MULTISCALE MODELLING OF HETEROGENEOUS MATERIALS

In this work an approach to solving coupled micro-macro problems was developed that enables efficient analyses of modern heterogeneous materials. It provides an efficient problem-solving tool for problems with complex microstructures, which are used in demanding structural components. An effective way of transferring the microscale information to the macroscale analysis is to use a multilevel finite-element approach-FE2. Within the FE2 framework one conducts an embedded micro-scale computation in order to extract the quantities required at a point of the macroscale finite-element mesh. The aplication of FE2 circumvents the need to construct an explicit macroscale constitution formulation, though at an increased computational cost. Here, a general method for the calculation of the consistent macroscopic stiffness matrix via a sensitivity analysis at the micro level was developed. The performance of the proposed method was studied for different microstructures with porosities and stiff inclusions.