NDLI: Waves and complexity of microstructured solids

Content Provider	IEEE Xplore Digital Library
Author	Pastrone, F. Engelbrecht, J.
Copyright Year	2012
Description	Author affiliation: Department of Mathematics, University of Torino, Via Carlo Alberto 10, 10123, Italy (Pastrone, F.) \|\| Centre for Nonlinear Studies, Institute of Cybernetics, Tallinn Technical University, Akadeemia Rd. 21, 12618, Estonia (Engelbrecht, J.)
Abstract	A complex system as it is understood nowadays is composed by its constituents that interact with each other resulting in emergent properties of the system as a whole. In mechanics the concepts of complexity has been analysed by Engelbrecht [7] with a focus on wave propagation. This theory is based on some cornerstones like the introduction of internal structures at different scales and the nonlinearity of the models which in other words means incorporating intrinsic microstructural and nonlinear effects. In this case complexity means that we have different scales, with several interaction processes which encompass many physically meaningful phenomena. Usually a microstructured body, as we shall see, is modeled as a solid with an internal structure at a different scale, which is apt to describe the mechanical behaviour of solids with dislocations, polycrystalline solids, ceramic composites, granular media, etc. One main aspect of such theories is that they always take into account the nonlinearity of the materials, the nonlocality and the interactions between micro- and macroscales. It is possible, and useful, to develop also models with a hierarchy of microstructures, i.e. a first level micro-structure which contains a second level micro-structure, and it is meaningful also the case of concurrent micro-structures (see Berezovski et al [1]). In this paper we want to analyze the subject, recalling some main results in the theory of complex microstructures, developing new results in the case of multiple microstructures, exploiting hierarchical governing equations and analyzing non-linear wave propagation, which is crucial to put in evidence the weight of the different scales and the interaction of micro- and macro-structures.
Starting Page	192
Ending Page	196
File Size	1144594
Page Count	5
File Format	PDF
ISBN	9781467344180
e-ISBN	9781467344197
DOI	10.1109/DD.2012.6402777
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2012-05-28
Publisher Place	Russia
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Microstructure Equations Mathematical model Solids Strain Diffraction
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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