Size effects in periodic composites via higher-order homogenisation

I start by making a 15-minute introduction to the classical pronlem of the mathematical theory of homogenisation. This will be followed by the description of a series of experiments that suggest that the (suitably normalised) strength of a plastically deformed solid may increase with diminishing sample size. I will show how such effects can be accounted for by considering higher-order terms in the classical problem of periodic homogenisation and propose a related variational framework that yields the desired higher-order (or "strain-gradient") constitutive laws.