Numerical solution of the two-yield elastoplastic minimization problem

doi:10.1007/s00607-007-0242-2

Numerical solution of the two-yield elastoplastic minimization problem

2007-10-09

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DOI：10.1007/s00607-007-0242-2

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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.

Keyword:

variational inequalities

elastoplastic materials

two-yield plasticity model

decomposition methods

method of Newton-Raphson

Numerical solution of the two-yield elastoplastic minimization problem

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