Micromechanics approach

The objective of aii micromechanics approaches is to determine the eiastic moduli or stiffnesses or compiiances of a composite materiai in terms of the eiastic moduii of the constituent materiais. For example, the elastic moduii of a fiber-reinforced composite materiai must be determined in terms of the properties of the fibers and the matrix and in terms of the reiative voiumes of fibers and matrix ... 

The micromechanics approaches presented in this book are an attempt to predict the mechanical properties of a composite material based on the mechanical properties of its constituent materials. In nearly all fiber-reinforced composite materials, there is considerable difference between expectation and reality. Thus, we must ask what is the usefulness of micromechanical analysis beyond gaining a feeling for why composite materials behave as they do Basically, there are two answers one related to designing a material and one related to designing a structure. 

A MICROMECHANICS APPROACH TO THE MECHANICALLY-INDUCED DISSOLUTION IN POROUS MEDIA... 

Estimates for the macroscopic drained stiffness tensor Chom(f) as a function of the morphological parameter can be derived from various micromechanical techniques. The micromechanical approach classically refers to the concept of strain concentration tensor, denoted here by A. By definition, in an evolution... 

Based on a local dissolution law, the micromechanical approach is able to discuss the effects of the local heterogeneity of the mechanical affinity on the dissolution process and to predict the evolution of the pore space morphology. Whenever it is possible to describe the latter by a scalar parameter , (22) yields its evolution (t) which captures the chemomechanical coupling in so far as it controls the evolution of the poroelastic coefficients in (13). Nevertheless, the implementation of this modelling requires to be able to determine the microscopic strain state along the fluid-solid interface by appropriate micromechanical techniques. 

Deude, V., Dormieux, L., Kondo, D. and Maghous, S. (2002) Micromechanical approach to non linear poroelasticity application to cracked rocks, Journal of Engineering Mechanics 128(8), 848-855... 

We consider an elastic solid weakened by a set of microcracks. The elastic free energy, used as thermodynamic potential, can be estimated by using micromechanics approaches (Krajcinovic 1989, Pensee and Kondo 2001). In this work, we assume an isotropic distribution of microcracks. We limit the present study to the case of fully open microcracks. However we account for an energy coupling between damage evolution and plastic flow. Therefore, the thermodynamic potential for dry material is obtained ... 

Once the constitutive equations and texmre changes of the two subphases are established, we can assemble them together in the RVE by the micromechanics approach. Figure 5.23 shows a schematic of the RVE. The detailed discussion can be found in Section 5.3.1 and Equation (5.2). 

In general, SMPF is perceived as a two-phase composite material with a crystalline phase mixed with an amorphous phase. A multiscale viscoplasticity theory is developed. The amorphous phase is modeled using the Boyce model, while the crystalline phase is modeled using the Hutchinson model. Under an isostrain assumption, the micromechanics approach is used to assemble the microscale RVE. The kinematic relation is used to link the micro-mechanics constitutive relation to the macroscopic constitutive law. The proposed theory takes into account the stress induced crystallization process and the initial morphological texture, while the polymeric texture is updated based on the apphed stresses. The related computational issue is discussed. The predictabihty of the model is vahdated by comparison wifli test results. It is expected that more accurate measurement of the stress and strain in the SMPF with large deformation may further enhance the predictability of the developed model. It is also desired to reduce the number of material parameters in the model. In other words, a deeper understanding and physics based theoretical modeling are needed. 

From a strictly theoretical point of view, the so-called constituent testing approach or micromechanics approach is the most valuable. Tests performed on composite constituents supply the required material constants of each phase of the composite material— namely for long-liber-reinforced composite— for the fiber and the matrix, to use in appropriate mixture rules. These rules obtained by physical and mechanical considerations are the basic relationships between the composite constituents, and they leads to a complete characterization of the final composite. 

Abstract This chapter describes the elastic qualities of advanced fibre-reinforced composites, in terms of characterization, measurement and prediction from the basic constituents, i.e. the fibre and matrix. The elastic analysis comprises applying micromechanics approaches to predict the lamina elastic properties from the basic constituents, and using classical lamination theory to predict the elastic properties of composite materials composed of several laminae stacked at different orientations. Examples are given to illustrate the theoretical analysis and give a full apprehension of its prediction capability. The last section provides an overview on identification methods for elastic proprieties based on full-field measurements. It is shown that these methodologies are very convenient for elastic characterization of anisotropic and heterogeneous materials. 

The typical building block of a composite structure is the lamina, with a typical thickness of 0.125 mm. The lamina stress-strain relationships are described for orthotropic, transverse isotropic and isotropic materials. When a lamina is reinforced with unidirectional fibres it can be assumed to be a transversely isotropic material. In this chapter, theoretical determination of lamina elastic properties, assumed to be a transversely isotropic material, using micromechanics approaches is presented and illustrated with experimental data. 

Results obtained from the literature are used to assess the prediction capabilities of the micromechanics approaches. In this case a unidirectional composite made using isotropic glass fibres and epoxy matrix with E = 73.1 GPa,... 

Aboudi J. (1991) Mechanics of Composite Materials A Unified Micromechanical Approach, Elsevier, Amsterdam. 

An additional result of general interest emanating from the micromechanical approach is embodied in the Laplace condition in the form ... 

Diani J, Bedoui F and Regnier G (2008) On the relevance of the micromechanics approach for predicting the linear viscoelastic behavior of semicrystalline PET, Mat Sci EnyA475 229-234. 

Due to the structure filler hierarchical morphology and surrounding polymer matrix at nanometer length scale, the well-defined concepts in conventional two-phase composites should not be directly applied to polymer nanocomposites. Polymer molecules and nanofillers have equivalent size and the polymer-filer interactions are highly dependent on the local molecular structure and bonding at the interface. Therefore, nanofillers and polymer chains structures cannot be considered as continuous phase at these length scales, and the bulk mechanical properties caimot be determined, for that reason, using traditional continuum-based micromechanical approaches [47,48]. 

Tomas J (2007) Adhesion of ultrafine particles—A micromechanical approach. Chem Eng Sci 62(7) 1997... 

Krajcinovic (6) develops a micromechanical approach and, with a deeper knowledge of how and when microcracks can first initiate, then propagate and finally coalesce, he is able to infer macro-scale conclusions. 

Expectedly quantitative results vary considerably from one fiber-rubber system to another, and other compounding ingredients may induce additional effects (positive or negative). The qualitative effects are completely in line with the expected role of short fibers, in agreement with micromechanic considerations (see Section 7.2). Certain authors have used well established micromechanic approaches, e.g., Voigt and Reuss averages (Equations 7.1 and 7.2), and Halpin-Tsai equations (Equation 7.5) to consider the effects on short natural fibers in rubber compounds. ... 

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