a cutoff that increases exponentially with the applied stress and diverges with system size at all stresses. These observations demonstrate that the avalanche dynamics of 2D dislocation systems is scale-free at every applied stress and, therefore, cannot be envisaged in terms of critical behavior associated with a depinning transition.

A multitude of systems ranging from the Barkhausen effect in ferromagnetic materials to plastic deformation and earthquakes respond to slow external driving by exhibiting intermittent, scale-free avalanche dynamics or crackling noise. The avalanches are power-law distributed in size, and have a typical average shape: these are the two most important signatures of avalanching systems. Here we show how the average avalanche shape evolves with the universality class of the avalanche dynamics by employing a combination of scaling theory, extensive numerical simulations and data from crack propagation experiments. It follows a simple scaling form parameterized by two numbers, the scaling exponent relating the average avalanche size to its duration and a parameter characterizing the temporal asymmetry of the avalanches. The latter reflects a broken time-reversal symmetry in the avalanche dynamics, emerging from the local nature of the interaction kernel mediating the avalanche dynamics.

We study avalanches in a model for a planar crack propagating in a disordered medium. Due to long-range interactions, avalanches are formed by a set of spatially disconnected local clusters, the sizes of which are distributed according to a power law with an exponent $\tau${}a=1.5. We derive a scaling relation $\tau${}a=2$\tau${}$-${}1 between the local cluster exponent $\tau${}a and the global avalanche exponent $\tau${}. For length scales longer than a crossover length proportional to the Larkin length, the aspect ratio of the local clusters scales with the roughness exponent of the line model. Our analysis provides an explanation for experimental results on planar crack avalanches in Plexiglas plates, but the results are applicable also to other systems with long-range interactions.

Plastic deformation of micron-scale crystalline solids exhibits stress-strain curves with significant sample-to-sample variations. It is a pertinent question if this variability is purely random or to some extent predictable. Here we show, by employing machine learning techniques such as regression neural networks and support vector machines that deformation predictability evolves with strain and crystal size. Using data from discrete dislocations dynamics simulations, the machine learning models are trained to infer the mapping from features of the pre-existing dislocation configuration to the stress-strain curves. The predictability vs strain relation is non-monotonic and exhibits a system size effect: larger systems are more predictable. Stochastic deformation avalanches give rise to fundamental limits of deformation predictability for intermediate strains. However, the large-strain deformation dynamics of the samples can be predicted surprisingly well.

A complete understanding of domain wall motion in magnetic nanowires is required to enable future nanowire based spintronics devices to work reliably. The production process dictates that the samples are polycrystalline. In this contribution, we present a method to investigate the effects of material grains on domain wall motion using the GPU-based micromagnetic software package MuMax3. We use this method to study current-driven vortex domain wall motion in polycrystalline Permalloy nanowires and find that the influence of material grains is fourfold: an extrinsic pinning at low current densities, an increasing effective damping with disorder strength, shifts in the Walker breakdown current density, and the possibility of the vortex core to switch polarity at grain boundaries.

The stress-driven motion of dislocations in crystalline solids, and thus the ensuing plastic deformation process, is greatly influenced by the presence or absence of various pointlike defects such as precipitates or solute atoms. These defects act as obstacles for dislocation motion and hence affect the mechanical properties of the material. Here we combine molecular dynamics studies with three-dimensional discrete dislocation dynamics simulations in order to model the interaction between different kinds of precipitates and a $\frac{1}{2}\langle 111\rangle \left\{110\right\}$ edge dislocation in BCC iron. We have implemented immobile spherical precipitates into the ParaDis discrete dislocation dynamics code, with the dislocations interacting with the precipitates via a Gaussian potential, generating a normal force acting on the dislocation segments. The parameters used in the discrete dislocation dynamics simulations for the precipitate potential, the dislocation mobility, shear modulus, and dislocation core energy are obtained from molecular dynamics simulations. We compare the critical stresses needed to unpin the dislocation from the precipitate in molecular dynamics and discrete dislocation dynamics simulations in order to fit the two methods together and discuss the variety of the relevant pinning and depinning mechanisms.