Analiza niegładka i metody niestandardowe w zagadnieniach mechaniki ciała stałego

Methods of nonsmooth analysis and nonstandard analysis are used to formulate and discuss some mechanical problems of composite materials. Firstly, the delamination problem of such structures is investigated. The corresponding variational formulations leading to the hemivariational inequalities are derived and analysed from the point of view of the existence of solutions. Secondly, by making use of some concepts and theorems of nonstandard analysis the microlocal homogenization method for periodic composities is formulated. It is an alternative to the well know asymptotic homogenization approach.