  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.
