Line and point defects in nonlinear anisotropic solids

Abstract

In this paper, we present some analytical solutions for the stress fields of nonlinear anisotropic solids with distributed line and point defects. In particular, we determine the stress fields of i) a parallel cylindricallysymmetric distribution of screw dislocations in infinite orthotropic and monoclinic media, ii) a cylindricallysymmetric distribution of parallel wedge disclinations in an infinite orthotropic medium, iii) a distribution of edge dislocations in an orthotropic medium, and iv) a spherically-symmetric distribution of point defects in a transversely isotropic spherical ball.

Strain Hardening From Elastic–Perfectly Plastic to Perfectly Elastic Flattening Single Asperity Contact

“…Contact mechanics is one of the most common problems in mechanical engineering and tribology, with a variety of applications in collision mechanics [1][2][3], joint structures [4,5], electrical contact [6], thermal contact [7], solid mechanics [8][9][10][11], seals and bearings [12], biomechanical systems [13,14], turbines [15], and additive manufacturing [16,17]. The studies in contact mechanics can be categorized into: single asperity spherical, elliptical, cylindrical and flat contacts, with single asperity spherical contact being the most employed one [18][19][20][21][22].…”

“…579 The reason for this trend can be the effect of E t /E s on the accuracy 580 of Eq. (11). To find the large deformation limit Eq.…”

Riemannian and Euclidean material structures in anelasticity

“…This means that Q 2 G X if and only if Q = Q a b e a (X ) # b (X ) for some ½Q a b 2 G. Hence, the material symmetry group G X for T X B depends on the natural moving frame, as already observed in Wang and Bloom [12]. For a discussion on material symmetry and defects in solids see Golgoon and Yavari [25].…”

“…The deformation gradient must satisfy local compatibility equations, which are written as ∂ A F a B = ∂ B F a A . 5 Compatibility equations can also be written in terms of the two-point derivatives of equation (25) as…”

“…Finally, as is well-known, the balance of linear momentum can be written in the ambient space in terms of the Cauchy stress s as r b s ab + .b a = .a a . Note that, using the two-point derivative notation (equation (25)), for a spatial tensor the three symbols r,r, and r are equivalent. Thus, there is only one form for the balance of linear momentum when it is written in terms of the Cauchy stress.…”