相关论文: Linearization of finite elasticity with surface te…

Compacted unbound granular materials are extensively used as sub-layer in pavement design. Most pavement design guides assume that they are responsible for the degradation and deformation of the roads and railways that they support. Biaxial…

Using a geometric formalism of elasticity theory we develop a systematic theoretical method for controlling and manipulating the mechanical response of slender solids to external loads. We formally express global mechanical properties…

In this paper, we study the boundary effect on the surface (or frame) tension of elastic membrane surface models. The frame tension generally depends only on the projected area of the boundary over which the surface spans. However, from a…

We present initial results regarding the existence, stability and interaction of linear and nonlinear vibrational modes in a system of two coupled, one dimensional lattices with unequal numbers of masses. The effects on these nonlinear…

Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…

We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface…

This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material…

A variational model for epitaxially-strained thin films on rigid substrates is derived both by {\Gamma}-convergence from a transition-layer setting, and by relaxation from a sharp-interface description available in the literature for…

With an aim to include the contribution of surface tension in the action of the boundary, we define the tangential pressure in terms of surface tension and Normal curvature in a more naturally geometric way. First, we show that the negative…

We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…

We study the effective behavior of random, heterogeneous, anisotropic, second order phase transitions energies that arise in the study of pattern formations in physical-chemical systems. Specifically, we study the asymptotic behavior, as…

We formulate a nonlinear continuum model of a graphene sheet supported by a flat rigid substrate. The sheet is parallel to the substrate and loaded on a pair of opposite edges. A typical cross-section of the sheet is modeled as an elastica.…

We compute the high-dimensional limit of the free energy associated with a multi-layer generalized linear model. Under certain technical assumptions, we identify the limit in terms of a variational formula. The approach is to first show…

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…

Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…

This paper is concerned with equilibrium configurations of one-dimensional particle system with non-convex nearest-neighbour and next-to-nearest-neighbour interactions and its passage to the continuum. The goal is to derive compactness…

In this paper we provide some more details on the numerical analysis and we present some enlightening numerical results related to the spectrum of a finite element least-squares approximation of the linear elasticity formulation introduced…

At the line of triple contact of an elastic body with two immiscible fluids, the body is subjected to a force concentrated on this line, the fluid-fluid surface tension. In the simple case of a semi-infinite body, limited by a plane, a…

We introduce an individual-based model for fiber elements having the ability to cross-link or unlink each other and to align with each other at the cross links. We first formally derive a kinetic model for the fiber and cross-links…

We consider a sequence of linear hyper-elastic, inhomogeneous and fully anisotropic bodies in a reference configuration occupying a cylindrical region of height epsilon. We then study, by means of Gamma-convergence, the asymptotic behavior…