Adhesive and Adhesive Joints Properties

Chapter 1

Abstract

Classifying the Existing

Continuum Theories of

Ideal-Surface Adhesion

and Golovina Natalya Yakovlevna

elasticity theories are identified.

1. Introduction

the paper [15].

3

scale effects, nonclassical physical parameters

framework of the classical theory of elasticity [1, 2, 11–14].

Belov Petr Anatolyevich, Lurie Sergey Albertovich

The chapter classifies the existing continuum theories of ideal-surface adhesion within the gradient theory of adhesion. Ideal surface herein means a defect-free surface, the deformed state of which is entirely defined by the displacement vector and its first (distortion) derivatives as well as its second (curvature) derivatives. Ideal surfaces have such kinematic variables as noncombined deformations and rotations. The classification is based on a formal quadratic form of potential surface energy, which comprises contracting the first-rank tensors (adhesive-force theory), second-rank tensors (adhesive-stress theory), and third-rank tensors (theory of adhesive couple stresses). To interpret the physical sense of the summands in the quadratic form of the potential-energy surface density, this research uses a rather common method of dividing the elastic solid into an internal solid plus a surface layer (adhesive, contact, boundary, or inter-phase layer). The formal structure of the adhesion-energy surface density is compared to the structure of the

thickness-averaged potential energy of a selected 3D layer. The chapter establishes the most general structure of adhesive-moduli tensors for the surfaces of classical elastic solids. The adhesive modules specific to the surfaces of a solid in gradient

Keywords: continuum adhesion theories, adhesive moduli, adhesive interaction,

Recent investigations of adhesive properties of surfaces and interfaces in deformable solids, in the mechanics of heterogeneous structures, and in the mechanics of composites are developed in various publications and analyzed in detail [1–10]. The first adhesion continuum theories were developed in the

The theory of Gurtin-Murdoch [11], which has become classical, was called as the theory of elasticity of surfaces. A generalization of this theory is proposed in
