Titlebook: IUTAM Symposium on Scaling in Solid Mechanics; Proceedings of the I F.M. Borodich (borodichfm@cardiff.ac.uk) Conference proceedings 2009 Sp

opinionated

Similarity Approach to Hertz Type Contact Problems,, some author’s results with examples of typical contact problems that sufficiently fully reflect the general nature of this scaling, and some illustrations of the approach by giving examples of its engineering applications, mainly to materials science.

prick-test

Chronic

Mathematical Foundations of Non-Classical Extensions of Similarity Theory, in the fields of case-based and rule-based reasoning, neural networks, data mining, pattern recognition and sound classification, is presented. It is shown that the validity of the extension can be guaranteed by a so-called embedding theorem based on the property of dimensional homogeneity.

CORD

河潭

Burst Statistics as a Criterion for Imminent Failure,nd ξ=5/2 elsewhere. We also study a network of electric fuses, and find numerically an exponent 2.0 near breakdown, and 3.0 elsewhere. We propose that this crossover in the size distribution may be used as a signal for imminent system failure.

CAMP

An Influence of the Elastic Properties of Composite Components on the Mechanical Response of Polycre internal structure of the composite material, FEA technique was used to get macroscopic stress-strain correlations. They include gradual changes of the internal structure of the material due to porosity and cracks development under tension.

exercise

Commodious

Modelling of Size Effects with Gradient-Enriched Continuum Theories, Law of Bažant. Finally, the energy dissipation in Elementary Volumes is shown to be size-dependent, where again a gradient damage theory has been used. This implies that Representative Volumes do not exist when the dissipated energy is considered.

冲击力

Scaling Laws for Properties of Materials with Imperfect Interfaces,fective properties of heterogeneous materials containing inhomogeneities with imperfect interfaces become dependent upon the size of the inhomogeneities. This size-dependence is shown to be captured by simple scaling laws depending upon the type of the interface imperfection.

VICT

Scaling of Effective Moduli of Generalised Continua,duli scale with an exponent α, the Cosserat moduli scale with exponents α and α+2. Using this rule, we determine the dispersion relations for travelling waves and find the full set of the exponents for the cases of material with cracks and pores.