Understanding how materials respond to external mechanical perturbation is a central problem of science and engineering.
While for most practical purposes it is useful to idealize the mechanical response of a material as a deterministic function
of the externally applied perturbation, disorder and fluctuations are unavoidable, leading to sample-to-sample variations
and non-trivial size effects. The size dependence of strength is a well known but still unresolved issue in the fracture of
materials and structures. The difficulty in addressing this problem stems from the complex interplay between microstructual
heterogeneity and long-range elastic interactions. Furthermore, in micro and nanoscale samples, the plastic yield strength
displays size effects and strain bursts, features that are not present in macroscopic samples where plasticity is a smooth
process. Large fluctuations both in fracture processes and in microscale plasticity make the use of conventional continuum
mechanics problematic and calls instead for a statistically based approach. These problems are becoming particularly
important in the current miniaturization trend towards nanoscale devices, since the relative amplitude of fluctuations grows as
the sample size is reduced. In this project, concepts and tools of statistical mechanics are used to address size effects and
fluctuations in the irreversible deformation and failure of materials. The general objective is to provide a quantitative theory
that can be used as base for setting reliable safety factors. The theory will be based on the renormalization group and will be
guided and validated by large scale numerical simulations such as molecular dynamics, discrete dislocation dynamics and
disordered network models. Finally, we will analyze experimental data present in the literature.