Connections between the morphoelastic treatment of growth-induced instabilities and earlier hyperelastic treatments of buckling under thrust

Abstract

In soft tissue, growth-induced instability is increasingly being viewed as a key agent in certain morphological developments, such as the folding of the cerebral cortex. As such, the study of growth-induced instability in the context of morphoelastic large deformation continuum mechanics is a burgeoning field of study. In this work, we examine some of the connections between these new developments and earlier work that can be viewed as the conventional—or no-growth—hyperelastic theory. By a systematic examination of a standard problem, certain direct correspondences are clarified which effectively permit results of a very general nature in the conventional theory to inform ongoing work in the morphoelastic theory.