Computational homogenization of elasto-plastic porous metals

Fritzen, Felix; Forest, Samuel; Böhlke, Thomas; Kondo, Djimédo; Kanit, Toufik

doi:10.1016/j.ijplas.2011.08.005

Cited by 176 publications

(139 citation statements)

References 48 publications

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“…As a first approximation, it seems reasonable to assume that the influence of the third invariant S 3 is negligible (Green, 1972;Abouaf, 1985;Geindreau et al, 1999b;Fritzen et al, 2012). Consequently, the macroscopic volumetric mechanical dissipation P v depends on the first and second stress and strain invariants and not only on the second ones as at the microscale 6.…”

Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

2017

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Abstract. While the homogenization of snow elastic properties has been widely reported in the literature, homogeneous rate-dependent behavior responsible for the densification of the snowpack has hardly ever been upscaled from snow microstructure. We therefore adapt homogenization techniques developed within the framework of elasticity to the study of snow viscoplastic behavior. Based on the definition of kinematically uniform boundary conditions, homogenization problems are applied to 3-D images obtained from X-ray tomography, and the mechanical response of snow samples is explored for several densities. We propose an original postprocessing approach in terms of viscous dissipated powers in order to formulate snow macroscopic behavior. Then, we show that Abouaf models are able to capture snow viscoplastic behavior and we formulate a homogenized constitutive equation based on a density parametrization. Eventually, we demonstrate the ability of the proposed models to account for the macroscopic mechanical response of snow for classical laboratory tests.

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Section: Macro-strain Paths Definition (Step 4)mentioning

confidence: 99%

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

2017

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“…Although many studies were dedicated to the development of yield criteria for plastic porous media, it seems that only few works have been devoted to three-dimensional computational homogenization involving multiple voids. To our knowledge, only Bilger et al [21], Fritzen et al [22] and Khdir et al [23] used this approach to estimate the overall yield surface of porous materials. Their computations were limited to spherical voids.…”

Section: Introductionmentioning

confidence: 99%

“…The pore clustering effect on the overall material response was the key point of their investigation. Fritzen et al [22] assumed the random porous media as a volume of porous material which is periodically arranged. The results highlighted by Fritzen et al [22] led them to extend the GT yield criterion in order to overcome the analytical/numerical discrepancies.…”

Section: Introductionmentioning

confidence: 99%

“…Fritzen et al [22] assumed the random porous media as a volume of porous material which is periodically arranged. The results highlighted by Fritzen et al [22] led them to extend the GT yield criterion in order to overcome the analytical/numerical discrepancies. Khdir et al [22] focused their investigations on the porous materials containing two populations of voids.…”

Section: Introductionmentioning

confidence: 99%

“…The results highlighted by Fritzen et al [22] led them to extend the GT yield criterion in order to overcome the analytical/numerical discrepancies. Khdir et al [22] focused their investigations on the porous materials containing two populations of voids. Their results showed that, for an identical fraction of porosities, there is no significant difference between a double and a single population of voids.…”

Section: Introductionmentioning

confidence: 99%

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Statistical Approach to the Representative Volume Element Size of Random Composites

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Apparent properties of random structures may be estimated by homogenization from the numerical solution of the PDE concerning the physical fields on real images or on simulations of random media in bounded domains. For this purpose, numerical calculations are made by Finite Elements or by FFT. This numerical approach involves a statistical definition of a representative volume element RVE to provide intervals of confidence of the estimated apparent properties. For large enough domains, bias errors generated by applied boundary conditions can be neglected. The statistical approach of the RVE is summarized. It is illustrated by examples of application to linear and nonlinear micromechanics, optics, fluid flows and wave propagation, for various types of microstructures of industrial materials, as well as of models of random sets.

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Computational homogenization of elasto-plastic porous metals

Cited by 176 publications

References 48 publications

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Numerical homogenization of the viscoplastic behavior of snow based on X-ray tomography images

Numerical Approach to Estimate the Effective Yield Surface of Random Porous Media for Spherical Voids

Statistical Approach to the Representative Volume Element Size of Random Composites

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