A FFT-Based Numerical Method for Computing the Mechanical Properties of Composites from Images of their Microstructures

The effective properties of composite materials are strongly influenced by the geometry of their microstructures, which can be extremely complex. Most of the numerical simulations known to the authors make use of two- or three-dimensional finite elements analyses which are often time consuming because of the complexity imposed by the requirement of extremely precise description of the reinforcements distribution. A numerical method is presented here that directly uses images of the microstructure - supposed to be periodically repeated - to compute the composite overall properties, as well as the local distribution of stresses and strains, without requiring further geometrical interpretation by the user. The linear elastic problem is examined first. Its analysis is based on the Lippmann-Schwinger’s equation, which is solved iteratively by means of the Green operator of an homogeneous reference medium. Then the method is extended to non-linear problems where the local stress strain relation is given by an incremental relation.