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An efficient solution scheme for small-strain crystal-elasto-viscoplasticity in a dual framework. (English) Zbl 1441.74044

Summary: Computational homogenization schemes based on the fast Fourier transform (FFT) enable studying the effective micromechanical behavior of polycrystalline microstructures with complex morphology. In the conventional strain-based setting, evaluating the single crystal elasto-viscoplastic constitutive law involves solving a non-linear system of equations which dominates overall runtime. Evaluating the inverse material law is much less costly in the small-strain context, because the flow rule is an explicit function of the stress.
We revisit the primal and dual formulation of the unit cell problem of computational homogenization and use state of the art FFT-based algorithms for its solution. Performance and convergence behavior of the different solvers are investigated for a polycrystal and a fibrous microstructure of a directionally solidified eutectic.

MSC:

74C10 Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity)
74E15 Crystalline structure
74M25 Micromechanics of solids

Software:

FFTW; Cython; Neper; FFTHomPy
PDFBibTeX XMLCite
Full Text: DOI

References:

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