Nonlinear Composites

Castañeda, Pedro Ponte; Suquet, Pierre

doi:10.1016/s0065-2156(08)70321-1

Cited by 543 publications

(344 citation statements)

References 113 publications

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“…The variational estimate of Ponte-Castañeda and Suquet [38][39][40][41][42][43], adapted and simplified for the monotonic uniaxial deformation of (incompressible) non-linear microcellular materials [6,44,45], allows an estimation of the in-situ stress-strain curves of the metal within the foams, knowing the relative density V m , the Young's modulus scaling law, and the uniaxial flow curve of the microcellular metal. The calculation is detailed in Appendix A. metal within these samples: as seen, the variational estimate collapses stress-strain curves of the five variously dense microcellular metal samples (Fig.…”

Section: Scaling Of the Flow Stressmentioning

confidence: 99%

“…The rationale behind this assumption is that (i) the Von Mises stress is the simplest scalar measure of stress driving dislocation motion in complex three-dimensional stress fields and (ii) σ eff is used, in the variational estimate, to deduce the appropriate matrix secant modulus that serves to derive the instantaneous non-linear deformation state in the metal making the foam [42,43].…”

Section: Appendix a -Estimating The Metal In-situ Flow Curve From Thamentioning

confidence: 99%

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Influence of microstructural heterogeneity on the scaling between flow stress and relative density in microcellular Al–4.5 %Cu

2014

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We explore the influence of the metal microstructure on the compressive flow stress of replicated microcellular 400 µm pore size Al-4.5wt%Cu solidified at two different solidification cooling rates, in as-cast and T6 conditions. It is found that the yield strength roughly doubles with age-hardening but does not depend on the solidification cooling rate.Internal damage accumulation, measured by monitoring the rate of stiffness loss with strain, is similar across the four microstructures explored and equals that measured in similar microcellular pure aluminium. In-situ flow curves of the metal within the open-pore microcellular material are back-calculated using the Variational Estimate of Ponte Castañeda and Suquet. Consistent results are obtained with heat-treated microcellular Al-4.5wt%Cu, and are also obtained with separate data for pure Al; however, for as-cast microcellular Al-4.5wt%Cu the back-calculated in-situ metal flow stress decreases, for both solidification rates, with decreasing relative density of the foam. We attribute this effect to an interplay between microstructural and mesostructural features of the microcellular material: variations in the latter with the former held constant can alter the scaling between flow stress and relative density within microcellular alloys.

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Section: Scaling Of the Flow Stressmentioning

confidence: 99%

Section: Appendix a -Estimating The Metal In-situ Flow Curve From Thamentioning

confidence: 99%

Influence of microstructural heterogeneity on the scaling between flow stress and relative density in microcellular Al–4.5 %Cu

2014

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“…Improved bounds for nonlinear composites were obtained by Willis [126] for nonlinear dielectrics, Ponte Castañeda and Willis [127] for two-phase random composites made of nonlinearly viscous phases, Suquet [128] for power-law composites, Olson [129] for perfectly plastic composites, and Talbot and Willis [130] for general classes of nonlinear composites. A significant development took place with the derivation of a nonlinear variational principle by Ponte Castañeda et al [131][132][133][134][135] to estimate the effective property of nonlinear incompressible and compressible composites, and in particular, composites made of a ductile and a brittle phase, based on the corresponding linear properties with the same microstructural distribution of phases. Later, exact second-order estimates were established by Ponte Castañeda [136].…”

Section: Introductionmentioning

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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“…To this end, the meso-scale BVP is defined on a Representative Volume Element (RVE), which represents the micro-structure and the micro-structural behavior in a statistically representative way. 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.…”

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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Nonlinear Composites

Cited by 543 publications

References 113 publications

Influence of microstructural heterogeneity on the scaling between flow stress and relative density in microcellular Al–4.5 %Cu

Influence of microstructural heterogeneity on the scaling between flow stress and relative density in microcellular Al–4.5 %Cu

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

A stochastic computational multiscale approach; Application to MEMS resonators

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