Related papers: Surface Growth in Deformable Solids using an Euler…
We derive the incremental equations for a hyperelastic solid that incorporate surface tension effect by assuming that the surface energy is a general function of the surface deformation gradient. The incremental equations take the same…
The paper studies a method for solving elliptic partial differential equations posed on hypersurfaces in $\mathbb{R}^N$, $N=2,3$. The method builds upon the formulation introduced in Bertalmio et al., J. Comput. Phys., 174 (2001),…
Taking the cue from experiments on actin growth on spherical beads, we formulate and solve a model problem describing the accretion of an incompressible elastic solid on a rigid sphere due to attachment of diffusing free particles. One of…
A new simulation method for solving fluid-structure coupling problems has been developed. All the basic equations are numerically solved on a fixed Cartesian grid using a finite difference scheme. A volume-of-fluid formulation (Hirt and…
This paper proposes a new general methodology for finite-time singularity formation for moving interface problems involving the incompressible Euler equations in the plane. The first problem considered is the two-phase Euler vortex sheets…
Since publication of the main contributions on the theory of kinetic roughening more than fifteen years ago, many works have been reported on surface growth or erosion that employ the framework of dynamic scaling. This interest was mainly…
In this paper we study the dynamics of a layer of incompressible viscous fluid bounded below by a rigid boundary and above by a free boundary, in the presence of a uniform gravitational field. We assume that a mass of surfactant is present…
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…
We focus on a highly nonlinear evolutionary abstract PDE system describing volume processes coupled with surfaces processes in thermoviscoelasticity, featuring the quasi-static momentum balance, the equation for the unidirectional evolution…
We present a comprehensive theoretical and computational model that explores the behavior of a thin hydrated film bonded to a non-hydrated / impermeable soft substrate in the context of surface and bulk elasticity coupled with surface…
In this work we present a discrete model that captures the fundamental properties of additively manufactured solids in a minimal setting. The model is based on simplified kinematics and allows for the onset of incompatible deformations…
A simple kinematic growth model for muscular arteries is presented which allows the incorporation of residual stresses such that a homeostatic in-vivo stress state under physiological loading is obtained. To this end, new evolution…
In this paper, we propose a multi-layered hyperelastic plate theory of growth within the framework of nonlinear elasticity. First, the 3D governing system for a general multi-layered hyperelastic plate is established, which incorporates the…
The paper presents results from kinetic Monte Carlo simulations of kinetic surface roughening using an important and experimentally relevant model of epitaxial growth -- the solid-on-solid model with Arrhenius dynamics. A restriction on…
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 purpose of this paper is to review some elasticity effects in epitaxial growth. We start by a description of the main ingredients needed to describe elasticity effects (elastic interactions, surface stress, bulk and surface elasticity,…
The wear volume is known to keep increasing during frictional processes, and Archard notably proposed a model to describe the probability of wear particle formation upon asperity collision in a two-body contact configuration. While this…
The immersed boundary method is a mathematical framework for modeling fluid-structure interaction. This formulation describes the momentum, viscosity, and incompressibility of the fluid-structure system in Eulerian form, and it uses…
When granular materials with interstitial liquid bridges are sheared in a split-bottom cell, a localized shear band develops, accompanied by a surface elevation. Cohesion, governed by the surface tension of the interstitial liquid, enhances…
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…