A FFT-Based Numerical Method for Computing the Mechanical Properties of Composites from Images of their Microstructures

Moulinec, Hervé; Suquet, Pierre

doi:10.1007/978-94-011-0059-5_20

Cited by 157 publications

(309 citation statements)

References 15 publications

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“…The full-field formulation based on fast Fourier transforms (FFT) [24] has proved to be a successful alternative modelling tool to simulate plastic deformation of polycrystals [25,26], especially when coupled with algorithms for DRX processes [8,27]. Viscoplastic full-field numerical modelling (in short VPFFT modelling) of the evolution of a polycrystalline aggregate under controlled strain boundary conditions can be applied to investigate the relative importance of deformation mechanisms and recrystallization processes on the development of ice fabrics and flow (e.g.…”

Section: Introductionmentioning

confidence: 99%

Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

Llorens

Griera

Steinbach

et al. 2017

Phil. Trans. R. Soc. A.

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One contribution of 11 to a theme issue 'Microdynamics of ice'. Subject Areas: glaciology Keywords:ice rheology, dynamic recrystallization, ice microstructure, non-basal activity, strain hardening The flow of glaciers and polar ice sheets is controlled by the highly anisotropic rheology of ice crystals that have hexagonal symmetry (ice lh). To improve our knowledge of ice sheet dynamics, it is necessary to understand how dynamic recrystallization (DRX) controls ice microstructures and rheology at different boundary conditions that range from pure shear flattening at the top to simple shear near the base of the sheets. We present a series of two-dimensional numerical simulations that couple ice deformation with DRX of various intensities, paying special attention to the effect of boundary conditions. The simulations show how similar orientations of c-axis maxima with respect to the finite deformation direction develop regardless of the amount of DRX and applied boundary conditions. In pure shear this direction is parallel to the maximum compressional stress, while it rotates towards the shear direction in simple shear. This leads to strain hardening and increased activity of non-basal slip systems in pure shear and to strain softening in simple shear. Therefore, it is expected that ice is effectively weaker in the lower parts of the ice sheets than in the upper parts. Strain-rate localization occurs in all simulations, especially in simple shear cases. Recrystallization suppresses localization, which necessitates the activation of hard, non-basal slip systems.This article is part of the themed issue 'Microdynamics of ice'.

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Section: Introductionmentioning

confidence: 99%

Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

Llorens

Griera

Steinbach

et al. 2017

Phil. Trans. R. Soc. A.

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“…The PFM theory can be traced back to Eshelby's classical work 22 on transformation-induced elasticity and has been employed in PF simulations of solid-solid phase transformations and even the modeling of deformation in amorphous alloys. 23,24 It is worth pointing out that Eshelby's pioneering work is also the basis for fast-Fourier-transform (FFT) based schemes for computing the micromechanical fields of periodic heterogeneous materials directly from an image of the microstructure (i.e., image-based approaches), 25,26 as well as the recently emerged FFT-based crystal plasticity models. [27][28][29] Here we extend the PFM theory by taking into account a general nonlinear coupling between OPs and SFTS tensors.…”

Section: Introductionmentioning

confidence: 99%

Effect of nonlinear and noncollinear transformation strain pathways in phase-field modeling of nucleation and growth during martensite transformation

Zhao

Chen

2017

npj Comput Mater

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The phase-field microelasticity theory has exhibited great capacities in studying elasticity and its effects on microstructure evolution due to various structural and chemical non-uniformities (impurities and defects) in solids. However, the usually adopted linear and/ or collinear coupling between eigen transformation strain tensors and order parameters in phase-field microelasticity have excluded many nonlinear transformation pathways that have been revealed in many atomistic calculations. Here we extend phasefield microelasticity by adopting general nonlinear and noncollinear eigen transformation strain paths, which allows for the incorporation of complex transformation pathways and provides a multiscale modeling scheme linking atomistic mechanisms with overall kinetics to better describe solid-state phase transformations. Our case study on a generic cubic to tetragonal martensitic transformation shows that nonlinear transformation pathways can significantly alter the nucleation and growth rates, as well as the configuration and activation energy of the critical nuclei. It is also found that for a pure-shear martensitic transformation, depending on the actual transformation pathway, the nuclei and austenite/martensite interfaces can have nonzero far-field hydrostatic stress and may thus interact with other crystalline defects such as point defects and/or background tension/ compression field in a more profound way than what is expected from a linear transformation pathway. Further significance is discussed on the implication of vacancy clustering at austenite/martensite interfaces and segregation at coherent precipitate/ matrix interfaces.

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“…The homogenization process on the RVE can be conducted in a semi-analytical way, as for the mean-field-homogenization method for which the average phase-fields of the meso-scale problem are considered in order to derive the macro-response, see for example [10][11][12] for a state-of-the-art review. The mesoscale BVP can also be solved, for more general constitutive behaviors and microstructures, in a numerical way by using a voxelization of the micro-structure as in the Fast-Fourier-Transform method introduced in [13] or a finite element discretization of the micro-structure as in the computational homogenization, also called FE 2 , method. Early developments of this last approach were proposed in [14] with the VCFEM (Voronoï Cell Finite Element Method).…”

Section: Introductionmentioning

confidence: 99%

A stochastic computational multiscale approach; Application to MEMS resonators

Lucas¹,

Golinval²,

Paquay³

et al. 2015

Computer Methods in Applied Mechanics and Engineering

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The aim of this work is to develop a stochastic multiscale model for polycrystalline materials, which accounts for the uncertainties in the micro-structure. At the finest scale, we model the micro-structure using a random Voronoï tessellation, each grain being assigned a random orientation. Then, we apply a computational homogenization procedure on statistical volume elements to obtain a stochastic characterization of the elasticity tensor at the meso-scale. A random field of the meso-scale elasticity tensor can then be generated based on the information obtained from the SVE simulations. Finally, using a stochastic finite element method, these meso-scale uncertainties are propagated to the coarser scale. As an illustration we study the resonance frequencies of MEMS micro-beams made of poly-silicon materials, and we show that the stochastic multiscale approach predicts results in agreement with a Monte Carlo analysis applied directly on the fine finite-element model, i.e. with an explicit discretization of the grains.

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A FFT-Based Numerical Method for Computing the Mechanical Properties of Composites from Images of their Microstructures

Cited by 157 publications

References 15 publications

Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

Dynamic recrystallization during deformation of polycrystalline ice: insights from numerical simulations

Effect of nonlinear and noncollinear transformation strain pathways in phase-field modeling of nucleation and growth during martensite transformation

A stochastic computational multiscale approach; Application to MEMS resonators

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