Continuum and discrete models of dislocation pile-ups. I Pile-up at a lock by Ockendon, J, Voskoboinikov, R, Chapman, S

“…A mathematical methodology for analysing pile-ups of large numbers of dislocations is described. …”

Continuum and discrete models of dislocation pile-ups. I. Pile-up at a lock by Voskoboinikov, R, Chapman, S, Ockendon, J, Allwright, D

Continuum and discrete models of dislocation pile-ups. II. Pile-up of screw dislocations at the interface in a bimetallic solid by Voskoboinikov, R, Chapman, S, Ockendon, J

“…The methodology developed in the precursor to this paper is used to find the positions of n screw dislocations in a pile-up against an interface bonding two crystalline solids. …”

Interconnection of continuum and discrete models of dislocation pile-ups by Voskoboinikov, R, Chapman, S, Ockendon, J

“…A new asymptotic approach for analysing pile-ups of large numbers of dislocations is described. …”

Matched asymptotic expansion in modelling of edge dislocation pile-ups by Voskoboinikov, R, Chapman, S, Ockendon, JR

“…We have already provided robust proof of the interconnection between continuum and discrete approaches to dislocation description and suggested a methodology for analyzing pile-ups of screw and edge dislocations in a uniform material and a pile-up of screw dislocations near an interface in a bimetallic solid. …”

Asymptotics of Edge Dislocation Pile-Up against a Bimetallic Interface by Voskoboinikov, R, Chapman, S, McLeod, J, Ockendon, JR

“…The approach developed in preceding papers is extended to derive the equilibrium positions of n edge dislocations in a linear pile-up stressed by a constant applied loading against an interface in a bimetallic solid. …”

Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals by Carpio, A, Chapman, S, Velazquez, J

Pile-up solutions for some systems of conservation laws modelling dislocation interaction in crystals by Carpio, A, Chapman, S, Velazquez, J

“…In both cases, solutions describing the formation of structures such as dislocation pile-ups are discussed.…”

ASYMPTOTIC ANALYSIS OF A SYSTEM OF ALGEBRAIC EQUATIONS ARISING IN DISLOCATION THEORY by Hall, C, Chapman, S, Ockendon, JR

“…The system of algebraic equations given by σnj=0, j≠=i sgn(xi-xj )|xi-xj|a = 1, i = 1, 2, ⋯ , n, x0 = 0, appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. …”

Asymptotic analysis of a system of algebraic equations arising in dislocation theory by Hall, C, Chapman, S, Ockendon, J

“…The system of algebraic equations given by $\sum_{j=0, j \neq i}^n sgn(x_i - x_j) / |x_i - x_j|^a = 1, i = 1, 2, \ldots n, x_0 = 0,$ appears in dislocation theory in models of dislocation pile-ups. Specifically, the case a = 1 corresponds to the simple situation where n dislocations are piled up against a locked dislocation, while the case a = 3 corresponds to n dislocation dipoles piled up against a locked dipole. …”

Modelling the transition from channel-veins to PSBs in the early stage of fatigue tests by Zhu, Y

“…The traditional method of multiple scales does not apply well to describe the pile-up of two arrays of dislocations of opposite signs on a pair of neighbouring glide planes in two dimensional space. …”