Local Homogenization of Composite Materials

Resumo

The homogenization process has as its basic premise to change multiphase materials into a single
material with a representative phase, regardless of which model is being used, whether based on the theory of
elasticity, solid mechanics, or the mean-fields micromechanics models. These models, however sophisticated they
may be, takes into account the interaction between the inclusions, the geometry of the inclusion up to the physical
nonlinearity of the problem, which is always associated with the geometric limitation of the global model. To
circumvent the geometric problem, it is proposed the development of a homogenization process that takes into
account the geometry of the problem, in addition to the volumetric fractions and properties of each phase. This
consideration is given by the generation of a quadtree recursive spatial subdivision, where the mesh nodes represent
the inclusions and the elements connected to the nodes represent the matrix. With this, it can be shown the
reduction of the global problem to a local problem of the Eshelby equivalent inclusion and homogenize of the
mesh node by node. The obtained results are a map of properties homogenized locally since each node has different
volumetric fractions for each problem of equivalent inclusion. This procedure opens a range of different
possibilities of materials, including the application in multiphase cementitious composite materials.