# Local Homogenization of Composite Materials

## Palavras-chave:

composite materials, local homogenization## 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.