Skip to main content

On the Role of Interface Energies in the Description of Material Behavior

  • Conference paper
Multiscale Problems in Science and Technology

Abstract

A possibility for a unified theory for phenomena such as plasticity, rupture, and damage is examined here. It is shown that a variety of responses can be obtained starting from a purely elastic scheme and allowing for the creation of discontinuities at the price of an interface energy. Moreover it is conceivable to relate, at least qualitatively, the expression chosen for the interface energy to the fine properties of the structure of matter. The paper is restricted to one-dimensional models; their two and three dimensional counterparts still exhibit challenging problems of mechanical interpretation and mathematical formulation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Barenblatt G.I. (1962) The mathematical theory of equilibrium cracks in brittle fracture, Adv. Appl. Mech. 7, 55–129.

    Article  MathSciNet  Google Scholar 

  2. Braides A., Coscia A. (1993) A singular perturbation approach to variational problems in fracture mechanics, Math. Mod. Meth. Appl. Sci 3, 303–340.

    Article  MathSciNet  MATH  Google Scholar 

  3. Choksi R., Del Piero G., Fonseca I., Owen D.R. (1999) Structured deformations as energy minimizers in models of fracture and hysteresis, Math, and Mech. of Solids 4, 321–356.

    Article  MATH  Google Scholar 

  4. Del Piero G., Owen D.R. (1993) Structured deformations of continua, Arch. Rational Mech. Analysis 124, 99–155.

    Article  MATH  Google Scholar 

  5. Del Piero G. (1998) Towards a unified approach to fracture, yielding, and damage. In: Inan E., Markov K.Z. (Eds.), Continuum Models and Discrete Systems, World Scientific, Singapore, 67–692.

    Google Scholar 

  6. Del Piero G., Truskinovsky L. (1998) A one-dimensional model for localized and distributed failure, J. Phys. IV France 8, Pr8, 95–102.

    Google Scholar 

  7. Del Piero G. (1999) One-dimensional ductile-brittle transition, yielding, and structured deformations. In: Argoul P., Frémond M., Nguyen Q.S. (Eds.) Variations of domains and free boundary problems in solid mechanics, Kluwer, Dordrecht, 203–210.

    Chapter  Google Scholar 

  8. Del Piero G., Truskinovsky L. (2001) Macro and micro cracking in onedimensional elasticity, Int. J. of Solids and Structures 38, 1135–1148.

    Article  MATH  Google Scholar 

  9. Del Piero G., Truskinovsky L., Elastic bars with cohesive energy, in preparation.

    Google Scholar 

  10. Griffith A. A. (1920) The phenomenon of rupture and flow in solids, Phil. Trans. Roy. Soc. London, A, 221, 163–198.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Del Piero, G. (2002). On the Role of Interface Energies in the Description of Material Behavior. In: Antonić, N., van Duijn, C.J., Jäger, W., Mikelić, A. (eds) Multiscale Problems in Science and Technology. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56200-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-56200-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43584-6

  • Online ISBN: 978-3-642-56200-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics