• Narasimha Boddeti, Washington State University

Topology optimization (TO) is a versatile design methodology that uses optimization to iteratively arrive at an optimal material layout (i.e., topology) for a structure and has been applied across various engineering disciplines. Multiscale topology optimization (MTO) refers to use of TO towards design of multiscale structures that are made of materials that span multiple lengths scales such as hierarchical lattice structures, architected cellular materials and fiber-based composites. While conventional design methods fix many of the available characteristic material parameters at different length scales, MTO can accommodate all (or most) of these as variables in the design optimization process. This enables simultaneous optimization of the structure at multiple length scales and blurs the distinction between material and structure. This presents engineers an extraordinary ability to design both material and structure through simultaneous optimization of the macroscale topology and the spatially varying meso/micro/nanostructure. MTO, thus, enables realization of interesting property gradients akin to those found in natural materials such as wood, bone, and nacre.

Various MTO approaches have been proposed with varying degrees of computational complexity. A vast majority of them are limited two material length scales. These can be broadly categorized based on their approach towards microstructure design. Some approaches make no assumptions about the microstructure and both macroscale topology and the microstructure are simultaneously optimized. This necessitates constraints on connectivity of microstructures at neighboring material points and is computationally intensive. The other approaches choose a family of microstructures or even a single fixed parametrized microstructure and employ analytical or numerical homogenization to realize multiscale structures at reduced computational complexity (as the microstructural behavior is not explicitly modeled). The latter approaches, however, need to be augmented with a dehomogenization method to realize a manufacturable shape for the optimal design.

While considerable progress has been made, there are still significant questions regarding the effectiveness of various MTO approaches such as the issue of scale separation, manufacturability of the optimal designs, practical use of MTO in engineering applications, singularities in dehomogenization methods and their effect on the optimality of the design, among others. This mini symposium, titled "Multiscale Topology Optimization", thus invites researchers to share their research ideas, views, and findings on this interesting topic.