Compression Instabilities of Tissues with Localized Strain Softening

TL;DR

This paper examines how localized strain softening in soft tissues, modeled by a specific strain-energy density, influences mechanical instabilities during compression and bending, revealing early instability only at severe compression ratios.

Contribution

It investigates the impact of a strain-energy density with localized strain softening on instability behaviors in soft tissues, comparing with classical neo-Hookean models.

Findings

Localized strain softening causes early instability at severe compression ratios.

Instability behavior remains similar to neo-Hookean solids at less severe strains.

The study provides insights into the mechanical behavior of tissues affected by Marfan's syndrome.

Abstract

The stress-strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be non-convex. More specifically, Haughton and Merodio recently proposed a strain-energy density leading to localized strain softening, in order to model the unusual mechanical behavior of these isotropic, incompressible tissues. Here we investigate how this choice of strain energy affects the results of some instabilities studies, such as those concerned with the compression of infinite and semi-infinite solids, slabs, and cylinders, or with the bending of blocks, and draw comparisons with known results established previously for the case of a classical neo-Hookean solid. We find that the localized strain softening effect leads to early instability only when instability occurs at severe compression ratios for neo-Hookean solids, as is the case for bulk, surface, and bending instabilities.