Related papers: On the incremental equations in surface elasticity
A hydroelastic problem of flexural--gravity waves scattering by a demarcation between two floating elastic plates is investigated within the frame of linear potential-flow theory, where the method of matched eigenfunction expansions is…
We investigate the emergence of isotropic linear elasticity in amorphous and polycrystalline solids, via extensive numerical simulations. We show that the elastic properties are correlated over a finite length scale $\xi_E$, so that the…
We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semi-infinite solid. With a view to model loaded elastomers and soft tissues, we focus on…
Large deformations of soft elastic beads spinning at high angular velocity in a denser background fluid are investigated theoretically, numerically, and experimentally using millimeter-size polyacrylamide hydrogel particles introduced in a…
This work investigates the morphological stability of a soft body composed of two heavy elastic layers, attached to a rigid surface and subjected only to the bulk gravity force. Using theoretical and computational tools, we characterize the…
The dynamics of a membrane is a coupled system comprising a moving elastic surface and an incompressible membrane fluid. We will consider a reduced elastic surface model, which involves the evolution equations of the moving surface, the…
The Young-Laplace's equation is established based on liquid membrane without shearing resistance. It is not valid for solid. By taking into account the in-plane shearing and transverse shearing within the surface layer, we reconstruct the…
This work focuses on the interfacial dynamics with interfacial mass flux in the presence of acceleration and surface tension. We employ the general matrix method to find the fundamental solutions for the linearized boundary value problem…
In this paper we consider a layer of incompressible viscous fluid lying above a flat periodic surface in a uniform gravitational field. The upper boundary of the fluid is free and evolves in time. We assume that a mass of surfactants…
An incremental (or tangent) bulk modulus for finite isotropic elasticity is defined which compares an increment in hydrostatic pressure with the corresponding increment in relative volume. Its positivity provides a stringent criterion for…
Many interesting shapes appearing in the biological world are formed by the onset of mechanical instability. In this work we consider how the build-up of residual stress can cause a solid to buckle. In all past studies a fictitious…
Two formulas that connect the derivatives of the double layer potential and of a related singular integral operator evaluated at some density $\vartheta$ to the $L_2$-adjoints of these operators evaluated at the density $\vartheta'$ are…
We evaluate the conditions for surface stability of a layered magnetoelastic half-space subjected to large deformations and a magnetic field. After reviewing the fundamental measures of deformation and summarizing the magnetostatic…
Wrinkles are often observed on the surfaces of compressed soft materials in nature. In the past few decades, the fascinating surface patterns have been studied extensively by using the linear bifurcation analysis under plane strain. The…
We have developed a simulation model to describe particle adsorption to and desorption from liquid interfaces. Using this model we formulate a closed interfacial equation of state for repulsive elastic spheres. The effect of a long-range…
Boundary conditions at a liquid-solid interface are crucial to dynamics of a liquid film coated on a fibre. Here a theoretical framework based on axisymmetric Stokes equations is developed to explore the influence of liquid-solid slip on…
Explicit expressions, for efficient application in engineering practice, are derived for generalized displacements and stresses in simply supported multi-layered wide plates and beams subjected to steady-state thermal and mechanical…
The topic faced here is the modeling of an axisymmetric multilayer structure. An exact analytical formulation is proposed in the framework of the plane strain problem for a cylinder encircled by annular layers. Isotropic linear…
We consider the free boundary problem for two layers of immiscible, viscous, incompressible fluid in a uniform gravitational field, lying above a general rigid bottom in a three-dimensional horizontally periodic setting. We establish the…
We investigate the finite bending and the associated bending instability of an incompressible dielectric slab subject to a combination of applied voltage and axial compression, using nonlinear electro-elasticity theory and its incremental…