Final Activity Report Summary - MESOMECHANICS (Mesomechanics: new insights from granular materials down to the nanoscale) The goal of the project has been the development of theoretical and computational techniques and models for the mechanics of materials and systems in which mesoscale effects (i.e. on intermediate scales between the particles and the macroscale) are important. The basic premise is that mesoscale properties and fields can be used as a unifying concept for modelling a wide class of systems, which includes granular matter, glasses, foams, dense colloids, nanoscale solids and micro/nanofluids. Common features include the lack of scale separation between the microscopic (particle) scale and the macroscale, the prominence of fluctuations and inhomogeneities, metastability and history dependence. The methodology is based on a systematic coarse graining technique which relies on spatial averaging to relate the microscopic (particle) and continuum descriptions. This approach emphasizes the scale (resolution) dependence of the pertinent fields, of crucial importance in such systems, and enables a quantitative evaluation and modeling of fluctuations and inhomogeneities. One main focus has been on granular materials, in which experiments can provide detailed microscopic (grain scale) information, e.g. the trajectories of the individual particles. A set of computational tools have been developed and used to analyse particle tracking data in several experiments on dense 2D and 3D granular materials, enabling the characterisation of the collective motion of grains as well as the corresponding fluctuations, which were shown to play an important role in the dynamics. Another focus has been the application of similar tools to analyse simulations of model glasses, which provide further microscopic information including, e.g. the interparticle forces. A new definition for the fluctuations in the particle displacements has been proposed, and used to identify local regions (of size on the order of a few particle diameters) of large fluctuations in elastic deformation. These appear to be analogous to defects in crystalline solids: we have shown that these 'defects' correspond to sites of local plastic rearrangements in subsequent plastic deformation. We also examined the validity of local linear elasticity in these systems as a function of the coarse graining scale, and found that it applies to a good accuracy down to about ten particle diameters (corresponding to a few nanometers in atomic or molecular glasses), below which classical elasticity breaks down and needs to be modified. We calculated the local elastic moduli (for the first time in a nonequlibrium disordered system), and shown that the major type of elastic inhomogeneity is local anisotropy (isotropy is recovered on larger scales). The results obtained provide a detailed characterisation of both the fluctuations and inhomogeneities in amorphous, emphasising the similarity between different types of such materials. They should enable the improvement of models for the elastic properties of amorphous materials, and provide a (currently lacking) micro/mesoscopic basis for phenomenological models for plastic flow, which are of both basic and practical importance.