Time integration scheme for elastoplastic models based on anisotropic strain‐rate potentials

Abstract

SUMMARYModelling of plastic anisotropy requires the definition of stress potentials (coinciding with the yield criteria in case of the associated flow rules) or, alternatively, plastic strain-rate potentials. The latter approach has several advantages whenever material parameters are determined by means of texture measurements and crystal plasticity simulations. This paper deals with a phenomenological description of anisotropy in elastoplastic rate-insensitive models by using strain-rate potentials. A fully implicit time integration algorithm is developed in this framework and implemented in a static-implicit finite element code. Algorithmic details are discussed, including the derivation of the consistent (algorithmic) tangent modulus and the numerical treatment of the yield condition. Typical sheet forming applications are simulated with the proposed implementation, using the recent non-quadratic strain-rate potential Srp2004-18p. Numerical simulations are carried out for materials that exhibit strong plastic anisotropy. The numerical results confirm that the presented algorithm exhibits the same generality, robustness, accuracy, and time efficiency as state-of-the-art yield criterion-based algorithms.

Numerical simulation of sheet metal forming using anisotropic strain-rate potentials

“…For more details, the reader may refer to Kim et al [21] and Rabahallah et al [36] for strain-rate potential models, Rabahallah et al [33] for the complete elastic-plasticity model and its numerical implementation, and to Rabahallah et al [34] for the parameter identification of the strain-rate potentials.…”

“…In order to avoid early divergence in the constitutive algorithm, a sub-stepping technique has also been developed and implemented. This is an extension to strain-rate potentials of the sub-stepping procedure introduced by Yoon et al [11,43] and it is described in detail in [33].…”

“…An implicit backward Euler state update algorithm has been developed for the aforementioned elastic-plastic model in the framework of finite strains; this algorithm is described in detail in [33]. The flow rule (3) and of the deviatoric part of the hypo-elastic law (4) take the following discrete (incremental) forms…”

“…In order to predict unloading and springback phenomena, more expensive elastic-plastic finite element implementations of strain-rate potentials have been performed by Van Houtte et al [28], Bacroix and Gilormini [29], Zhou et al [30], and Li et al [31]. Recently, Kim et al [32] and Rabahallah et al [33] proposed generic computer implementations for strain rate potentials (using shell and solid elements, respectively) and implemented several models, including the Srp2004-18p potential [21].…”

“…Particular attention is given to the impact of the parameter identification method on the FE predictions. For this purpose, Srp2004-18p has been implemented in the FE code Abaqus, together with other models used in the comparison [33]. The modeling and computational issues of this work are summarized in Section 2, and the FE simulations are analyzed in Section 3, which is the main part of the paper.…”