Topic
Representative elementary volume
About: Representative elementary volume is a research topic. Over the lifetime, 4105 publications have been published within this topic receiving 86863 citations.
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TL;DR: In this paper, numerical simulations using the Fast Fourier Transform (FFT) are performed on different classes of microstructure corresponding to different spatial distributions of voids, and an image analysis tool is proposed for the statistical characterization of the porosity distribution.
99 citations
TL;DR: In this article, the multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross-ply polymer matrix composite laminate.
Abstract: This paper addresses the multi-scale modeling aspects of damage in composite materials. The multiplicity of the scales of the operating mechanisms is discussed and clarified by taking examples of damage in a unidirectional ceramic matrix composite and in a cross ply polymer matrix composite laminate. Two multi-scale modeling strategies––the hierarchical and the synergistic––are reviewed in the context of deformational response. Finally, the “big picture” as it relates to the cost-effective manufacturing of composite structures intended for long-term performance is outlined and desired future direction in multi-scale modeling is discussed.
99 citations
TL;DR: In this paper, the intrinsic role of the size of the microstructural representative volume element (RVE) in a second-order computational homogenization is investigated, which is based on a proper incorporation of the macroscopic gradient of the deformation tensor and the associated higher-order stress measure into the multiscale framework.
Abstract: In this paper the intrinsic role of the size of the microstructural representative volume element (RVE) in a second-order computational homogenization is investigated. The presented second-order computational homogenization is an extension of the classical first-order computational homogenization scheme and is based on a proper incorporation of the macroscopic gradient of the deformation tensor and the associated higher-order stress measure into the multiscale framework. The macroscopic homogenized continuum obtained through this scheme is the full second gradient continuum. It is demonstrated with several examples that the size of the microstructural RVE used in a second-order computational homogenization scheme may be related to the length scale of the associated macroscopic homogenized higher-order continuum. It is shown that the analytical second-order homogenization of a microstructurally homogeneous linearly elastic material leads to the second gradient elastic Mindlin’s continuum on the macroscale, where the resulting macroscopic length scale parameter is proportional to the RVE size. Several numerical microstructural and multiscale analyses reveal the significance of the contribution of the physical and geometrical nonlinearities in the relation between the RVE size and the calculated macroscopic response. Based on the obtained results, some conclusions are drawn with respect to the choice of the microstructural RVE in the second-order computational homogenization analysis.
98 citations
TL;DR: In this paper, the authors revisited an ancient paper (Auriault and Bonnet, 1985) which points out the existence of cut-off frequencies for long acoustic wavelength in high-contrast elastic composite materials, i.e., when the wavelength is large with respect to the characteristic heterogeneity length.
98 citations
TL;DR: In this article, the authors evaluated the homogeneous properties of the active layer of macro fiber composite transducers using finite element periodic homogenization (FEMH) for both d 31 and d 33 -MFCs.
98 citations