Dislocation-mediated growth of bacterial cell walls

Recent experiments have illuminated a remarkable growth mechanism of rod-shaped bacteria: proteins associated with cell wall extension move at constant velocity in circles oriented approximately along the cell circumference (Garner et al., Science (2011), Dominguez-Escobar et al. Science (2011), van Teeffelen et al. PNAS (2011). We view these as dislocations in the partially ordered peptidoglycan structure, activated by glycan strand extension machinery, and study theoretically the dynamics of these interacting defects on the surface of a cylinder. Generation and motion of these interacting defects lead to surprising effects arising from the cylindrical geometry, with important implications for growth. We also discuss how long range elastic interactions and turgor pressure affect the dynamics of the fraction of actively moving dislocations in the bacterial cell wall.Comment: to appear in PNA

Scale-free phase field theory of dislocations

According to recent experimental and numerical investigations if the characteristic size of a specimen is in the submicron size regime several new interesting phenomena emerge during the deformation of the samples. Since in such a systems the boundaries play a crucial role, to model the plastic response of submicron sized crystals it is crucial to determine the dislocation distribution near the boundaries. In this paper a phase field type of continuum theory of the time evolution of an ensemble of parallel edge dislocations with identical Burgers vectors, corresponding to the dislocation geometry near boundaries, is presented. Since the dislocation-dislocation interaction is scale free ($1/r$), apart from the average dislocation spacing the theory cannot contain any length scale parameter. As shown, the continuum theory suggested is able to recover the dislocation distribution near boundaries obtained by discrete dislocation dynamics simulations

Efficient numerical method to handle boundary conditions in 2D elastic media

A numerical method is developed to efficiently calculate the stress (and displacement) field in finite 2D rectangular media. The solution is expanded on a function basis with elements that satisfy the Navier-Cauchy equation. The obtained solution approximates the boundary conditions with their finite Fourier series. The method is capable to handle Dirichlet, Neumann and mixed boundary value problems as well and it was found to converge exponentially fast to the analytical solution with respect to the size of the basis. Possible application in discrete dislocation dynamics simulations is discussed and compared to the widely used finite element methods: it was found that the new method is superior in terms of computational complexity.Comment: 21 pages, 10 figure

Plastic deformation of microsamples: Intermittent dislocation avalanches and their acoustic emission

On the micrometer scale, deformation properties of metals change profoundly: the smooth and continuous behavior of bulk materials is often replaced by jerky flow due to random strain bursts of various sizes. The reason for this behavior is the complex intermittent redistribution of lattice dislocations due to external loading. This process also leads to the formation of the uneven step-like surface upon deformation. Our highly sensitive micromechanical platform can detect the strain bursts caused by dislocation avalanches in three different ways: (i) by stress and strain measurements using a capacitive displacement sensor measuring the elongation of a spring, (ii) by detection of the emitted acoustic signal using a sensitive piezoelectric transducer and (iii) by visual images using the electron beam of the SEM. In my presentation, I will present two of our recent results obtained with the help of this toolbox. Please click Download on the upper right corner to see the full abstract

Instability of dislocation fluxes in a single slip: Deterministic and stochastic models of dislocation patterning

We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism that relates the formation of heterogeneous patterns with a well-defined wavelength to the stress-driven dynamics of dislocation densities that tries to minimize the internal energy while subject to dynamic constraints and a density-dependent, friction-like flow stress. This leads us to an interpretation that resolves the old "energetic vs dynamic" controversy regarding the physical origin of dislocation patterns and emphasizes the hydrodynamic nature of the instability that leads to dislocation patterning, which we identify as an instability of dislocation transport that is not dependent on processes such as dislocation multiplication or annihilation. We demonstrate the robustness of the developed patterning scenario by considering the simplest possible case (plane strain, single slip) in two model versions that consider the same driving stresses but implement the transport of dislocations that controls dislocation density evolution in two very different manners, namely (i) a hydrodynamic formulation that considers transport equations that are continuous in space and time, assuming that the dislocation velocity depends linearly on the local driving stress, and (ii) a stochastic cellular automaton implementation that assumes spatially and temporally discrete transport of discrete "packets" of dislocation density that move according to an extremal dynamics. Despite the differences, we find that the emergent patterns in both models are mutually consistent and in agreement with the prediction of a linear stability analysis of the continuum model. We also show how different types of initial conditions lead to different intermediate evolution scenarios that, however, do not affect the properties of the fully developed patterns

Enabling quantitative analysis of in situ TEM experiments: A high-throughput, deep learning-based approach tailored to the dynamics of dislocations

In situ TEM is by far the most commonly used microscopy method for imaging dislocations, i.e., line-like defects in crystalline materials. However, quantitative image analysis so far was not possible, implying that also statistical analyses were strongly limited. In this work, we created a deep learning-based digital twin of an in situ TEM straining experiment, additionally allowing to perform matching simulations. As application we extract spatio-temporal information of moving dislocations from experiments carried out on a Cantor high entropy alloy and investigate the universality class of plastic strain avalanches. We can directly observe stick- slip motionof single dislocations and compute the corresponding avalanche statistics. The distributions turn out to be scale-free, and the exponent of the power law distribution exhibits independence on the driving stress. The introduced methodology is entirely generic and has the potential to turn meso-scale TEM microscopy into a truly quantitative and reproducible approach