Avalanches, precursors and finite size fluctuations in a mesoscopic model of amorphous plasticity

We discuss avalanche and finite size fluctuations in a mesoscopic model to describe the shear plasticity of amorphous materials. Plastic deformation is assumed to occur through series of local reorganizations. Yield stress criteria are random while each plastic slip event induces a quadrupolar long range elastic stress redistribution. The model is discretized on a regular square lattice. Shear plasticity can be studied in this context as a depinning dynamic phase transition. We show evidence for a scale free distribution of avalanches $P(s)\propto S^{-\kappa}$ with a non trivial exponent $\kappa \approx 1.25$ significantly different from the mean field result $\kappa = 1.5$. Finite size effects allow for a characterization of the scaling invariance of the yield stress fluctuations observed in small samples. We finally identify a population of precursors of plastic activity and characterize its spatial distribution

Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity

A mesoscopic model for shear plasticity of amorphous materials in two dimensions is introduced, and studied through numerical simulations in order to elucidate the macroscopic (large scale) mechanical behavior. Plastic deformation is assumed to occur through a series of local reorganizations. Using a discretization of the mechanical fields on a discrete lattice, local reorganizations are modeled as local slip events. Local yield stresses are randomly distributed in space and invariant in time. Each plastic slip event induces a long-ranged elastic stress redistribution. Rate and thermal effects are not discussed in the present study. Extremal dynamics allows for recovering many of the complex features of amorphous plasticity observed experimentally and in numerical atomistic simulations in the quasi-static regime. In particular, a quantitative picture of localization, and of the anisotropic strain correlation both in the initial transient regime, and in the steady state are provided. In addition, the preparation of the amorphous sample is shown to have a crucial effect of on the localization behavior

When less is more: Robot swarms adapt better to changes with constrained communication

To effectively perform collective monitoring of dynamic environments, a robot swarm needs to adapt to changes by processing the latest information and discarding outdated beliefs. We show that in a swarm composed of robots relying on local sensing, adaptation is better achieved if the robots have a shorter rather than longer communication range. This result is in contrast with the widespread belief that more communication links always improve the information exchange on a network. We tasked robots with reaching agreement on the best option currently available in their operating environment. We propose a variety of behaviors composed of reactive rules to process environmental and social information. Our study focuses on simple behaviors based on the voter model—a well-known minimal protocol to regulate social interactions—that can be implemented in minimalistic machines. Although different from each other, all behaviors confirm the general result: The ability of the swarm to adapt improves when robots have fewer communication links. The average number of links per robot reduces when the individual communication range or the robot density decreases. The analysis of the swarm dynamics via mean-field models suggests that our results generalize to other systems based on the voter model. Model predictions are confirmed by results of multiagent simulations and experiments with 50 Kilobot robots. Limiting the communication to a local neighborhood is a cheap decentralized solution to allow robot swarms to adapt to previously unknown information that is locally observed by a minority of the robots

Simple individual behavioural rules for improving the collective behaviours of robot swarms

Swarm robotics is an ongoing area of research that is expected to revolutionise various real-world domains such as agriculture and space exploration. Swarm robotics systems are composed of a large number of simple and autonomous robots. Each robot locally interacts with other robots and with the environment following a set of behavioural rules. These individual interactions enable the swarm to exhibit interesting collective behaviours and to accomplish specific tasks. The main challenge in designing robot swarms is to determine the behavioural rules that each robot should follow so that the swarm as a whole can perform the desired task. The performance of robot swarms in a given task depends on the designer's choice of appropriate individual behavioural rules. In this thesis, we investigate simple individual behavioural rules for improving the performance of robot swarms in two major tasks. Using simple behavioural rules makes the designed solutions possibly usable with simpler platforms such as micro- and nanorobots. The first task we address is known as the best-of-n decision problem where the swarm is required to select the best option among n available alternatives. Solving the best-of-n decision problem is considered to be a fundamental cognitive skill for robot swarms as it influences the swarm's success in other tasks. In this thesis, we introduce individual behavioural rules to improve the performance of robot swarms in the best-of-n problem. Through these rules, robots vary their interaction strength over time in a decentralised fashion to balance the acquisition and the dissemination of information. The proposed behavioural rules allow swarms of simple noisy robots with constrained communication to limit the effect of individual errors and make highly accurate collective decisions in a predictable time. In some scenarios where the best option changes over time, the swarm is required to switch its decision accordingly. In this thesis, we introduce individual behavioural rules through which the robots process new information and discard outdated beliefs. These behavioural rules enable robot swarms to adapt their decisions to various environmental changes, including the appearance of better choices or the disappearance of the current swarm's choice. Our analysis shows that relying on local communication is more favourable for achieving adaptation. This result highlights the benefit of the local sensing and communication characterising biological and artificial swarms. The second task we address in this thesis is the collective resource collection task. In this task, the robots are asked to retrieve objects that are clustered at unknown locations in the environment. We address this task because of its numerous potential real-world applications. In many of these applications, the objects to collect are assigned different importance or value. In this thesis, we introduce a bio-inspired individual behaviour that allows robot swarms to perform quality-based resource collection. Similarly to foraging ants, in our proposed behaviour, the robots coordinate their collection efforts by laying and sensing virtual pheromone trails. The use of pheromone trails offers an advantageous implementation of the memory and communication capabilities necessary for the efficient collection of clustered objects. The proposed behaviour allows robot swarms to satisfy various collection objectives and achieve an optimal resource collection behaviour in the case of relatively small swarms. In this thesis, we analyse swarm robotics systems using both minimalistic tools such as stochastic and multi-agent simulations, and more advanced tools such as physics-based simulations and real robot experiments. Using these tools, we demonstrate the effectiveness of the proposed individual behavioural rules in improving the performance of robot swarms in the addressed tasks. The results we present in this thesis are of potential interest to both engineers designing robot swarms, and biologists investigating the behavioural rules followed by individuals in living collective organisms

Strain localization and anisotropic correlations in a mesoscopic model of amorphous plasticity

A mesoscopic model for shear plasticity of amorphous materials in two dimensions is introduced, and studied through numerical simulations in order to elucidate the macroscopic (large scale) mechanical behavior. Plastic deformation is assumed to occur through a series of local reorganizations. Using a discretization of the mechanical fields on a discrete lattice, local reorganizations are modeled as local slip events. Local yield stresses are randomly distributed in space and invariant in time. Each plastic slip event induces a long-ranged elastic stress redistribution. Rate and thermal effects are not discussed in the present study. Extremal dynamics allows for recovering many of the complex features of amorphous plasticity observed experimentally and in numerical atomistic simulations in the quasi-static regime. In particular, a quantitative picture of localization, and of the anisotropic strain correlation both in the initial transient regime, and in the steady state are provided. In addition, the preparation of the amorphous sample is shown to have a crucial effect of on the localization behavior

Plasticity-induced structural anisotropy of silica glass

Amorphous silica density at ambient pressure is known to depend on thermal history (through the quenching rate) but also, at room temperature, on the maximum pressure applied in the past. Here we show that beyond density, a mechanical loading can endow the structure with an orientational order. Molecular dynamics simulations show evidence that amorphous silica develops a permanent anisotropic structure after extended shear plastic flow. This anisotropy which survives for an unstressed specimen is revealed markedly by the fabric tensor computed over the Si-O-Si orientations, albeit the SiO4 tetrahedra microstructure remains mostly unaltered

Sophisticated collective foraging with minimalist agents: a swarm robotics test

How groups of cooperative foragers can achieve efficient and robust collective foraging is of interest both to biologists studying social insects and engineers designing swarm robotics systems. Of particular interest are distance-quality trade-offs and swarm-size-dependent foraging strategies. Here we present a collective foraging system based on virtual pheromones, tested in simulation and in swarms of up to 200 physical robots. Our individual agent controllers are highly simplified, as they are based on binary pheromone sensors. Despite being simple, our individual controllers are able to reproduce classical foraging experiments conducted with more capable real ants that sense pheromone concentration and follow its gradient. One key feature of our controllers is a control parameter which balances the trade-off between distance selectivity and quality selectivity of individual foragers. We construct an optimal foraging theory model that accounts for distance and quality of resources, as well as overcrowding, and predicts a swarmsize-dependent strategy. We test swarms implementing our controllers against our optimality model and find that, for moderate swarm sizes, they can be parameterised to approximate the optimal foraging strategy. This study demonstrates the sufficiency of simple individual agent rules to generate sophisticated collective foraging behaviour

Path independent integrals to identify localized plastic events in two dimensions

We use a power expansion representation of plane elasticity complex potentials due to Kolossov and Muskhelishvili, to compute the elastic fields induced by a localized plastic deformation event. Far from its center, the dominant contributions correspond to first order singularities of quadrupolar and dipolar symmetry which can be associated respectively to pure deviatoric and pure volumetric plastic strain of an equivalent circular inclusion. Constructing holomorphic functions from the displacement field and its derivatives, it is possible to define path independent Cauchy integrals which capture the amplitudes of these singularities. Analytical expressions and numerical tests on simple finite element data are presented. The development of such numerical tools is of direct interest for the identification of local structural reorganizations which are believed to be the key mechanisms for plasticity of amorphous materials

When less is more: Robot swarms adapt better to changes with constrained communication

To effectively perform collective monitoring of dynamic environments, a robot swarm needs to adapt to changes by processing the latest information and discarding outdated beliefs. We show that in a swarm composed of robots relying on local sensing, adaptation is better achieved if the robots have a shorter rather than longer communication range. This result is in contrast with the widespread belief that more communication links always improve the information exchange on a network. We tasked robots with reaching agreement on the best option currently available in their operating environment. We propose a variety of behaviors composed of reactive rules to process environmental and social information. Our study focuses on simple behaviors based on the voter model—a well-known minimal protocol to regulate social interactions—that can be implemented in minimalistic machines. Although different from each other, all behaviors confirm the general result: The ability of the swarm to adapt improves when robots have fewer communication links. The average number of links per robot reduces when the individual communication range or the robot density decreases. The analysis of the swarm dynamics via mean-field models suggests that our results generalize to other systems based on the voter model. Model predictions are confirmed by results of multiagent simulations and experiments with 50 Kilobot robots. Limiting the communication to a local neighborhood is a cheap decentralized solution to allow robot swarms to adapt to previously unknown information that is locally observed by a minority of the robots

Shear band dynamics from a mesoscopic modeling of plasticity

The ubiquitous appearance of regions of localized deformation (shear bands) in different kinds of disordered materials under shear is studied in the context of a mesoscopic model of plasticity. The model may or may not include relaxational (aging) effects. In the absence of relaxational effects the model displays a monotonously increasing dependence of stress on strain-rate, and stationary shear bands do not occur. However, in start up experiments transient (although long lived) shear bands occur, that widen without bound in time. I investigate this transient effect in detail, reproducing and explaining a t^1/2 law for the thickness increase of the shear band that has been obtained in atomistic numerical simulations. Relaxation produces a negative sloped region in the stress vs. strain-rate curve that stabilizes the formation of shear bands of a well defined width, which is a function of strain-rate. Simulations at very low strain-rates reveal a non-trivial stick-slip dynamics of very thin shear bands that has relevance in the study of seismic phenomena. In addition, other non-stationary processes, such as stop-and-go, or strain-rate inversion situations display a phenomenology that matches very well the results of recent experimental studies.Comment: 10 pages, 10 figure