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.

No abstract

In this work, a novel, displacement-driven approach to crystal plasticity based on embedded strong discontinuities (ESDA) is presented, cf. [1,2]. In contrast to the classical strain-driven approach, which connects the Schmid stress to the slip strain at a certain slip system, the novel approach applies a traction-separation law to connect the Schmid stresses to the slip displacements. Surprisingly, both models show similar mathematical structures, which allows to develop a unifying algorithmic formulation. The elaborated algorithmic formulation is fully implicit and the inequalities characterizing rateindependent crystal plasticity theory are solved efficiently by means of so-called Fischer-Burmeister NCP functions, cf. [3]. The resulting solution scheme is extremely robust -even for an arbitrary number of simultaneously active slip systems.

In the present work, classical local crystal plasticity is reformulated using incremental energy minimization. The resulting constrained optimization problem is efficiently solved by a nonlinear complementary problem, which additionally solves the problem of determination of the set of active slip systems. The model is extended to a nonlocal, gradient-enhanced, formulation by employing and adapting the micromorphic approach. By doing so, the implementation of the gradient-enhanced model is almost identical to that of the original local one, with the exception of additional balance equations.