Update on a class of gradient theories

• Published in: Mechanics of materials 2003-03, Vol.35 (3), p.259-280
• Main Author: Aifantis, E.C.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Physics; Solid mechanics; Structural and continuum mechanics; Viscoelasticity, plasticity, viscoplasticity
• ISSN: 0167-6636; 1872-7743
• DOI: 10.1016/S0167-6636(02)00278-8

This article, written in honor of Professor Nemat-Nasser, provides an update of the standard theories of dislocation dynamics, plasticity and elasticity properly modified to include scale effects through the introduction of higher order spatial gradients of constitutive variables in the governing equations of material description. Only a special class of gradient models, namely those developed by the author and his co-workers, are considered. After a brief review of the basic mathematical structure of the theory and certain gradient elasticity solutions for dislocation fields, the physical origin and form of the gradient terms (for all classes of elastic, plastic, and dislocation dynamics behavior), along with the nature of the associated phenomenological coefficients are discussed. Applications to the interpretation of deformation patterning and size effects are given. Two new features are noted: the role of wavelet analysis and stochasticity in interpreting deformation heterogeneity measurements and serrations of the stress–strain graph.