Multiresolution analysis of elastic degradation in heterogeneous materials

In this study we examine the stiffness properties of heterogeneous elastic materials and their degradation at different levels of observations. To thi s end we explore the opportunities and limitations of multiresolution wavel et analysis, where successive Haar transformations lead to a recursive sepa ration of the stiffness properties and the response into coarse- and fine-s cale features. In the limit, this recursive process results in a homogeniza tion parameter which is an average measure of stiffness and strain energy c apacity at the coarse scale. The basic concept of multiresolution analysis is illustrated with one- and two-dimensional model problems of a two-phase particulate composite representative of the morphology of concrete material s. The computational studies include the microstructural features of concre te in the form of a bi-material system of aggregate particles which are imm ersed in a hardened cement paste taking due account of the mismatch of the two elastic constituents.