A model for hierarchical patterns under mechanical stresses

Abstract

We present a model for mechanically-induced pattern formation in growing biological tissues and discuss its application to the development of leaf venation networks. Drawing an analogy with phase transitions in solids, we use a phase field method to describe the transition between two states of the tissue, e.g. the differentiation of leaf veins, and consider a layered system where mechanical stresses are generated by differential growth. We present analytical and numerical results for one-dimensional systems, showing that a combination of growth and irreversibility gives rise to hierarchical patterns. Two-dimensional simulations suggest that such a mechanism could account for the hierarchical, reticulate structure of leaf venation networks, yet point to the need for a more detailed treatment of the coupling between growth and mechanical stresses.

To appear in Philosophical Magazine. 18 pages, 8 figures

References in corpus (6)

• Dynamic instabilities of fracture under biaxial strain using a phase field model
• Phase Field Modeling of Fast Crack Propagation
• Phase field theory of polycrystalline solidification in three dimensions
• The role of elastic stresses on leaf venation morphogenesis
• Study of the branching instability using a phase field model of inplane crack propagation
• Crack propagation as a free boundary problem

Cited by in corpus (3)

• Optimal elasticity of biological networks
• Softening induced instability of a stretched cohesive granular layer
• Limitations of the modelling of crack propagating through heterogeneous material using a phase field approach