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, a nanoscale mechanical deformation measurement method was employed to obtain the Young's modulus and Poisson's ratio of polycrystalline silicon for Microelectromechanical Systems (MEMS) from different facilities, and to assess the scale at which these effective properties are valid in MEMS design.
Abstract: A nanoscale mechanical deformation measurement method was employed to obtain the Young’s modulus and Poisson’s ratio of polycrystalline silicon for Microelectromechanical Systems (MEMS) from different facilities, and to assess the scale at which these effective properties are valid in MEMS design. The method, based on in situ Atomic Force Microscope (AFM) imaging and Digital Image Correlation (DIC) analysis, employed 2–2.5 μm thick freestanding specimens with surface measurement areas varying between 1×2 and 5×15 μm2. The effective mechanical properties were quite invariant with respect to the fabrication facility: the Poisson’s ratio of polycrystalline silicon from the Multi-user MEMS Processes (MUMPs) and from Sandia’s Ultra planar four layer Multilevel MEMS Technology (SUMMiT-IV) was 0.22±0.02, while the elastic moduli for MUMPs and SUMMiT-IV polysilicon were 164±7 and 155±6 GPa, respectively. The AFM/DIC method was used to determine the size of the material domain whose mechanical behavior could be described by the isotropic constants. For SUMMiT polysilicon with columnar grains and 650 nm average grain size, it was found that a 10×10-μm2 specimen area, on average containing 15×15 columnar grains, was a representative volume element. However, the axial displacement fields in 4×4 or 2×2 μm2 areas could be highly inhomogeneous and the effective behavior of these specimen domains could deviate significantly from that described by isotropy. As a consequence, the isotropic material constants are applicable to MEMS components comprised of 15×15 or more grains, corresponding to specimen areas equal to 10×10 μm2 for SUMMiT and 5×5 μm2 for MUMPs, and do not provide an accurate description of the mechanics of smaller MEMS components.
98 citations
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TL;DR: In this article, the effect of porosity on the transverse mechanical properties of unidirectional fiber-reinforced composites is studied by means of computational micromechanics.
98 citations
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TL;DR: In this article, a hierarchical multiscale modeling approach is used to investigate three-dimensional (3D) strain localization in granular media, where a hierarchical coupling of finite element method and discrete element method (DEM) is employed to treat a boundary value problem of a granular material and the required constitutive relation for FEM is derived directly from the DEM solution of a GEM Gauss integration points as the representative volume element (RVE).
98 citations
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TL;DR: In this paper, the authors propose a method for the construction of statistically similar representative volume elements (SSRVEs), which have much less complexity but reflect the essential morphological attributes of the microscale.
Abstract: For the direct incorporation of micromechanical information into macroscopic boundary value problems, the FE2-method provides a suitable numerical framework. Here, an additional microscopic boundary value problem, based on evaluations of representative volume elements (RVEs), is attached to each Gauss point of the discretized macrostructure. However, for real random heterogeneous microstructures the choice of a “large” RVE with a huge number of inclusions is much too time-consuming for the simulation of complex macroscopic boundary value problems, especially when history-dependent constitutive laws are adapted for the description of individual phases of the mircostructure. Therefore, we propose a method for the construction of statistically similar RVEs (SSRVEs), which have much less complexity but reflect the essential morphological attributes of the microscale. If this procedure is prosperous, we arrive at the conclusion that the SSRVEs can be discretized with significantly less degrees of freedom than the original microstructure. The basic idea for the design of such SSRVEs is to minimize a least-square functional taking into account suitable statistical measures, which characterize the inclusion morphology. It turns out that the combination of the volume fraction and the spectral density seems not to be sufficient. Therefore, a hybrid reconstruction method, which takes into account the lineal-path function additionally, is proposed that yields promising realizations of the SSRVEs. In order to demonstrate the performance of the proposed procedure, we analyze several representative numerical examples.
98 citations
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TL;DR: In this article, a phenomenological model describing superelasticity, shape memory effect under constant stress and the reorientation process in the martensitic phase is proposed, based on a thermodynamic description of the phase transformation which involves two internal variables: the overall martensite volume fraction and the mean transformation strain.
97 citations