Growth and patterns of residually stressed core-shell soft sphere

Abstract Many biological tissues and organisms are in a state of residual stress, which should be considered rather than ignored as in many previous studies. In this work, we establish a theoretical model to study the growth and patterns of a residually stressed core–shell soft sphere. The effect of the initial residual stress is considered by employing a modified multiplicative decomposition growth model. Numerical solution of the marginal instability relies on gaining a critical differential growth ratio which depends on the initial residual stress, geometry, and material elasticity. Results show that the initial residual stress can not only well regulate the growth procedure but also affect the critical pattern of the growing instability. Compared with the way of changing material elasticity or geometrical size, it is more effective in practice. This work may help understand the morphological transition of residually stressed soft matters, and provide insights into the growth self-assembly and biomedical engineering.