Related papers: Growth of Form in Thin Elastic Structures
A static variational model for shape formation in heteroepitaxial crystal growth is considered. The energy functional takes into account surface energy, elastic misfit-energy and nucleation energy of dislocations. A scaling law for the…
Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those…
We describe a novel crystal growth instability that enhances the development of thin edges, promoting the formation of plate-like or hollow columnar morphologies. This instability arises when diffusion-limited growth is coupled with…
In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Non-mechanical stimuli, such as one that tends to modify the rest curvature of an…
Open cellular solids usually possess random microstructures that may contain a characteristic length scale, such as the cell size. This gives rise to size dependent mechanical properties where large systems behave differently from small…
Growth-induced instabilities are ubiquitous in biological systems and lead to diverse morphologies in the form of wrinkling, folding, and creasing. The current work focusses on the mechanics behind growth-induced wrinkling instabilities in…
Spontaneous growth of long-wavelength deformations is a defining feature of active fluids with orientational order. We investigate the effect of biaxial rectangular confinement on the instability of initially shear-aligned 3D isotropic…
We identify effective models for thin, linearly elastic and perfectly plastic plates exhibiting a microstructure resulting from the periodic alternation of two elastoplastic phases. We study here both the case in which the thickness of the…
The growth of an elastic film adhered to a confining substrate might lead to the formation of delimitation blisters. Many results have been derived when the substrate is flat. The equilibrium shapes, beyond small deformations, are…
We model the formation and evolution of wrinkles in a floating elastic sheet under uniaxial compression. This is a canonical setup in the study of wrinkling, and whilst its static equilibrium configuration is well characterised, its…
Heterogeneous materials, such as rocks and concrete, have a complex dynamics including hysteresis, nonlinear elasticity and viscoelasticity. It is very sensitive to microstructural changes and damage. The goal of this paper is to propose a…
Symmetry-breaking instabilities play an important role in understanding the mechanisms underlying the diversity of patterns observed in nature, such as in Turing's reaction--diffusion theory, which connects cellular signalling and transport…
A thin flat rectangular plate supported on its edges and subjected to in-plane loading exhibits stable post-buckling behaviour. However, the introduction of a nonlinear (softening) elastic foundation may cause the response to become…
In this article we study synchronization of systems of homogeneous phase-coupled oscillators with plastic coupling strengths and arbitrary underlying topology. The dynamics of the coupling strength between two oscillators is governed by the…
An important question in biology is how the relative size of different organs is kept nearly constant during growth of an animal. This property, called proportionate growth, has received increased attention in recent years. We discuss our…
Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant…
Various models of tumor growth are available in the litterature. A first class describes the evolution of the cell number density when considered as a continuous visco-elastic material with growth. A second class, describes the tumor as a…
Cellular patterns formed by self-organization of dislocations are a most conspicuous feature of dislocation microstructure evolution during plastic deformation. To elucidate the physical mechanisms underlying dislocation cell structure…
We present an original approach for predicting the static recrystallization texture development during annealing of deformed crystalline materials. The microstructure is considered as a population of subgrains and grains whose sizes and…
Leaves and flowers frequently have a characteristic rippling pattern at their edges. Recent experiments found similar patterns in torn plastic. These patterns can be reproduced by imposing metrics upon thin sheets. The goal of this paper is…