An information theoretic argument on the form of damage accumulation in solids

D. Bhate, K. Mysore, G. Subbarayan

Research output: Contribution to journalArticle

6 Scopus citations

Abstract

An approach to modeling failure that is inspired by two experimentally observed facts is presented. These observations are: (1) cracks grow as the end result of a irreversible, dissipative process, and (2) fracture has an inherent lengthscale, timescale and/or spatial hierarchy influenced by the (possibly dynamically changing) microstructural state. The second of these facts enables one to view the seemingly deterministic cracks observed at higher levels of hierarchy as resulting from uncertain events at lower-levels of hierarchy associated with microstructural variations. A key mathematical result developed in Information Theory together with the maximum entropy principle of Statistical Mechanics is utilized to derive a form of damage that is maximally non-committal about microstructural uncertainty in lower levels of fracture hierarchy. The irrecoverable energy that is expended in the creation of new surfaces or in plastic dissipation is associated with the microstructural damage using continuum thermodynamics and J2 plasticity theory. The formulated result is shown to provide an exponential form of damage accumulation under constant dissipation rate, and a form similar to the popular Smith-Ferrante traction-separation law of cohesive zone models under conditions of decreasing dissipation rate. Finally, the model is validated through comparisons with experimental observations of damage accumulation during cyclic fatigue testing of solder alloys.

Original languageEnglish (US)
Pages (from-to)184-195
Number of pages12
JournalMechanics of Advanced Materials and Structures
Volume19
Issue number1-3
DOIs
StatePublished - Jan 1 2012
Externally publishedYes

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Keywords

  • Cohesive Zone Models
  • Continuum Thermodynamics
  • Fracture
  • Information Theory
  • Maximum Entropy Principle
  • Solder

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Mathematics(all)
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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