Concurrent Multiscale Topology Optimization of Lattice Meta-materials using a Multiscale Moving Morphable Component Framework
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Development of additive manufacturing techniques (e.g. 3D-printing) has enabled the fabrication of complex geometries such as meta-materials. Their high specific energy absorption capabilities make them of interest for applications such as automotive crash, where non-linear plastic material behavior is prominent and gradient information is not easily accessible or reliable. This motivates the application of population-based optimization algorithms to topology optimization in crash-worthiness analysis. For the modeling of structures made of strut-based lattice meta-materials, commonly a macroscale detailing the overall structure and its partitioning into sub cells, and a microscale describing the geometry of these sub-cells, is defined. Due to the prohibitively high computational cost of a finely meshed FE model of multiscale structures, several multiscale modeling approaches, such as the FE2 method or offline homogenization, have been developed. For multi-query applications, the expense of using these methods for varying, generally anisotropic microstructures with plastic material behavior is still high and has motivated the application of model order reduction to the FE2 method [1]. Alternatively, simplified modeling may increase efficiency while sacrificing some level of accuracy. For example, Schwahofer et al. have performed Free Material Optimization for orthotropic unit cells and semi-periodic designs based on simplified modeling of a unit cell’s trusses via beam elements [2]. In this contribution, we discuss the capabilities of an extension of the Moving Morphable Components (MMC) framework [3] to encode multiscale design parameters within its parametrization, paired with a simplified modeling approach for strut-based lattices based on beam elements. With the above-described method, concurrent macroscale topology optimization and microscale shape optimization is realized while maintaining a relatively low dimensionality of the optimization problem. The latter is especially beneficial for population-based methods since these generally exhibit convergence issues with increasing dimensionality. The results are optimized macroscale topologies with a non-periodic lattice microscale structure.
