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

Issa, Sally (author): Lund University,Lunds universitet,Hållfasthetslära,Institutionen för byggvetenskaper,Institutioner vid LTH,Lunds Tekniska Högskola,Solid Mechanics,Department of Construction Sciences,Departments at LTH,Faculty of Engineering, LTH

Wallin, Mathias (author): Lund University,Lunds universitet,Hållfasthetslära,Institutionen för byggvetenskaper,Institutioner vid LTH,Lunds Tekniska Högskola,Solid Mechanics,Department of Construction Sciences,Departments at LTH,Faculty of Engineering, LTH

Ristinmaa, Matti (author): Lund University,Lunds universitet,Hållfasthetslära,Institutionen för byggvetenskaper,Institutioner vid LTH,Lunds Tekniska Högskola,Solid Mechanics,Department of Construction Sciences,Departments at LTH,Faculty of Engineering, LTH

Hallberg, Håkan (author): Lund University,Lunds universitet,Hållfasthetslära,Institutionen för byggvetenskaper,Institutioner vid LTH,Lunds Tekniska Högskola,Solid Mechanics,Department of Construction Sciences,Departments at LTH,Faculty of Engineering, LTH

(creator_code:org_t)

2018-03-20
2018
English.
In: Computational Mechanics. - : Springer Science and Business Media LLC. - 0178-7675 .- 1432-0924. ; 62:6, s. 1429-1441

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Abstract Subject headings

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.

By the author/editor: Issa, Sally; Wallin, Mathias; Ristinmaa, Matti; Hallberg, Håkan

About the subject

NATURAL SCIENCES: NATURAL SCIENCES; and Mathematics; and Computational Ma ...

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