2D and Axisymmetric Incompressible Elastic Green's Functions

TL;DR

This paper compiles and extends Green's functions for 2D and axisymmetric incompressible elastic solids, including large pre-strain effects, providing tools for analyzing stability and deformation in such materials.

Contribution

It provides a comprehensive list of Green's functions for isotropic incompressible solids, extending to neo-Hookean models with pre-strain, and reproduces the Biot instability.

Findings

Green's functions for pre-strained half-spaces reproduce Biot instability.

Extended isotropic incompressible theory to neo-Hookean solids with large pre-strain.

Compiled a comprehensive list of 2D and axisymmetric Green's functions.

Abstract

We compile a list of 2-D and axisymmetric Green's functions for isotropic full and half spaces, to complement our letter "Linear elasticity of incompressible solids". We also extend the isotropic exactly incompressible linear theory from our letter to include isotropic neo-Hookean solids subject to a large pre-strain, and present Green's functions in these cases. The Green's function for a pre-strained half-space reproduces the Biot instability.