Related papers: Growth induced instabilities in a circular hyperel…
We consider mechanically-induced pattern formation within the framework of a growing, planar, elastic rod attached to an elastic foundation. Through a combination of weakly nonlinear analysis and numerical methods, we identify how the shape…
In this paper, a theoretical scheme is proposed for shape-programming of thin hyperelastic plates through differential growth. First, starting from the 3D governing system of a hyperelastic (neo-Hookean) plate, a consistent finite-strain…
A continuum model for growth of solids is developed, considering adatom deposition, surface diffusion, and configuration dependent incorporation rate. For amorphous solids it is related to surface energy densities. The high adatom density…
We theoretically study the Plateau-Rayleigh instability of a thin viscous film covering a fiber consisting of a rigid cylindrical core coated with a thin compressible elastic layer. We develop a soft-lubrication model, combining the…
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this…
The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are…
We study the Plateau-Rayleigh instability of a viscoelastic soft solid layer coated on a rigid cylinder i.e., a soft fibre with a rigid core. The onset of instability is examined using a linear stability analysis. We find that increasing…
The paper deals with the interaction between buckling and resonance instabilities of mechanical systems. Taking into account the effect of geometric nonlinearity in the equations of motion through the geometric stiffness matrix, the problem…
Regularity properties of solutions for a class of quasi-stationary models in one spatial dimension for stress-modulated growth in the presence of a nutrient field are proven. At a given point in time the configuration of a body after pure…
We investigate the growth of a pattern of liquid crests emerging in a layer of magnetic liquid when subjected to a magnetic field oriented normally to the fluid surface. After a steplike increase of the magnetic field, the temporal…
Growth and folding in one-layered model tissue sheets are studied in a stochastic, lattice-free single cell model which considers the discrete cellular structure of the tissue, and a coarse grained analytical approach. The polarity of the…
Motivated by the redrawing of hot glass into thin sheets, we investigate the shape and stability of a thin viscous sheet that is inhomogeneously stretched in an imposed non-uniform temperature field. We first determine the associated base…
Instabilities of fluid-fluid interfaces are ubiquitous in passive soft matter. Adding activity to the interface or either fluid can dramatically change the stability of the interface. Using experiment and theory, we investigate the…
Spontaneous material shape changes, such as swelling, growth or thermal expansion, can be used to trigger dramatic elastic instabilities in thin shells. These instabilities originate in geometric incompatibility between the preferred…
The response of paper to humidity variations is a complex multi-scale problem. The hygroscopic swelling of individual fibres and their interactions within the fibrous network govern the macroscopic response. At this scale, moisture induced…
We developed a consistent mathematical model for isotropic crystal growth on a substrate covered by the mask material with a periodic series of parallel long trenches where the substrate is exposed to the vapor phase. Surface diffusion and…
We investigate the theoretical nonlinear response, Hessian stability, and possible wrinkling behaviour of a voltage-activated dielectric plate immersed in a tank filled with silicone oil. Fixed rigid electrodes are placed on the top and…
The planar front of a growing a crystal is often destroyed by instabilities. In the case of growth from a condensed phase, the most frequent ones are diffusion instabilities, which will be but briefly discussed in simple terms in chapter…
Linear and weakly nonlinear stability analyses of an externally shear-imposed, gravity-driven falling film over a uniformly heated wavy substrate are studied. The longwave asymptotic expansion technique is utilized to formulate a single…
In this paper we consider the inverse problem of determining a rigid inclusion inside a thin plate by applying a couple field at the boundary and by measuring the induced transversal displacement and its normal derivative at the boundary of…