2025/05/08 by Xuenan Li, Robert V. Kohn, Li, Xuenan +1 · 1 citation
Engineering · Materials Science · #49N99 #74B20 #74Q05 #Acoustic Wave Phenomena Research #Cellular and Composite Structures #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlocal and gradient elasticity in micro/nano structures
paper · pdf · doi:10.48550/arxiv.2505.05436
openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We study the sense in which the continuum limit of a broad class of discrete materials with periodic structures can be viewed as a nonlinear elastic material. While we are not the first to consider this question, our treatment is more general and more physical than those in the literature. Indeed, it applies to a broad class of systems, including ones that possess mechanisms; and we discuss how the degeneracy that plagues prior work in this area can be avoided by penalizing change of orientation. A key motivation for this work is its relevance to mechanism-based mechanical metamaterials. Such systems often have ``soft modes'', achieved in typical examples by modulating mechanisms. Our results permit the following more general definition of a soft mode: it is a macroscopic deformation whose effective energy vanishes -- in other words, one whose spatially-averaged elastic energy tends to zero in the continuum limit.