UC Santa Barbara

Cellular structures, including stochastic foams and ordered lattices, have been used extensively in a wide range of engineering applications. The nearly-constant crushing stress of stochastic foams make them particularly useful for energy absorption. Ordered lattices, on the other hand, are better suited for stiff and strong load-bearing components. Despite their higher strength, ordered lattices fail by internal buckling and exhibit concurrent strain softening during compressive loading, making them undesirable for energy absorption applications. The performance gaps between existing stochastic foams and ordered lattices appear large and motivate the current work.

The overarching goal of this work is to identify design strategies for tailoring the compressive properties of cellular structures, targeting in particular concepts that provide combinations of high strength and high straining capacity. A two-pronged approach is employed. The first involves ordered bi-material lattices in which material choices are based on local mechanical requirements. The issues are addressed through a combination of analytical models, finite element simulations, and experimental studies on select lattice structures. Two broad classes of bi-material lattices are introduced: one in 2D and one in 3D. The study on 2D lattices focuses on identifying and analyzing a primitive structural motif and demonstrating the concept by printing and testing rudimentary 2D designs. The ensuing results yield guidelines for bi-material lattice design (to mitigate the most common failure modes) and highlight deficiencies in the nature of macroscopic straining and in joint design. The study on the 3D versions addresses some of these deficiencies. The focus is specifically on design of joints to facilitate articulation over a wide rotational range and the morphology of structural elements that enable strain reversibility. It also examines the potential for tailoring the topology and morphology of the structural elements to improve load bearing capacity. Structures that combine struts with plate elements appear to exhibit the greatest potential. The studies on both 2D and 3D bi-material lattices demonstrate how emergent multi-material printing capabilities can be exploited in expanding the design space for future lattice materials.

The second prong focuses on the connections between specific microstructural features of stochastic foams and mechanical response. This is done by computationally generating a large number of stochastic foams, analyzing various microstructural characteristics, and simulating their compressive response. Results indicate that cell size polydispersity governs the compressive response of foams. Foams with tight distributions in cell size exhibit stronger responses but are also more sensitive to boundary conditions and finite foam dimensions. This work offers insight into variables that must be considered when tailoring the response of foams including cell size polydispersity, number of cells spanning a unit dimension, and boundary conditions.