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Improvements for finite‐element implementation of the Gurson Model
Author(s) -
Mahnken R.
Publication year - 2000
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200008014112
Subject(s) - smoothing , finite element method , quadratic equation , mathematics , representation (politics) , void (composites) , function (biology) , convergence (economics) , mathematical optimization , computer science , geometry , structural engineering , engineering , statistics , materials science , evolutionary biology , politics , political science , law , economics , composite material , biology , economic growth
In this contribution three modifications for the plastic potential of the Gurson model are proposed, which give, from the numerical point of view, some improvements for the finite‐element implementation. Firsty a linear representation is used, which shows superior convergence property in the local iteration procedure compared to the original quadratic representation. Furthermore the cosh‐function appearing in the original formulation is replaced by a modified Cosh‐function, thus avoiding the overflow effect in the local iteration procedure for in‐between values. Additionally a smoothing technique is applied to the modified void volume function f*]f[ introduced by Tvergaare & Needleman ]3[. A numerical example illustrates the advantage of the proposed approach.