The Existence of Interfacial Couples in Infinitesimal Elasticity

Abstract

SummaryThe existence of interfacial couples in general crystalline media is established and an extension of the Cauchy stress principle is formulated in this paper. A strict method of treating the homogeneous deformation of an infinite lattice is also presented. The relevance of interfacial couples in the theory of elasticity is discussed together with a critical survey of the recent work in this field.

Elasticity, piezoelectricity and crystal lattice dynamics

“…Interest in the gradient type of theory was stimulated, in 1960, by Aero and Kuvshinskii [14], Grioli [15], Rajagopal [16] and Truesdell and Toupin [17] who took into account the first gradient of the rotation:…”

Size effects in two-dimensional Voronoi foams: A comparison between generalized continua and discrete models

“…In the early 1960s, the subject of the theory of elasticity with couple stresses is reopened and Cosserat-type theories are discussed independently by several authors. Among them, Grioli (1960), Rajagopal (1960), Truesdell and Toupin (1960), Aero and Kuvshinskii (1961), Eringen (1962), Mindlin and Tiersten (1962) and Koiter (1964) investigated a special case of the Cosserat continuum theory, in which the rotation of the rigid Cosserat triad is not an independent kinematic variable but is defined in terms of the displacement gradients. In this paper, we will refer to this theory as the couple stress theory (see Table 1, bottom right).…”

Microstructure in Linear Elasticity,

“…Omitting the body force and taking the divergence and curl of (9.31), we find the equations governing the prop- The theory of elasticity with couple-stresses, which is considered in [5][6][7][8][9][10], is based on the same kinematics as is classical elasticity; but the potential energy-density is as-…”