UC Santa Barbara

Periodic truss structures can be designed with high specific stiffness and specific strength, exceeding those of stochastic foams by an order of magnitude at low relative densities. Despite the recognition of the enormous potential of periodic trusses, stochastic foams are still used in many applications. Two factors that limit the adoption of trusses are addressed in the present work: (i) there are no widely-accepted descriptors of truss structure, and (ii) many studies neglect effects that come into play in real (finite) truss structures. Instead, previous analyses largely focused on notional truss materials: aggregates of many struts with dimensions much smaller than macroscopic scales of interest. This approach fails to capture the effects of external boundaries which are key to understanding the performance of manufactured trusses. The goals of the present study are to: (i) develop a conceptual framework for classification of truss topologies that enables identification of topologies with potentially attractive mechanical attributes; (ii) couple this framework with robust finite element models to predict deformation and failure of trusses; and (iii) provide new insights into the roles of realistic features that can limit truss performance, including the presence of free surfaces, nodes with finite stiffness and strength, and defects in the form of individual missing struts. These goals are pursued through a combination of finite element simulations of the mechanical responses of trusses under compressive, tensile or shear loadings and experimental studies on mechanical properties of select truss structures, employing digital image correlation to examine in detail deformation and failure of individual constituent struts as well as the structure as a whole.

The present work begins by establishing a system for classification of truss structure. By systematically stepping through and analyzing structure types identified through the classification system, several maximally-stiff, elastically-isotropic trusses are identified. In finite-sized trusses, strain elevations are obtained in struts near the external free boundaries: a consequence of reduced nodal connectivity and thus reduced constraint on strut deformation and rotation. Some of these effects can be mitigated by circular nodal fillets, which are shown to enhance the bending stiffness of the strut ends and thus increase the stress for buckling (by ≈ 20% for the geometries tested). In all trusses studied, the strain elevations due to bulk defects (distant from free surfaces) are comparable to or lower than those associated with the surfaces themselves. Although defects located at truss corners and truss edges cause the highest elevations in strut strains, their effects on truss strength are small (5–25%). The results provide a set of design guidelines that, when used in combination, yield trusses that are defect tolerant, possess high stiffness and achieve the full strength potential of the truss.