Work

Periodic Auxetics: Structure and Design

Year: 2017

Type: article

Abstract: Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson's ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present article, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids.

Source: The Quarterly Journal of Mechanics and Applied Mathematics

DOI: 10.1093/qjmam/hbx028

Authors: Ciprian S Borcea, Ileana Streinu

Institutions: Rider University, Smith College

Language: English

Topic: Cellular and Composite Structures

Subfield: Mechanical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, National Institutes of Health, National Institute of General Medical Sciences

Awards: AF:Medium:Collaborative:RUI:Structure in Motion:Algorithms for Kinematic Design, AF: Small: Collaborative:RUI: Mathematical foundations of reconfiguration algorithms for geometrically constraint structures, AF: Small: Collaborative:RUI: Mathematical foundations of reconfiguration algorithms for geometrically constraint structures, AF:Medium:Collaborative:RUI:Structure in Motion:Algorithms for Kinematic Design, Rigidity and flexibility of large bio-molecular assemblies