Summary
This paper concentrates on fast calculation techniques for the two-yield elastoplastic problem, a locally defined, convex but non-smooth minimization problem for unknown plastic-strain increment matrices P 1 and P 2. So far, the only applied technique was an alternating minimization, whose convergence is known to be geometrical and global. We show that symmetries can be utilized to obtain a more efficient implementation of the alternating minimization. For the first plastic time-step problem, which describes the initial elastoplastic transition, the exact solution for P 1 and P 2 can even be obtained analytically. In the later time-steps used for the computation of the further development of elastoplastic zones in a continuum, an extrapolation technique as well as a Newton-algorithm are proposed. Finally, we present a realistic example for the first plastic and the second time-steps, where the new techniques decrease the computation time significantly.
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Hofinger, A., Valdman, J. Numerical solution of the two-yield elastoplastic minimization problem. Computing 81, 35–52 (2007). https://doi.org/10.1007/s00607-007-0242-2
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DOI: https://doi.org/10.1007/s00607-007-0242-2