Compression stiffening in biological tissues: on the possibility of classic elasticity origins

TL;DR

This paper investigates compression stiffening in biological tissues and biomaterials, demonstrating that classic elasticity theories can explain this phenomenon, which is observed across various tissues and materials, highlighting their mechanical similarities.

Contribution

It extends the understanding of compression stiffening to new biomaterials and shows that classic elasticity theories can account for this behavior based on reference states and pre-stress conditions.

Findings

Compression stiffening observed in brain, liver, fat tissues, agarose gel, and fruit flesh.

Classic elasticity theories by Barron and Klein, and Birch, can explain linear compression stiffening.

The applicability of each theory depends on the material's reference state and axial stress development.

Abstract

Compression stiffening, or an increase in shear modulus with increasing compressive strain, has been observed in recent rheometry experiments on brain, liver, and fat tissues. Here, we extend the known types of biomaterials exhibiting this phenomenon to include agarose gel and fruit flesh. Further, we show that two different results from classic elasticity theory can account for the phenomenon of linear compression stiffening. One result is due to Barron and Klein, extended here to the relevant geometry and pre-stresses; the other is due to Birch. For incompressible materials, there are no adjustable parameters in either theory. Which one applies to a given situation is a matter of reference state, suggesting that the reference state is determined by the tendency of the material to develop, or not develop, axial stress (in excess of the applied pre-stress) when subjected to torsion at constant axial strain. Our experiments and analysis also strengthen the notion that seemingly distinct animal and plant tissues can have mechanically similar behavior under certain conditions.