Peridynamic Surface Elasticity Formulation Based on Modified Core–Shell Model

Abstract

Continuum mechanics is widely used to analyse the response of materials and structures to external loading conditions. Without paying attention to atomistic details, continuum mechanics can provide us very accurate predictions as long as continuum approximation is valid. There are various continuum mechanics formulations available in the literature. The most common formulation was proposed by Cauchy 200 years ago and the equation of motion for a material point is described by using partial differential equations. Although these equations have been successfully utilised for the analysis of many different challenging problems of solid mechanics, they encounter difficulties when dealing with problems including discontinuities such as cracks. In such cases, a new continuum mechanics formulation, peridynamics, can be more suitable since the equations of motion in peridynamics are in integro-differential equation form and do not contain any spatial derivatives. In nano-materials, material properties close to the surfaces can be different than bulk properties. This variation causes surface stresses. In this study, modified core–shell model is utilised to define the variation of material properties in the surface region by considering surface effects. Moreover, directional effective material properties are obtained by utilising analytical and peridynamic solutions.