A morphoelastic stability framework for post-critical pattern formation in growing thin biomaterials

Morphological instabilities play a key role in the evolution of form and function growing biomaterials. Spatially varying differential growth, particular, leads to residual stresses that for soft materials or slender geometries are favourably relieved by out-of-plane buckling wrinkling. While onset instability biomaterials has been studied extensively, post-critical regime remains poorly understood. To this end, paper presents robust computational modelling framework morphoelastic associated pattern formation. The seven-parameter shell element—commonly used elasto-plastic analysis engineering materials—is implemented alongside multiplicative decomposition deformation gradient tensor into growth an elastic part. governing nonlinear equations solved using generalised path-following/numerical continuation solver facilitates comprehensive exploration stability landscape through pinpointing critical points branch switching at bifurcations. utility power is demonstrated unveiling complex formation phenomena arise as result sequentially occurring morphological instabilities. In we highlight central exponential edge plays fractal wrinkling patterns, blooming doubly-curved flower petals, wavy daffodil trumpets. addition, ability track parameter space enables efficient sensitivity studies material parameters on presented thus versatile tool biological systems design biotechnology applications.