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**Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals.**
*(English)*
Zbl 1446.74103

Summary: Recently, two-scale FE-FFT-based methods (e.g.,
[J. Spahn et al., Comput. Methods Appl. Mech. Eng. 268, 871–883 (2014; Zbl 1295.74006);
the first author et al. Comput. Methods Appl. Mech. Eng. 305, 89–110 (2016; Zbl 1425.74477)] have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton-Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests.

### MSC:

74E15 | Crystalline structure |

74E30 | Composite and mixture properties |

74S05 | Finite element methods applied to problems in solid mechanics |

74C05 | Small-strain, rate-independent theories of plasticity (including rigid-plastic and elasto-plastic materials) |

74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |

74Q15 | Effective constitutive equations in solid mechanics |

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\textit{J. Kochmann} et al., Comput. Mech. 61, No. 6, 751--764 (2018; Zbl 1446.74103)

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