Identification of microstructure from macroscopic measurement using inverse multiscale analysis

Most of the tailored materials are heterogeneous at the ingredient level. Analysis of those heterogeneous structures requires the knowledge of microstructure. With the knowledge of microstructure, multiscale analysis is carried out with homogenization at the micro level. Second-order homogenization is carried out whenever the ingredient size is comparable to the structure size. Therefore, knowledge of microstructure and its size is indispensable to analyzing those heterogeneous structures. Again, any structural response contains all the information of microstructure, like microstructure distribution, volume fraction, size of ingredients, etc. Here, inverse analysis is carried out to identify a heterogeneous microstructure from macroscopic measurement. Two-step inverse analysis is carried out in the identification process; in the first step, the macrostructures length scale and effective properties are identified from the macroscopic measurement using gradient-based optimization. In the second step, those effective properties and length scales are used to determine the microstructure in inverse second-order homogenization.