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Response discontinuities in the solution of the incremental Mori-Tanaka scheme for elasto-plastic composites
Arch. Mech. 69 (1), 3-27, 2017
Keywords: mean-field homogenization; Mori-Tanaka method; incremental scheme; composite materials; elasto-plasticity
Abstract
The incremental Mori–Tanaka model of elasto-plastic composites is discussed, and the corresponding finite-step formulation is shown to lead to discontinuities in the overall response at the instant of elastic-to-plastic transition in the matrix. Specifically, two situations may be encountered: the incremental equations may have two solutions or no solution. In the former situation, switching between the two solutions is associated with a jump in the overall stress. Response discontinuities are studied in detail for a special case of proportional deviatoric loading. The discontinuities constitute an undesirable feature of the incremental Mori–Tanaka scheme that apparently has not been discussed in the literature so far. Remedies to the related problems are briefly discussed.