Classic crystal plasticity theory vs crystal plasticity theory based on strong discontinuities—Theoretical and algorithmic aspects. (13th December 2018)

• Record Type: Journal Article
• Authors: Fohrmeister, V.; Díaz, G.; Mosler, J.
• Is Part Of: International journal for numerical methods in engineering. Volume 117:Number 13(2019)
• Page Start: 1283
• Page End: 1303
• Publication Date: 2018-12-13
• Subjects: active set strategy -- crystal plasticity theory -- multisurface plasticity -- strong discontinuities -- texture evolution; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.6000
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: This paper deals with two different approaches suitable for the description of plasticity in single crystals. The first one is the standard approach that is based on a continuous deformation mapping. Plasticity is driven by a classic Schmid‐type relation connecting the shear stresses to the shear strains at a certain slip system. By way of contrast, the second approach is nonstandard. In this novel model, localized plastic deformation at certain slip planes is approximated by a strong discontinuity (discontinuous deformation mapping). Accordingly, a modified Schmid‐type model relating the shear stresses to the shear displacements (displacement jump) is considered in this model. Although both models are indeed different, it is shown that they can be characterized by almost the same set of equations, eg, by a multiplicative decomposition of the deformation gradient into an elastic part and a plastic part. This striking analogy eventually leads to a unifying algorithmic formulation covering both models. Since the set of active slip systems is not known in advance, its determination is of utmost importance. This problem is solved here by using the nonlinear complementarity problem (NCP) as advocated by Fischer and Burmeister. While this idea is not new, it is shown that the NCP problem is well posed, independent of the number of active slip systems. To be more explicit, the tangent matrix in the return‐mapping scheme is regular even for more than five simultaneously active slip systems. Based on this algorithm, texture evolution in a polycrystal is analyzed by means of both models and the results are compared in detail.