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Bibliographic Details
Main Authors: Li, Xuenan, Kohn, Robert V.
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2509.16907
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Table of Contents:
  • There is a growing mechanics literature concerning the macroscopic properties of mechanism-based mechanical metamaterials. This amounts mathematically to a homogenization problem involving nonlinear elasticity. A key goal is to identify the "soft modes" of the metamaterial. We achieve this goal using methods from homogenization for some specific 2D examples -- including discrete models of the Rotating Squares metamaterial and the Kagome metamaterial -- whose soft modes are compressive conformal maps. The innovation behind this achievement is a new technique for bounding the effective energy from below, which takes advantage of the metamaterial's structure and symmetry.