Biomechanical modeling of surface wrinkling of soft tissues with growth-dependent mechanical properties

This paper explores growth induced morphological instabilities in biological soft materials. In view of that the growth of a living tissue not only changes its geometry but also can alter its mechanical properties, we suggest a refined volumetric growth model incorporating the effects of growth on the mechanical properties of materials. Analogy between this volumetric growth model and the conventional thermal stress model is addressed for both small and finite deformation problems, which brings great ease for the finite element analysis based on the suggested model. Examples of growth induced surface wrinkling behavior in soft composites, including core-shell soft cylinders and three-layered soft tissues, are explored. The results and discussions foresee possible applications of the model in understanding the correlation between the morphogenesis and growth of soft biological tissues (e.g. skins and tumors), as well as in evaluating the deformation and surface instability behavior of soft artificial materials induced by swelling/shrinkage.