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Register a new userMacroscopic and Microscopic Investigation on the History Dependence of the Mechanical Behaviour of Powders
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D. Kadau
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As an example for history dependent mechanical behaviour of cohesive powders experiments and computer simulations of uniaxial consolidation are compared. Some samples were precompacted transversally to the consolidation direction and hence had a different history. The experiments were done with two carbonyl iron powders, for which the average particle diameters differed by a factor of ca. 2. Whereas the particle diameter was the only characteristic length in the simulations, the evaluation of the experimental data indicates that at least a second characteristic length must be present.
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A novel method to investigate the compaction behaviour of cohesive powders is presented. As a sample, a highly porous agglomerate formed by random ballistic deposition (RBD) of micron sized spherical particles is used. A nanomanipulator deforms this small structure under scanning electron microscope observation, allowing for the tracking of individual particle motion. Defined forces are applied and the resulting deformations are measured. The hereby obtained results are compared to results from threedimensional discrete element simulations as well as macroscopic compaction experiments. Relevant simulation parameters are determined by colloidal probe measurements.
We study the history dependence of the mechanical properties of granular media by numerical simulations. We perform a compaction of frictional disk packings in a two-dimensional system by controlling the area of the domain with various strain rates. We then find the strain rate dependence of the critical packing fraction above which the pressure becomes finite. The observed behavior makes a contrast with the well-studied jamming transitions for frictionless disk packings. We also observe that the elastic constants of the disk packings depend on the strain rate logarithmically. This result provides a experimental test for the history dependence of granular systems.
This article is mostly based on a talk I gave at the March 2021 meeting (virtual) of the American Physical Society on the occasion of receiving the Dannie Heineman prize for Mathematical Physics from the American Institute of Physics and the American Physical Society. I am greatly indebted to many colleagues for the results leading to this award. To name them all would take up all the space allotted to this article. (I have had more than 200 collaborators so far), I will therefore mention just a few: Michael Aizenman, Bernard Derrida, Shelly Goldstein, Elliott Lieb, Oliver Penrose, Errico Presutti, Gene Speer and Herbert Spohn. I am grateful to all of my collaborators, listed and unlisted. I would also like to acknowledge here long time support form the AFOSR and the NSF.
The main subject of the thesis is the study of stationary nonequilibrium states trough the use of microscopic stochastic models that encode the physical interaction in the rules of Markovian dynamics for particles configurations. These models are known as interacting particles systems and are simple enough to be treated analytically but also complex enough to capture essential physical behaviours. The thesis is organized in two parts. The part 1 is devoted to the microscopic theory of the stationary states. We characterize these states developing some general structures that have an interest in themselves. In this part there is an interlude dedicated to discrete calculus on discrete manifolds with an exposition a little bit different to the one available in literature and some original definitions. The part 2 studies the problem macroscopically. In particular we consider the large deviations asymptotic behavior for a class of solvable one dimensional models of heat conduction. Both part 1 and 2 begin with an introduction of motivational character followed by an overview of the relevant results and a summary explaining the organization. Even tough the two parts are strictly connected they can be read independently after chapter 1. The material is presented in such a way to be self-consistent as much as possible.
A wide range of materials can exist in microscopically disordered solid forms, referred to as amorphous solids or glasses. Such materials -- oxide glasses and metallic glasses, to polymer glasses, and soft solids such as colloidal glasses, emulsions and granular packings -- are useful as structural materials in a variety of contexts. Their deformation and flow behaviour is relevant for many others. Apart from fundamental questions associated with the formation of these solids, comprehending their mechanical behaviour is thus of interest, and of significance for their use as materials. In particular, the nature of plasticity and yielding behaviour in amorphous solids has been actively investigated. Different amorphous solids exhibit behaviour that is apparently diverse and qualitatively different from those of crystalline materials. A goal of recent investigations has been to comprehend the unifying characteristics of amorphous plasticity and to understand the apparent differences among them. We summarise some of the recent progress in this direction. We focus on insights obtained from computer simulation studies, and in particular those employing oscillatory shear deformation of model glasses.
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