We present a new framework for the simultaneous optimiziation of both the topology as well as the relative density grading of cellular structures and materials, also known as lattices. Due to manufacturing constraints, the optimization problem falls into the class of NP-complete mixed-integer nonlinear programming problems. To tackle this difficulty, we obtain a relaxed problem from a multiplicative split of the relative density and a penalization approach. The sensitivities of the objective function are derived such that any gradient-based solver might be applied for the iterative update of the design variables. In a next step, we introduce a material model that is parametric in the design variables of interest and suitable to describe the isotropic deformation behavior of quasi-stochastic lattices. For that, we derive and implement further physical constraints and enhance a physics-augmented neural network from the literature that was formulated initially for rhombic materials. Finally, to illustrate the applicability of the method, we incorporate the material model into our computational framework and exemplary optimize two-and three-dimensional benchmark structures as well as a complex aircraft component.
Towards end-to-end optimization in multimaterial 3D printing
addressline= Sibley School of Mechanical；Aerospace Engineering, Cornell University , city= Ithaca , state= NY , country= USA；addressline= Department of Aerospace \& Mechanical Engineering, University of Southern California , city= Los Angeles , state= CA , country= USA；addressline= Department of Materials Science；Engineering, Technion - Israel Institute of Technology , city= Haifa , country= Israel；addressline= Pasteur Labs , city= Brooklyn , state= NY , country= USA
