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

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

Guerrilla Performance Analysis for Robot Swarms: Degrees of Collaboration and Chains of Interference Events

Scalability is a key feature of swarm robotics. Hence, measuring performance depending on swarm size is important to check the validity of the design. Performance diagrams have generic qualities across many different application scenarios. We summarize these findings and condense them in a practical performance analysis guide for swarm robotics. We introduce three general classes of performance: linear increase, saturation, and increase/decrease. As the performance diagrams may contain rich information about underlying processes, such as the degree of collaboration and chains of interference events in crowded situations, we discuss options for quickly devising hypotheses about the underlying robot behaviors. The validity of our performance analysis guide is then made plausible in a number of simple examples based on models and simulations.SCOPUS: cp.kinfo:eu-repo/semantics/publishe