Microscopic stress-constrained two-scale topology optimisation for additive manufacturing

The extraordinary mechanical properties of additive manufactured two-scale lattice structures can be substantially enhanced by employing optimisation techniques at both macroscopic and microscopic scales. Nonetheless, maintaining structural strength in designs that simultaneously incorporate complicated macroscopic and microscopic configurations presents a significant challenge. In this study, a two-scale topology optimisation method with microscopic stress constraints is proposed to find a two-scale structure with maximised stiffness while making the microscopic stress satisfy specified strength criteria. Herein, a two-scale structural stress characterisation based on the microscopic characterised stress field is firstly established to avoid the great computational effort caused by microscopic stress analysis at every macroscopic localisation. Then, a two-scale stress-constrained aggregation strategy is proposed to reduce the vast number of stress constraints involved in two-scale optimisation. The sensitivities of the aggregated stress constraints are derived using the adjoint variable method, and the optimisation problem is solved using a gradient-based mathematical algorithm. Numerical examples illustrate the effect of the stress constraints by comparing the optimisation results with and without microscopic stress constraints. Finally, specimens optimised using the proposed method are realised through additive manufacturing, and the results are further validated by testing stress distribution using a non-contact full-field strain measurement system.