Micromechanical modeling of random or imperfect composites (original) (raw)
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International Journal for Multiscale Computational Engineering, 2013
A two-layer statistically equivalent periodic unit cell is offered to predict a macroscopic response of plain weave multilayer carbon-carbon textile composites. Fallingshort in describing the most severe geometrical imperfections of these material systems, the original formulation presented in [1] is substantially modified, now allowing for nesting and mutual shift of individual layers of textile fabric in all three directions. Yet, the most valuable asset of the present formulation is seen in the possibility of reflecting the influence of meso-scale porosity through a system of distorted voids. Numerical predictions of both the effective thermal conductivities and elastic stiffnesses provided through the application of extended finite element method are compared with available laboratory data and the results derived using the Mori-Tanaka averaging scheme to support credibility of the present approach, about as much as the reliability of local mechanical properties found from nanoindentation tests performed directly on the analyzed composite samples.
Peridynamic Micromechanics of Random Structure Composites
Springer eBooks, 2012
In this chapter, we consider the solution methods of the GIE of peridynamic micromechanics. These methods are based on extraction from the material properties a constituent of the matrix properties. Effective moduli are expressed through the average local interface polarization tensor over the surface of the extended inclusion phase rather than over an entire space. Any spatial derivatives of displacement fields are not required. The basic hypotheses of locally elastic micromechanics are generalized to their peridynamic counterparts. In particular, in the generalized effective field method (EFM) proposed, the classical effective field hypothesis is relaxed, and the hypothesis of the ellipsoidal symmetry of the random structure of CMs is not used. One demonstrates some similarity and difference with respect to other methods (the dilute approximation and Mori-Tanaka approach) of micromechanics of peridynamic CMs. Estimation of macroscopic effective response of heterogeneous media with random structures in an averaged (or homogenized) meaning in terms of the mechanical and geometrical properties of constituents is a central focus of micromechanics denoted as micro-to-macro modeling. The general results establishing the links between the effective properties and the corresponding mechanical and transformation influence functions were inspired by Hill [640] for locally elastic composites. Some basic representations analogous to the mentioned above were generalized in Chap. 17 to the thermoperidynamics of CMs. The displacement field estimations in the constituents, in turn, are based on a substitution into the one or another micromechanical scheme of a solution (called basic problem) for one inclusion inside the infinite matrix subjected to some effective field. So, for locally elastic random structure CMs, a number of micromechanical models inspired by Eshelby [449] (see Chap. 3) were proposed in the literature for describing the thermoelastic behavior of composites with ellipsoidal inclusions (see Chaps. 8-12). Numerical solutions for the basic problem are considered in Sect. 18.1, whereas the different micromechanical models are generalized to their peridynamic counterparts in Sects. 18.2-18.4.
Computer Methods in Applied Mechanics and Engineering, 2019
An inverse Mean-Field Homogenization (MFH) process is developed to improve the computational efficiency of non-linear stochastic multiscale analyzes by relying on a micro-mechanics model. First full-field simulations of composite Stochastic Volume Element (SVE) realizations are performed to characterize the homogenized stochastic behavior. The uncertainties observed in the non-linear homogenized response, which result from the uncertainties of their micro-structures, are then translated to an incrementalsecant MFH formulation by defining the MFH input parameters as random effective properties. These effective input parameters, which correspond to the micro-structure geometrical information and to the material phases model parameters, are identified by conducting an inverse analysis from the full-field homogenized responses. Compared to the direct finite element analyzes on SVEs, the resulting stochastic MFH process reduces not only the computational cost, but also the order of uncertain parameters in the composite micro-structures, leading to a stochastic Mean-Field Reduced Order Model (MF-ROM). A data-driven stochastic model is then built in order to generate the random effective properties under the form of a random field used
Micromechanical analysis of periodic masonry
2009
In the present paper, the TFA homogenization procedure is extended to the case of nonuniform eigenstrain in the inclusions, in order to deduce the overall response of regular masonry arrangements to be used for the multiscale analysis of masonry walls.
Micromechanical analysis of periodic composites by prescribing the average stress
Annals of Solid and Structural Mechanics
A new method for the micromechanical finite element analysis of unidirectional composites is presented. The method is especially effective in time-dependent analyses, as those involving viscoplasticity and viscoelasticity. The microstructure of the composites under consideration is characterized by periodicity and central symmetry, which allow analysing half of a unit cell for solving the micromechanical problem. Half of the unit cell contains only half of the continuous fibre and this makes the numerical analyses inexpensive in terms of computer memory usage and processing time. New boundary conditions are presented in order to prescribe the average stress on half of the unit cell of hexagonal and rectangular distributions of heterogeneities in the case of static analysis. Then, the new boundary conditions are used to prescribe the precise rate of the average stress in time-dependent analyses. With respect to other existing procedures, the proposed method is easy to adopt in commercial software and it does not require the modification of parts of the source code that are not usually accessible to the user. The proposed method is applied to the interesting case of composites with aligned long fibres imperfectly bonded to a viscoelastic matrix. The numerical simulations carried out in this work provide the loci of the average stress and strain corresponding to the initiation of the fibre-matrix debonding, which determines a considerable decay of the composite stiffness and strength. The influence of the geometrical properties of the microstructure is evaluated by analysing both hexagonal and rectangular distributions of fibres. The numerical results show how the inelastic behaviour of the matrix affects the loci corresponding to the initiation of the debonding.
A micromechanical model for linear homogenization of brick masonry
Materials and Structures, 1999
A micromechanical model, originally developed for long-fiber composites, is applied to determination of the overall linear-elastic mechanical properties of simpletexture brick masonry. The model relies upon exact solution after Eshelby and describes brickwork as a mortar matrix with insertions of elliptic cylinder-shaped bricks. The macroscopic elastic constants are derived from the mechanical properties of the constituent materials and the phase volume ratios. The ability of the suggested model to predict the behavior of real brickwork has been checked by performing uniaxial compression tests on brick masonry panels of two types, with cement mortar and lime mortar. The results obtained through the proposed model fit experimental data more closely than other models selected from the literature for the sake of comparison. riiiii[ii~;:j 1359-5997/99 9 I~LEM
International Journal for Numerical Methods in Engineering, 2012
The purpose of this elaboration is to develop an efficient method for a determination of the probabilistic entropy loss in the homogenization process of the periodic composites with random material characteristics. A definition of this entropy convenient for the Gaussian continuous distribution is adopted and implemented into the computer algebra system MAPLE. Homogenization of the fiber-reinforced composite with randomly defined Young's moduli of the constituents is carried out in the FEM and homogenization-oriented code based on the four-noded plane strain elements. Probabilistic procedure has triple character and is alternatively based on the Monte Carlo simulation, on the generalized stochastic perturbation-based analysis, and on the recently developed semi-analytical determination of homogenized tensor using the response function method. Because of this triple usage of the probabilistic methods, it is possible to make a detailed comparison of all those techniques, especially in view of the entropy variation during the homogenization. This procedure may be linked with other homogenization techniques, also for various constitutive models and/or for the upper and lower bounds on the effective tensor components.
Stochastic finite element analysis of composite structures based on material microstructure
Composite Structures, 2015
The linking of microstructure uncertainty with the random variation of material properties at the macroscale is particularly needed in the framework of the stochastic finite element method (SFEM) where arbitrary assumptions are usually made regarding the probability distribution and correlation structure of the macroscopic mechanical properties. This linking can be accomplished in an efficient manner by exploiting the excellent synergy of the extended finite element method (XFEM) and Monte Carlo simulation (MCS) for the computation of the effective properties of random two-phase composites. The homogenization is based on Hill's energy condition and involves the generation of a large number of random realizations of the microstructure geometry based on a given volume fraction of the inclusions and other parameters (shape, number, spatial distribution and orientation). In this paper, the mean value, coefficient of variation and probability distribution of the effective elastic modulus and Poisson ratio are computed taking into account the material microstructure. The effective properties are used in the framework of SFEM to obtain the response of a composite structure and it is shown that the response variability can be significantly affected by the random microstructure.
Thermoelastic homogenization of periodic composites using an eigenstrain-based micromechanical model
Applied Mathematical Modelling, 2020
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Composite Structures, 2011
This work investigates the possibility to predict the auxetic behavior of composites consisting of non-auxetic phases by means of micromechanical models based on Eshelby’s inclusion concept. Two specific microstructures have been considered: (i) the three-layered hollow-cored fibers-reinforced composite and (ii) a microstructure imitating the re-entrant honeycomb micro-architecture. The micromechanical analysis is based on kinematic integral equations as a formal solution of the inhomogeneous material problem. The interaction tensors between the inhomogeneities are computed thanks to the Fourier’s transform. The material anisotropy due to the morphological and topological textures of the inhomogeneities was taken into account thanks to the multi-site approximation of these tensors. In both cases, the numerical results show that auxetic behavior cannot be captured by such models at least in the case of elastic and isotropic phases. This conclusion is supported by corresponding finite element investigations of the second microstructure that indicate that auxetic behavior can be recovered by introducing joints between inclusions. Otherwise, favorable issues are only expected with auxetic components.► Auxetic behavior of isotropic biphasic composite materials using Mori–Tanaka model. ► Multi-coated inhomogeneities model for auxetic behavior of composite materials. ► Multi-site Mori–Tanaka model to account for the interactions among inhomogeneities. ► Finite element modeling of composite materials with re-entrant microstructure.