Integrating lattice materials science into the traditional processing-structure-properties paradigm

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Integrating lattice materials science into the traditional processing– structure–properties paradigm Frank W. Zok

, Materials Department, University of California, Santa Barbara, CA 93106, USA

Address all correspondence to Frank W. Zok at [email protected] (Received 18 September 2019; accepted 19 November 2019)

Abstract Periodic lattice materials have been studied extensively in numerous science and engineering fields. Despite the vast knowledge that has emerged, the activities have been stove-piped within individual research communities, often in isolation from those in related fields. To bring this work into a holistic framework, the present article considers the elements needed to integrate the study of lattice materials into the processing–structure–properties paradigm that underpins materials science as an academic discipline. The emphasis is on concepts of structure involving topology, morphology, and defects of lattice materials, with illustrations of structure–property relations in the context of lattice strength.

Introduction Lattice materials comprising periodic arrays of interconnected struts have emerged as a new class of engineering materials with potential for use in an incredibly diverse range of applications, including structural biomedical implants,[1–3] aerospace and naval structures,[4] force protection systems,[5,6] thermal management,[5] actuation,[7–9] high-performance running shoes,[10] and photonic and phononic crystals.[11,12] They can be designed to exhibit unusual properties, including negative thermal expansion,[13] negative Poisson’s ratio,[14] fluid-like elasticity (with an extraordinarily high ratio of bulk to shear moduli),[15] unusually high damping capacity,[16] and negative mass density.[17] When the arrays are large, with individual unit cells being small relative to macroscopic length scales of interest, lattices can be treated effectively as other engineering materials in the sense that their properties can be couched in terms of their volume-averaged response to external stimuli. In establishing relationships between macroscopic properties and lattice structure, questions arise about the nature of structure of lattice materials and how characteristics of structure can be integrated into the materials science paradigm. The field of materials science as an academic discipline is founded principally on relationships between processing, structure, and properties (Fig. 1). Here, structure encompasses the organization of atoms or molecules relative to one another, often in the form of crystals; boundaries between domains of differing orientation and/or composition; and defects that disrupt periodic arrangements at length scales ranging from the atomic to the macroscopic. Some of the important structural characteristics—including crystalline grains, grain and interphase boundaries, dislocations, precipitates, solute atoms, and

vacancies—are depicted schematically in Figs. 2(a)–2(d). Although these characteristics are relevant to the constituent materials from which l