Micromechanics as a Basis for Damage Mechanics
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Micromechanics
Representative elementary volume
Basis (linear algebra)
Micromechanics models of composite materials are preferred in the analysis and design of composites for their high computational efficiency. However, the accuracy of the micromechanics models varies widely, depending on the volume fraction of inclusions and the contrast of phase properties, which have not been thoroughly studied, primarily due to the lack of complete and representative experimental data. The recently developed microstructure-free finite element modeling (MF-FEM) is based on the fact that, for a particulate-reinforced composite, if the characteristic size of the inclusions is much smaller than the composite representative volume element (RVE), the elastic properties of the RVE are independent of inclusion shape and size. MF-FEM has a number of advantages over the conventional microstructure-based finite element modeling. MF-FEM predictions have good to excellent agreement with the reported experiment results. In this study, predictions produced by MF-FEM are used in replace of experimental data to compare the accuracy of selected micromechanics models of particulate composites. The results indicate that, only if both the contrasts in phase Young's moduli and phase Poisson's ratios are small, the micromechanics models are able to produce accurate predictions. In other cases, they are more or less inaccurate. This study may serve as a guide for the appropriate use of the micromechanics models.
Micromechanics
Representative elementary volume
Volume fraction
Multiscale Modeling
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In this paper, we proposed a revised Mori–Tanaka model for the effective estimation of the elastic properties at lower fiber volume fraction. A review of some notable micromechanics-based models with the theories proposed by Voigt and Reuss, Hashin–Shtrikman model, Mori–Tanaka method and dilute dispersion scheme is carried out, and a critique is presented focusing on the limitations of these models. Finite Element (FE) simulations are performed using Representative Volume Element (RVE) technique to rationalize the analytical results. Our results revealed that revised Mori–Tanaka estimates and FE predictions are in agreement. Elastic properties of the test material are dependent on size of RVE suggesting the effective elastic modulus evaluated using RVE forms the lower bounds of true effective values. However, we still believe that there is room for the debate for evaluating the elastic properties of these composites at larger volume fractions with the inclusion of Eshelby’s tensor in Mori–Tanaka scheme. Thus the efficacy of micromechanics-based models for the effective estimation of elastic properties of polymer matrix composites is highlighted. Our findings may provide new significant insights of the effective estimation of elastic properties of PMC using micromechanics-based approach.
Micromechanics
Representative elementary volume
Volume fraction
Matrix (chemical analysis)
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Micromechanics
Representative elementary volume
Basis (linear algebra)
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This article provides a brief introduction to micromechanics using linear elastic materials as an example. The fundamental micromechanics concepts including homogenization and dehomogenization, representative volume element (RVE), unit cell, average stress and strain theories, effective stiffness and compliance, Hill-Mandel macrohomogeneity condition. This chapter also describes the detailed derivations of the rules of mixtures, and three full field micromechanics theories including finite element analysis of a representative volume element (RVE analysis), mathematical homogenization theory (MHT), and mechanics of structure genome (MSG). Theoretical connections among the three full field micromechanics theories are clearly shown. Particularly, it is shown that RVE analysis, MHT and MSG are governed by the same set of equations for 3D RVEs with periodic boundary conditions. RVE analysis and MSG can also handle aperiodic or partially periodic materials for which MHT is not applicable. MSG has the unique capability to obtain the complete set of 3D properties and local fields for heterogeneous materials featuring 1D or 2D heterogeneities.
Micromechanics
Representative elementary volume
Homogenization
Periodic boundary conditions
Linear elasticity
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A novel method for analyzing tubular composites was developed by obtaining a curved representative volume element (RVE) from the transformation of a flat RVE. There was found to be a discrepancy in the stress between the two RVE models of approximately 15%. The curved RVE model was validated using an isotropic material.
Micromechanics
Representative elementary volume
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Micromechanics
Representative elementary volume
Matrix (chemical analysis)
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Abstract In a woven fabric composite, arrangement and behavior of the fibers contained in the yarn and the yarns themselves lead to an intricate deformation mechanism. The current research, therefore, intends to propose a simplified mathematical micromechanics model for calculating mechanical properties of the plain weave composite using finite element analysis (FEA). A repetitive volume element (RVE) cell approach has been adopted for properties evaluation of plain weave composites. The FEA allows the modeling and portrayal of fabrics by taking into account various geometric parameters such as the yarn undulation, the probability of existence of consonances in a unit cell and interaction between warp and fill tows. These factors help in generating a mesh close to the actual fabric/composite. Additionally, a technique to represent the internal layout of composite structure employing actual dimensions of yarn geometry using conventional measurement devices, rather than using the demanding method of obtaining measurements from photomicrographs of sectioned laminates, is also proposed. The geometric symmetries as reported in the available literature were also incorporated during the model formulation. The theory of comparative displacements was then used to construe these symmetries into appropriate mechanical terms. Consequently, this leads to the formulation of boundary conditions for the RVE. The proposed finite element micromechanics model is different from the existing models in a way that it defines the yarn cross-sectional path based upon computational fluid dynamics technique rather than conventionally obtained photomicrographic results or the proposed sinusoidal paths by various researchers. Experiments were then performed on the laminates used for obtaining the geometric parameters with the aim of supporting the validity of the suggested model. The results of computational analysis were found to be in good agreement with the outcomes of experimental investigation.
Micromechanics
Representative elementary volume
Plain weave
Periodic boundary conditions
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Micromechanics
Microscale chemistry
Representative elementary volume
Damage mechanics
Fiber-reinforced composite
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Micromechanics
Representative elementary volume
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Micromechanics
Representative elementary volume
Homogenization
Digital image correlation
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