Damage in a random microstructure: Size effects, fractals, and entropy maximization

Conference · Wed Nov 01 00:00:00 EST 1989 · Applied Mechanics Reviews; (United States)

OSTI ID:5408968

Ostoja-Starzewski, M ^[1]

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1. Purdue Univ., Lafayette, IN (USA)

In this paper a micromechanical approach to damage growth in graph-representable microstructures is presented. Damage is defined as an elastic inelastic transition in the grain boundaries and is represented in terms of a binary or ternary random field Z on the graph. A method based on the percolation theory brings out the size effects in scatter of strength, and the fractal character of damage geometry, and thus provides a basis for a multifractal model of a range of damage phenomena. The Markov property of field Z leads to a description of Z in terms of Gibbs probability measures and establishes a link between the entropy of disorder of Z and the physical entropy of damage in the ensemble of material specimens. Derivation of stochastic constitutive laws is outlined using the formalism of free energy and the dissipation function extended to random media.

• OSTI ID: 5408968
• Report Number(s): CONF-8901202-; CODEN: AMREA
• Journal Information: Applied Mechanics Reviews; (United States), Vol. 42:11; Conference: PACAM '89: 1st Pan American congress of applied mechanics, Rio de Janeiro (Brazil), Jan 1989; ISSN 0003-6900
• Country of Publication: United States
• Language: English

Related Subjects

36 MATERIALS SCIENCE
DAMAGE
MATHEMATICAL MODELS
MICROSTRUCTURE
GRAPHS
CRACK PROPAGATION
DISSIPATION FACTOR
ENTROPY
FRACTALS
FREE ENERGY
GRAIN BOUNDARIES
CRYSTAL STRUCTURE
ENERGY
PHYSICAL PROPERTIES
THERMODYNAMIC PROPERTIES
360102* - Metals & Alloys- Structure & Phase Studies
360202 - Ceramics
Cermets
& Refractories- Structure & Phase Studies
360602 - Other Materials- Structure & Phase Studies