  Biological soft tissues exhibit elastic properties which can be dramatically
different from rubber-type materials (elastomers). To gain a better
understanding of the role of constitutive relationships in determining material
responses under loads we compare three different types of instabilities (two in
compression, one in extension) in hyperelasticity for various forms of strain
energy functions typically used for elastomers and for soft tissues.
Surprisingly, we find that the strain-hardening property of soft tissues does
not always stabilize the material. In particular we show that the stability
analyses for a compressed half-space and for a compressed spherical thick shell
can lead to opposite conclusions: a soft tissue material is more stable than an
elastomer in the former case and less stable in the latter case.
