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Size-Dependent Behavior of Materials: Governing Equations and Crack Path Dependence

This article explores the concept of size-dependent behavior in materials, focusing on the assumption that governing equations are size-independent. The constitutive model, equilibrium equations, and the impact of size on material behavior are discussed, including the role of dislocation cores and quantum mechanics within specific size ranges. The influence of residual stress on crack path is also examined.

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Size-Dependent Behavior of Materials: Governing Equations and Crack Path Dependence

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  1. 3/22/2002, FridayMultiscale Concept

  2. Size Scale

  3. Continuum Mechanics Assumption Governing equations are size independent Constitutive model, equilibrium equations,…

  4. Material Behavior isSize Dependent r > ry, elastic r < ry, plastic

  5. Dislocation Core Outside r1, no distortion; Inside r0, dislocation core, quantum mechanics Between r0 and r1, elastic field

  6. Void Stress Field a > a0, Lame’s classical solution for an elastic 2D plate. a ~ a0, interatomic traction on the surface.

  7. Crack-path Dependence on Residual Stress

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