Kelp blade morphogenesis through wrinkling mechanical instabilities

Brown macroalgae, also known as kelp, form an important marine ecosystems and their varied morphology directly affects their function and survival. A kelp individual is composed of a holdfast that anchors it to the sea floor, a stipe that rises to the water surface, and leaf-like structures known as blades. A close inspection of the blades' surface reveals complex and diverse types of wrinkled patterns. The morphogenesis of these surfaces could be linked to the differential growth across the thickness of the blade. Indeed, the outer layers (i.e, the meristoderm) grow through cell proliferation while pulling on a passive inner core (i.e., the medulla and cortex). This incompatibility in growth eventually leads to a surface instability called wrinkling which has mostly been characterized in bi-layers systems. Here, we model the kelp blades as a tri-layer to study the influence of wrinkling instabilities. Using a combination of reduced-order models and finite element simulations, we characterize the influence of material and geometrical parameters (e.g., layers' modulus, thickness, boundary conditions) on the wrinkling onset and the post-instability deformation of the system. In light of numerical predictions, we experimentally reproduce and control wrinkled surfaces on pre-stretched polymers. Our results shed light onto the role of wrinkling in the morphogenesis of kelp blade and are used to induce wrinkles in artificial systems.