The solution is given for the state of stress induced in an infinite plane by a uniform distribution of edge dislocations present over a general triangle. This provides the basis of a ‘perturbation element’ for modelling macroscopic plastic flow, providing a systematic and internally consistent way of developing a plasticity solution from an underlying elasticity solution to a problem.
BlomerusP. M.HillsD. A.An efficient procedure for modelling limited plastic flowProc. Instn Mech. Engrs, Part C: J. Mechanical Engineering Science, 1998, 212 (C8), 731–740.
2.
BlomerusP. M.HillsD. A.KellyP. A.The distributed dislocation method applied to the analysis of elastoplastic strain concentrationsJ. Mechanics Physics Solids, 1999, 47, 1007–1026.
3.
HillsD. A.LimmerL.Modelling plasticity using strain nuclei In Modern Practice in Stress and Vibration Analysis (Ed. BeckerA. A.), 2002, pp. 445–57 (Engineering Materials Advisory Services, Solihull).
4.
MuskhelishviliN. I.Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics, 2nd edition (translated from the 1946 text) (Ed. RadokJ. R. M.), 1953 (Noordhoff, Leiden).
