Compression instabilities of tissues with localized strain softening

The stress-strain relationship of biological soft tissues affected by Marfan's syndrome is believed to be nonconvex. 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.