Lattice materials open a large design space with respect to mechanical properties such as stiffness or strength, and weight. Recent and anticipated advances in additive manufacturing techniques are opening the floor for structural integration on a material scale. This poses the need for efficient and robust design approaches. To overcome the excessive computational demand for full-fidelity mechanical characterization of such lattices, homogenization is an effective choice to replace a fully-resolved simulation representing each and every strut and node in the truss by an efficient continuum representation.  However, the challenge to bridge between continuum and discrete scale design parameters arises. Projection-based methods have proven to provide near-optimal results while being computationally efficient, yet restrict the design space and require careful postprocessing on the microscale.  

We borrow from crystallography principles and propose a lattice generation procedure that generalizes the design space of general classes of truss networks (including periodic and structurally graded ones) while assuring robust microstructure constructability and printability. The approach is generally applicable to 2D and 3D, bending- and stretching-dominated lattices. In conjunction with a semi-analytical, homogenization-based continuum model that admits effective property prediction without full-scale discrete lattice simulations, a generic and efficient exploration of truss lattices is possible. Periodic and graded lattice studies are performed and, embedded in homogenization-based topology optimization, near-optimal lattice-based structures are generated for a variety of load cases.

Topology optimization of functionally graded truss lattices based on nonlinear homogenization

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