Related papers: A Model for Elastic Evolution on Foliated Shapes
Vertex Models, as used to describe cellular tissue, have an energy controlled by deviations of each cell area and perimeter from target values. The constrained nonlinear relation between area and perimeter leads to new mechanical response.…
Soft elastic capsules which are driven through a viscous fluid undergo shape deformation coupled to their motion. We introduce an iterative solution scheme which couples hydrodynamic boundary integral methods and elastic shape equations to…
Two-dimensional (2D) mechanical models of confluent tissues have related the mechanical state of a monolayer of cells to the average perimeter length of the cell cross sections, predicting floppiness or rigidity of the material. For the…
Thin bilayers made of elastic sheets with different strain recoveries can be used for dynamic shape morphing through ambient stimuli, such as temperature, mass diffusion, and light. As a fundamentally different approach to designing…
Using a mean field approach and simulation, we study the non-linear mechanical response of the vertex model (VM) of biological tissue under compression and dilation. The VM is known to exhibit a transition between rigid and fluid-like, or…
A number of factors, such as, cell-cell interactions and self-propulsion of cells driven by cytoskeletal forces determine tissue morphologies and dynamics. To explore the interplay between these factors in controlling the dynamics at the…
Calculating by analytical theory the deformation of finite-sized elastic bodies in response to internally applied forces is a challenge. Here, we derive explicit analytical expressions for the amplitudes of modes of surface deformation of a…
Soft porous materials, such as biological tissues and soils, are exposed to periodic deformations in a variety of natural and industrial contexts. The detailed flow and mechanics of these deformations have not yet been systematically…
We investigate finite-strain elastoplastic evolution in the nonassociative setting. The constitutive material model is formulated in variational terms and coupled with the quasistatic equilibrium system. We introduce measure-valued…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
Growth-elasticity is a powerful model framework for understanding complex shape development in soft biological tissues. At each instant, by mapping how continuum building blocks have grown geometrically and how they respond elastically to…
Disordered materials are often out of equilibrium and evolve very slowly. This allows a memory of the imposed strains or preparation conditions to be encoded in the material. Here we consider "directed aging", where the elastic properties…
Confined thin structures are ubiquitous in nature. Spatial and length constraints have led to a number of novel packing strategies at both the micro-scale, as when DNA packages inside a capsid, and the macro-scale, seen in plant root…
We study a model for the deformation of a visco-elasto-plastic material that is nearly incompressible. It originates from geophysics, is given in the Eulerian description and combines a Kelvin-Voigt rheology in the spherical part with a…
We introduce a definition of finite-time curvature evolution along with our recent study on shape coherence in nonautonomous dynamical systems. Comparing to slow evolving curvature preserving the shape, large curvature growth points reveal…
Fluid elements deform in turbulence by stretching and folding. In this work, by projecting the material deformation tensor onto the largest stretching direction, the dynamics of folding is depicted through the evolution of the material…
Using field theoretic approach, we study equilibrium shape deformation of a vesicle induced by the presence of enclosed flexible polymers, which is a simple model of drug delivery system or endocytosis. To evaluate the total free energy of…
Constraints on changes in expression levels across all cell components imposed by the steady growth of cells have recently been discussed both experimentally and theoretically. By assuming a small environmental perturbation and considering…
During the early-stages of embryo development, morphogenesis--- the emergence of shape and form in living organisms--- is almost exclusively associated with monolayers of tightly bound epithelial cells. To understand how such tissues change…
Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and…