Meso-scale approximations cover an intermediate range of problems between homogenisation approximations of periodic composites and heterogeneous solids with finite number of finite size defects. Meso-scale approximations provide elegant analytical representation of the physical fields, and they do not require periodicity constraints or any other assumptions commonly attributed to the homogenisation approaches. Models of densely perforated solids are considered, which also include analysis of Green’s kernels. Special cases are discussed to show a combined approach incorporating meso-scale uniform asymptotics and homogenisation approximations. The lecture focuses mainly on static problems for the Laplacian or the Navier systems. Extensions to problems of time-harmonic waves are also discussed.
The lecture is based on the joint work with V.G. Maz’ya and M.J. Nieves.