Dominant negative Poynting effect for soft tissues

TL;DR

This paper reveals that soft tissues can exhibit both positive and negative Poynting effects during shear, with a dominant negative effect linked to fiber inextensibility, challenging traditional assumptions based on isotropic materials.

Contribution

It identifies three shear modes in soft tissues that produce both positive and negative Poynting effects, highlighting the role of fiber inextensibility as a key mechanism.

Findings

Negative Poynting effect dominates in one shear mode.

Positive Poynting effect is smaller and occurs in two other modes.

Fiber inextensibility is the primary cause of the negative effect.

Abstract

We identify three distinct shearing modes for simple shear deformations of transversely isotropic soft tissue which allow for both positive and negative Poynting effects (that is, they require compressive and tensile lateral normal stresses, respectively, in order to maintain simple shear). The positive Poynting effect is that usually found for isotropic rubber. Here, specialisation of the general results to three strain-energy functions which are quadratic in the anisotropic invariants, linear in the isotropic strain invariants and consistent with the linear theory suggests that there are two Poynting effects which can accompany the shearing of soft tissue: a dominant negative effect in one mode of shear and a relatively small positive effect in the other two modes. We propose that the relative inextensibility of the fibres relative to the matrix is the primary mechanism behind this large negative Poynting effect.