Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale

A homogenization framework is developed that accounts for the effect of size at the microor nanoscale. This is achieved by endowing the interfaces of the microor nanoscopic features with their own independent structure, using the theory of surface elasticity. Following a standard small-strain approach for the microscopic deformation in terms of the macroscopic strain tensor, a Hill-type averaging condition is used to link the two scales. A procedure for determining overall effective properties in the case of composites with elastic components and elastic material interfaces is presented. A special example of multilayered composites demonstrates the correlation between a material interface and a very thin interphase layer.