A Multiresolution Transformation Rule of Material Defects

The ability to quantify the material damage at different length scales is critical in the multiscale analysis of material behavior from nanoscale to macroscale. In this article, on the basis of the equivalence of complementary elastic energy we propose a multiresolution rule that transforms different levels of material defects to the equivalent degradation of material properties. It facilitates a sequential memory-efficient processing of massive material defects in a multiresolution framework, and also supports a functionality of partial damage conversion to serve different needs in subsequent numerical analyses. Numerical simulation was conducted with different settings of material defects. The analysis results indicate the efficacy of the proposed method, offering a potential (i) to interface between multiscale material defects and (ii) as an effective method of homogenization for the determination of the damage variable in continuum damage mechanics.