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.

翻译：大多数定制化材料在组分层面具有非均质性。分析此类非均质结构需要掌握微观结构信息。在已知微观结构的前提下，可通过微观尺度均质化进行多尺度分析。当组分尺寸与结构尺寸相当时，需采用二阶均质化方法。因此，微观结构及其尺寸信息是分析此类非均质结构的必要前提。值得注意的是，任何结构响应均包含微观结构的全部信息，如微观结构分布、体积分数、组分尺寸等。本研究通过逆向分析从宏观测量中识别非均质微观结构。识别过程采用两步逆向分析法：第一步通过基于梯度的优化方法，从宏观测量中识别宏观结构长度尺度与等效属性；第二步在逆向二阶均质化过程中，利用这些等效属性与长度尺度确定微观结构。