Solution of two-dimensional plasticity problems with discrete dislocations
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This paper discusses a numerical method for solving small strain plasticity problems on a small scale with plastic flow represented by the collective motion of a large number of discrete dislocations. The dislocations are modeled as line defects in a linear elastic medium and here attention is restricted to plane strain configurations with edge dislocations on parallel slip planes. The deformation history is calculated in a linear incremental manner. At each instant, superposition is used to represent the solution in terms of the infinite medium solution for the discrete dislocations and a complimentary solution that enforces the boundary conditions on the finite body. The complimentary solution is non-singular and is obtained from a finite element solution of a linear elastic boundary value problem. The lattice resistance to dislocation motion, dislocation nucleation and annihilation are accounted for through a set of constitutive rules. Obstacles leading to possible dislocation pile-ups are also accounted for. The relaxation of an initial random distribution of dislocations is shown. Solutions are also presented for the evolution of dislocation distributions and plastic response for solids subject to an imposed overall shear strain. Results are given for a sample with free edges and for a cell model using periodic boundary conditions.
American Society of Mechanical Engineers, Aerospace Division (Publication) AD
author list (cited authors)
van der Giessen, E., & Needleman, A.
complete list of authors
van der Giessen, E||Needleman, A