Related papers: An asymptotically consistent morphoelastic shell m…

In this paper we derive, by two$-$scale convergence, periodically wrinked shell models starting from three dimensional linear elasticity, depending of the behaviour of the small parameter $\varepsilon>0$ and $p>1$, differents theories…

The deformation problem for a transversely isotropic elastic layer bonded to a rigid substrate and coated with a very thin elastic layer made of another transversely isotropic material is considered. The leading-order asymptotic models (for…

The buckling of a soft elastic sample under growth or swelling has highlighted a new interest in materials science, morphogenesis, and biology or physiology. Indeed, the change of mass or volume is a common fact of any living species, and…

The existence of a crumpled phase for self-avoiding elastic surfaces was postulated more than three decades ago using simple Flory-like scaling arguments. Despite much effort, its stability in a microscopic environment has been the subject…

A rising wave of technologies and instruments are enabling more labs and clinics to make a variety of measurements related to tissue viscoelastic properties. These instruments include elastography imaging scanners, rheological shear…

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…

This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first…

Characterizing the softness of deformable materials having partial elastic and partial viscous behaviour via soft lubrication experiments has emerged as a versatile and robust methodology in recent times. However, a straightforward…

The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…

Most biological tissues grow by the synthesis of new material close to the tissue's interface, where spatial interactions can exert strong geometric influences on the local rate of growth. These geometric influences may be mechanistic, or…

The maintenance of tissue and organ structures during dynamic homeostasis is often not well understood. In order for a system to be stable, cell renewal, cell migration and cell death must be finely balanced. Moreover, a tissue's shape must…

The asymptotic shape of randomly growing radial clusters is studied. We pose the problem in terms of the dynamics of stochastic partial differential equations. We concentrate on the properties of the realizations of the stochastic growth…

Cosserat rod theory is the popular approach to modeling ferromagnetic soft robots as 1-Dimensional (1D) slender structures in most applications, such as biomedical. However, recent soft robots designed for locomotion and manipulation often…

We propose a three dimensional mechanical model of embryonic tissue dynamics. Mechanically coupled adherent cells are represented as particles interconnected with elastic beams which can exert non-central forces and torques. Tissue…

We derive a large-strain plate model that allows to describe transient, coupled processes involving elasticity and solvent migration, by performing a dimensional reduction of a three-dimensional poroelastic theory. We apply the model to…

During development, epithelial tissues undergo extensive morphogenesis based on coordinated changes of cell shape and position over time. Continuum mechanics describes tissue mechanical state and shape changes in terms of strain and stress.…

The goal of this paper is to apply the recently developed theory of buckling of arbitrary slender bodies to a tractable yet non-trivial example of buckling in axially compressed circular cylindrical shells, regarded as three-dimensional…

Solvent-based techniques usually involve preparing dilute blends of electron-donor and electron-acceptor materials dissolved in a volatile solvent. After some form of coating onto a substrate, the solvent evaporates. An initially…

During embryonic development tissue morphogenesis and signaling are tightly coupled. It is therefore important to simulate both tissue morphogenesis and signaling simultaneously in in silico models of developmental processes. The resolution…

Incompressibility, nonlinear deformation under stress and viscoelasticity are the fingerprint of soft tissue mechanical behavior. In order to model soft tissues appropriately, we must pursue to complete these requirements. In this work we…