Related papers: An asymptotically consistent morphoelastic shell m…

The rheological properties of biological tissues, though fundamental to many physiological and pathological processes such as embryonic development, wound healing, and tumor progression, remain poorly understood. A recent study showed that…

We propose a method for deriving equivalent one-dimensional models for slender non-linear structures. The approach is designed to be broadly applicable, and can handle in principle finite strains, finite rotations, arbitrary cross-sections…

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the…

Starting from the three-dimensional Cosserat elasticity, we derive a two-dimensional model for isotropic elastic shells. For the dimensional reduction, we employ a derivation method similar to that used in classical shell theory, as…

Understanding how cells respond to external stimuli is a central challenge in biomedical research and drug development. Current computational frameworks for modelling cellular responses remain restricted to two-dimensional representations,…

Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…

We present a numerical study to characterize nonlinear unsteady aeroelastic interactions of two-dimensional flexible wings at high angles of attack. The coupled fluid-flexible wing system is solved by a body-fitted variational aeroelastic…

We study the shape, elasticity and fluctuations of the recently predicted (cond-mat/9510172) and subsequently observed (in numerical simulations) (cond-mat/9705059) tubule phase of anisotropic membranes, as well as the phase transitions…

How morphogenesis depends on cell properties is an active direction of research. Here, we focus on mechanical models of growing plant tissues, where microscopic (sub)cellular structure is taken into account. In order to establish links…

Remarkably persistent mixing and non-mixing regions (islands) are observed to coexist in a three-dimensional dynamical system where randomness is expected. The track of an x-ray opaque particle in a spherical shell half-filled with dry…

Widespread processes in nature and technology are governed by the dynamical transition whereby a material in an initially solid-like state then yields plastically. Major unresolved questions concern whether any material will yield smoothly…

Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical…

We argue that the standard classification of isometric deformations into infinitesimal v.s. finite is inadequate for the study of compliant shell mechanisms. Indeed, many compliant shells, particularly ones that are periodically corrugated,…

Biological cells can actively tune their intracellular architecture according to their overall shape. Here we explore the rheological implication of such coupling in a minimal model of a dense cellular material where each cell exerts an…

We consider a multiscale approach based on immersed methods for the efficient computational modeling of tissues composed of an elastic matrix (in two or three-dimensions) and a thin vascular structure (treated as a co-dimension two…

We present a constitutive model capturing some of the experimentally observed features of soft biological tissues: nonlinear viscoelasticity, nonlinear elastic anisotropy, and nonlinear viscous anisotropy. For this model we derive the…

Using formal asymptotic methods we derive a free boundary problem representing one of the simplest mathematical descriptions of the growth and death of a tumour or other biological tissue. The mathematical model takes the form of a closed…

Morphological trends in growing colonies of living cells are at the core of physiological and evolutionary processes. Using active gel equations, which include cell division, we show that shape changes during the growth can be regulated by…

Shell model turbulence is a simplified mathematical framework that captures essential features of incompressible fluid turbulence such as the energy cascade, intermittency and anomalous scaling of the fluid observables. We perform a…

Here we develop a lung ventilation model, based a continuum poroelastic representation of lung parenchyma and a 0D airway tree flow model. For the poroelastic approximation we design and implement a lowest order stabilised finite element…