Diagonally implicit Runge–Kutta (DIRK) integration applied to finite strain crystal plasticity modeling

Research output: Contribution to journalArticle


Diagonally implicit Runge–Kutta methods (DIRK) are evaluated and compared to standard solution procedures for finite strain crystal plasticity boundary value problems. The structure of the DIRK implementation is similar to that of a conventional implicit backward Euler scheme. It is shown that only very small modifications are required in order to transform the numerical scheme from one into the other. This similarity permits efficient adaption of the integration procedure to a particular problem. To enforce plastic incompressibility, different projection techniques are evaluated. Rate dependent crystal plasticity, using a single crystal is simulated under various load cases as well as a larger polycrystalline sample. It is shown that the two-stage DIRK scheme combined with a step size control and a time continuous projection technique for the update of the plastic deformation gradient is in general more accurate than the implicit backward Euler and an update based on exponential mapping.


Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Computational Mathematics


  • Crystal plasticity, Diagonally implicit Runge–Kutta, Implicit Euler, Numerical integration
Original languageEnglish
Pages (from-to)1429-1441
JournalComputational Mechanics
Issue number6
Early online date2018 Mar 20
Publication statusPublished - 2018
Publication categoryResearch