A dynamical interpretation of flutter instability in a continuous medium

Flutter instability in an infinite medium is a form of material instability corresponding to the occurrence of complex conjugate squares of the acceleration wave velocities. Although its occurrence is known to be possible in elastoplastic materials with nonassociative flow law and to correspond to some dynamically growing disturbance, its mechanical meaning has to date still eluded a precise interpretation. This is provided here by constructing the infinite-body, time-harmonic Green's function for the loading branch of an elastoplastic material in flutter conditions. Used as a perturbation, it reveals that flutter corresponds to a spatially blowing-up disturbance, exhibiting well-defined directional properties, determined by the wave directions for which the eigenvalues become complex conjugate. Flutter is shown to be connected to the formation of localized deformations, a dynamical phenomenon sharing geometrical similarities with the well-known mechanism of shear banding occurring under quasi-static loading. Flutter may occur much earlier than shear banding in a process of continued plastic deformation.Comment: 32 pages, 12 figure

An elastoplastic framework for granular materials becoming cohesive through mechanical densification. Part II - the formulation of elastoplastic coupling at large strain

The two key phenomena occurring in the process of ceramic powder compaction are the progressive gain in cohesion and the increase of elastic stiffness, both related to the development of plastic deformation. The latter effect is an example of `elastoplastic coupling', in which the plastic flow affects the elastic properties of the material, and has been so far considered only within the framework of small strain assumption (mainly to describe elastic degradation in rock-like materials), so that it remains completely unexplored for large strain. Therefore, a new finite strain generalization of elastoplastic coupling theory is given to describe the mechanical behaviour of materials evolving from a granular to a dense state. The correct account of elastoplastic coupling and of the specific characteristics of materials evolving from a loose to a dense state (for instance, nonlinear --or linear-- dependence of the elastic part of the deformation on the forming pressure in the granular --or dense-- state) makes the use of existing large strain formulations awkward, if even possible. Therfore, first, we have resorted to a very general setting allowing general transformations between work-conjugate stress and strain measures; second, we have introduced the multiplicative decomposition of the deformation gradient and, third, employing isotropy and hyperelasticity of elastic response, we have obtained a relation between the Biot stress and its `total' and `plastic' work-conjugate strain measure. This is a key result, since it allows an immediate achievement of the rate elastoplastic constitutive equations. Knowing the general form of these equations, all the specific laws governing the behaviour of ceramic powders are finally introduced as generalizations of the small strain counterparts given in Part I of this paper.Comment: 18 pages, 1 figur

Ignorance is not always Bliss: Feedback and Dynamics in Public Good Experiments

In this paper we study the effects of providing additional feedback about individual contributions and earnings on the dynamics of contributions in a repeated public good game. We include treatments where subjects can freely choose whether to obtain additional information about individual contributions or individual earnings. We find that, in the aggregate, contributions decline less fast when additional information about contributions and earnings is provided on top of aggregate information. We also find that there exist substantial but intuitively appealing differences in the way individuals react to feedback. Particularly, individuals with a high propensity to contribute tend to imitate the highest contributor more often and are more inclined to obtain feedback about individual contributions than about individual earnings than individuals with a lower propensity to contribute.voluntary contributions;experiment;repeated interaction;feedback;imitation

An experiment on experimental instructions

In this paper we treat instructions as an experimental variable. Using a public good game, we study how the instructions' format affects the participants' understanding of the experiment, their speed of play and their experimental behavior. We show that longer instructions do not significantly improve the subjects' understanding of the experiment; on-screen instructions shorten average decision times with respect to on-paper instructions, and requiring forced inputs reduces waiting times, in particular for the slowest subjects. Consistent with cognitive load theory, we find that short, on-screen instructions which require forced inputs improve on subjects' comprehension and familiarity with the experimental task, and they contribute to reduce both decision and waiting times without affecting the overall pattern of contributions.

Inference via low-dimensional couplings

We investigate the low-dimensional structure of deterministic transformations between random variables, i.e., transport maps between probability measures. In the context of statistics and machine learning, these transformations can be used to couple a tractable "reference" measure (e.g., a standard Gaussian) with a target measure of interest. Direct simulation from the desired measure can then be achieved by pushing forward reference samples through the map. Yet characterizing such a map---e.g., representing and evaluating it---grows challenging in high dimensions. The central contribution of this paper is to establish a link between the Markov properties of the target measure and the existence of low-dimensional couplings, induced by transport maps that are sparse and/or decomposable. Our analysis not only facilitates the construction of transformations in high-dimensional settings, but also suggests new inference methodologies for continuous non-Gaussian graphical models. For instance, in the context of nonlinear state-space models, we describe new variational algorithms for filtering, smoothing, and sequential parameter inference. These algorithms can be understood as the natural generalization---to the non-Gaussian case---of the square-root Rauch-Tung-Striebel Gaussian smoother.Comment: 78 pages, 25 figure

An experiment on experimental instructions

In this paper we treat instructions as an experimental variable. Using a public good game, we study how the instructions' format affects the participants' understanding of the experiment, their speed of play and their experimental behavior. We show that longer instructions do not significantly improve the subjects' understanding of the experiment; on-screen instructions shorten average decision times with respect to on-paper instructions, and requiring forced inputs reduces waiting times, in particular for the slowest subjects. Consistent with cognitive load theory, we find that short, on-screen instructions which require forced inputs improve on subjects' comprehension and familiarity with the experimental task, and they contribute to reduce both decision and waiting times without affecting the overall pattern of contributions.Cognitive load theory, Comprehension, Distraction, Experimental instructions

The dynamics of a shear band

A shear band of finite length, formed inside a ductile material at a certain stage of a con- tinued homogeneous strain, provides a dynamic perturbation to an incident wave field, which strongly influences the dynamics of the material and affects its path to failure. The investigation of this perturbation is presented for a ductile metal, with reference to the incremental mechanics of a material obeying the J 2-deformation theory of plasticity (a special form of prestressed, elastic, anisotropic, and incompressible solid). The treatment originates from the derivation of integral representations relating the incremental mechan- ical fields at every point of the medium to the incremental displacement jump across the shear band faces, generated by an impinging wave. The boundary integral equations (under the plane strain assumption) are numerically approached through a collocation technique, which keeps into account the singularity at the shear band tips and permits the analysis of an incident wave impinging a shear band. It is shown that the presence of the shear band induces a resonance, visible in the incremental displacement field and in the stress intensity factor at the shear band tips, which promotes shear band growth. Moreover, the waves scattered by the shear band are shown to generate a fine texture of vibrations, par- allel to the shear band line and propagating at a long distance from it, but leaving a sort of conical shadow zone, which emanates from the tips of the shear band