A different catch for Poisson

Date
2022-05-04
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Theoretical analyses, computations, and experiments of multiscale materials: A tribute to Francesco dell’Isola
Print ISSN
1869-8433
Electronic ISSN
Publisher
Springer
Volume
175
Issue
Pages
3 - 23
Language
English
Type
Book Chapter
Journal Title
Journal ISSN
Volume Title
Series
Advanced Structured Materials;
Abstract

Poisson’s ratio, similar to other material parameters of isotropic elasticity, is determined via experiments corresponding to small strains. Yet at small-strain linear elasticity, Poisson’s ratio has a dual nature; although commonly understood as a geometrical parameter, Poisson’s ratio is also a material parameter. From a geometrical perspective only, the concept of Poisson’s ratio has been extended to large deformations by Beatty and Stalnaker. Here, through a variational analysis, we firstly propose an alternative relationship between the Poisson ratio and stretches at finite deformations such that the nature of Poisson’s ratio as a material parameter is retained. In doing so, we introduce relationships between the Poisson ratio and stretches at large deformations different than those established by Beatty and Stal naker. We show that all the nonlinear definitions of Poisson’s ratio coincide at the reference configuration and thus, material and geometrical descriptions too coincide, at small-strains linear elasticity. Secondly, we employ this variational approach to bring in the notion of nonlinear Poisson’s ratio in peridynamics, for the first time. In particular, we focus on bond-based peridynamics. The nonlinear Poisson’s ratio of bond-based peridynamics coincides with 1/3 for two-dimensional and 1/4 for three-dimensional problems, at the reference configuration.

Course
Other identifiers
Book Title
Theoretical analyses, computations, and experiments of multiscale materials: A tribute to Francesco dell’Isola
Keywords
Non-linear Poisson’s ratio, Variational elasticity, Peridynamics
Citation
Published Version (Please cite this version)