Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials

Miehé, Christian; Schröder, Jörg; Schotte, Jan

doi:10.1016/s0045-7825(98)00218-7

Cited by 563 publications

(351 citation statements)

References 33 publications

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“…Slip gradients in the direction of the slip will be accommodated by edge dislocations while slip gradients perpendicular to the slip direction will be accommodated by screw dislocations. For the edge dislocations ( = 1… 12) the GND densities are obtained from the slip gradients by (26) and for the screw dislocations ( = 13… 18) by ( )…”

Section: Strain Gradient Induced Back Stressmentioning

confidence: 99%

“…Some more recent examples applicable to the class of unit cell methods are the first order [26,27] and second order [28] computational homogenization methods and the crystal plasticity work by Evers [29] that considered the effect of multiple differently oriented grains in an FCC metal. Finally, Fedelich [30,31] used a Fourier series homogenization method to model the mechanical behaviour of Ni-base superalloys.…”

Section: Introductionmentioning

confidence: 99%

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Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Tinga

Brekelmans

Geers

2008

Philosophical Magazine

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Section: Strain Gradient Induced Back Stressmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Tinga

Brekelmans

Geers

2008

Philosophical Magazine

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“…based on the Taylor-type models (Taylor 1938, van Houtte 1988, Mathur and Dawson 1989, Bronkhorst et al 1992, Miehe et al 1999 or self-consistent schemes (see, e.g. Molinari et al 1987).…”

Section: Homogenization Of the Stressesmentioning

confidence: 99%

“…In order to perform reliable forming simulations, micromechanically based material models offer the opportunity to incorporate microstructural information directly into the material model and to establish a sound physical basis for the model. Taylor-type polycrystal models (Taylor 1938, van Houtte 1988, Mathur and Dawson 1989, Bronkhorst et al 1992, Miehe et al 1999 or self-consistent schemes (see, e.g. Molinari et al 1987) belong to this class of micromechanically based material models.…”

Section: Introductionmentioning

confidence: 99%

Finite element simulation of metal forming operations with texture based material models

Böhlke

Risy

Bertram

2006

Modelling Simul. Mater. Sci. Eng.

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In this paper two different texture-dependent material models based on the Taylor assumption are discussed and applied to the simulation of deep drawing operations of aluminium. From the numerical point of view, large-scale FE computations based on the Taylor model are very time-intensive and storageconsuming if the crystallographic texture is approximated by several hundred discrete crystals. Furthermore, the Taylor model in its standard form, which is based on discrete crystal orientations, has the disadvantage that the anisotropy is significantly overestimated if only a small number of crystal orientations are used. We quantitatively analyse this overestimation of anisotropy and suggest two Taylor-type models which allow us to reduce the sharpness of the crystallite orientation distribution function related to single crystals or texture components. One model is an elastic-viscoplastic Taylor model based on discrete orientations. The sharpness is reduced by modelling the isotropic background texture by an isotropic material law. The other model is a rigidviscoplastic material one, which is based on continuous model functions on the orientation space. This model allows for a direct incorporation of the scattering around an ideal texture component since the model contains the half-width as a microstructural parameter which can be biased. These models are used to compute yield stresses, R values and earing profiles. The predictions are compared with experimental data.

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“…This idea has been further developed in Refs. [222] and [352][353][354][355][356][357][358][359][360][361][362][363]. Mo€ es et al [364] presented an extended version of the classical finite element method, referred to as XFEM, to solve microproblems involving complex geometries [365].…”

Section: Analysis At the Rve Levelmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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Computational homogenization analysis in finite plasticity Simulation of texture development in polycrystalline materials

Cited by 563 publications

References 33 publications

Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Incorporating strain gradient effects in a multiscale constitutive framework for nickel-base superalloys

Finite element simulation of metal forming operations with texture based material models

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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