A spectral method solution to crystal elasto-viscoplasticity at finite strains

Strain localization and damage in dual phase steels investigated by coupled in-situ deformation experiments and crystal plasticity simulations

“…While exactly the same CP model introduced earlier is used for the simulations, the complex shape of the indentation experiment requires to use the finite element method (FEM) instead of spectral method. Earlier work reveals that both formulations provide similar micro-mechanical response (Eisenlohr et al, 2013). More details on the application of this optimization procedure for the determination of ferrite parameters are given in (Tasan et al, submitted for publication).…”

“…On the other hand, since the spectral method uses trigonometric polynomials for the approximation of boundary value problem, the microstructure is periodically repeated in all three directions, i.e. periodic boundary conditions are enforced (Eisenlohr et al, 2013). The effects of this artificial periodicity are analyzed by two sets of preceding simulations.…”

An integrated full-field model of concurrent plastic deformation and microstructure evolution: Application to 3D simulation of dynamic recrystallization in polycrystalline copper

“…These previous results provide confidence that stress/strain localizations predicted by the FFT-EVP will at least be statistically representative of those occurring in the material and sufficient to accurately predict evolution of the dislocation densities required for modeling nucleation and growth of new grains during DRX, even if the specific spatial values differ. Recently Eisenlohr et al (2013) demonstrated a FFT formulation which incorporates finite deformation kinematics, which utilizes the 1st Piola-Kirchhoff stress and the deformation gradient as work conjugate stress/deformation measures. Coupling of the finite strain FFT with phase field equations poses several additional computational difficulties, namely that the Fourier grid for the finite strain FFT is naturally formulated in the material or reference configuration while the spectral grid for the phase field is defined in the spatial or deformed state.…”

“…On one hand, the field of crystal plasticity has benefited substantially from multi-scale experiments and simulations linking mechanical properties of materials with the evolution of contained structural defects such as dislocations under an applied stress or displacement field. At the mesoscale, this understanding has been implemented into physics-based constitutive theories (Arsenlis and Parks, 2002;Arsenlis et al, 2004;Cheong and Busso, 2004;Ma et al, 2006;Gao and Huang, 2003;Beyerlein and Tomé, 2008) and implemented into homogenized deformation models such as self-consistent schemes (Lebensohn and Tomé, 1993;Niezgoda et al, 2014) or full-field simulations such as finite element based crystal plasticity (FE-CP) (Kalidindi et al, 1992;Beaudoin et al, 1995;Roters et al, 2010) or fast Fourier transform (FFT) based crystal plasticity (FFT-CP) models (Lebensohn, 2001;Lebensohn et al, 2012;Eisenlohr et al, 2013). On the other hand, the microstructural evolution in crystals, such as grain growth (Chen and Yang, 1994;Kazaryan et al, 2002;Moelans et al, 2008b), static recrystallization (Moelans et al, 2013), rafting in superalloy (Zhou et al, 2010;Gaubert et al, 2010) and many other phenomena (Chen, 2002;Wang and Li, 2010) have been well studied using phase-field (PF) simulations.…”

Linking atomistic, kinetic Monte Carlo and crystal plasticity simulations of single‐crystal tungsten strength

“…This open source software allows the integration of the constitutive models within different solvers for mechanical equilibrium: a spectral method based solver and two commercial FEM solvers such as Abaqus and MSC.Marc. Based on its performance for single crystals, we have chosen the spectral method solution described in [70,71] to perform tensile tests in single-crystal tungsten. The set of nonlinear equations (1), (2), (3) and (7), for which the dependency is summarized in Fig.…”