Consistent machine learning for topology optimization with microstructure-dependent neural network material models

Abstract: Additive manufacturing methods together with topology optimization have enabled the creation of multiscale structures with controlled spatially-varying material microstructure. However, topology optimization or inverse design of such structures in the presence of nonlinearities remains a challenge due to the expense of computational homogenization methods and the complexity of differentiably parameterizing the microstructural response. A solution to this challenge lies in machine learning techniques that offer efficient, differentiable mappings between the material response and its microstructural descriptors. This work presents a framework for designing multiscale heterogeneous structures with spatially varying microstructures by merging a homogenization-based topology optimization strategy with a consistent machine learning approach grounded in hyperelasticity theory. We leverage neural architectures that adhere to critical physical principles such as polyconvexity, objectivity, material symmetry, and thermodynamic consistency to supply the framework with a reliable constitutive model that is dependent on material microstructural descriptors. Our findings highlight the potential of integrating consistent machine learning models with density-based topology optimization for enhancing design optimization of heterogeneous hyperelastic structures under finite deformations.