  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.
