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Elasticity with Hierarchical Disarrangements: A Field Theory That Admits Slips and Separations at Multiple Submacroscopic Levels

  • Luca Deseri
  • David R. OwenEmail author
Article
  • 38 Downloads

Abstract

The complexity and variety of geometrical changes in physical systems at submacroscopic levels has led to various approaches to the broadening of the classical theory of finite elasticity. One approach, the field theory “elasticity with disarrangements”, employed the multiscale geometry of structured deformations in order to incorporate the effects of disarrangements such as slips and separations at a single submacroscopic level on the macroscopic response of a continuous body. This article extends that field theory by enriching the underlying geometry so as to include the effects of disarrangements at more than one submacroscopic level. The resulting field theory broadens the scope of this approach, sharpens the description of the physical nature of dissipative mechanisms that can arise, and increases the variety of systems of contact forces that can serve as boundary loadings for a body that evolves via multiscale geometrical processes.

Keywords

Structured deformations Hierarchies Multiscale geometry Elasticity Disarrangements Field theory 

Mathematics Subject Classification

74A 74B20 74C15 74M25 

Notes

Acknowledgement

The partial support from the grant ERC-2013-ADG-340561-INSTABILITIES is gratefully acknowledged.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.DICAM-Mechanical, Civil and Environmental EngineeringUniversity of TrentoTrentoItaly
  2. 2.MEMS-Mechanical Engineering and Materials Sciences, Swanson School of EngineeringUniversity of PittsburghPittsburghUSA
  3. 3.Department of Civil and Environmental EngineeringCarnegie Mellon UniversityPittsburghUSA
  4. 4.Department Mechanical EngineeringCarnegie Mellon UniversityPittsburghUSA
  5. 5.THMR-Department of Nanomedicine-Houston Methodist HospitalHoustonUSA
  6. 6.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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