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Showing papers on "Micromechanics published in 2009"


Journal ArticleDOI
TL;DR: In this article, the nonlinear bending of simply supported, functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a transverse uniform or sinusoidal load in thermal environments is investigated.

958 citations


Journal ArticleDOI
TL;DR: In this paper, the effects of sonication time on the mechanical properties of multiscale composites, which contain reinforcements at varying scales, were studied, and a combination of Halpin-Tsai equations and woven fiber micromechanics was used in hierarchy to predict the structural properties of multi-scale composites.

364 citations


Journal ArticleDOI
TL;DR: In this article, the authors provide a critical review of the various micromechanical approaches that had evolved along different paths, and outline recent emerging trends, including the recent incorporation of parametric mapping into this approach has made it competitive with the finite-element method.
Abstract: Outside of the classical microstructural detail-free estimates of effective moduli, micromechanical analyses of macroscopically uniform heterogeneous media may be grouped into two categories based on different geometric representations of material microstructure. Analysis of periodic materials is based on the repeating unit cell (RUC) concept and the associated periodic boundary conditions. This contrasts with analysis of statistically homogeneous materials based on the representative volume element (RVE) concept and the associated homogeneous boundary conditions. In this paper, using the above classification framework we provide a critical review of the various micromechanical approaches that had evolved along different paths, and outline recent emerging trends. We begin with the basic framework for the solution of micromechanics problems independent of microstructural representation, and then clarify the often confused RVE and RUC concepts. Next, we describe classical models, including the available RVE-based models, and critically examine their limitations. This is followed by discussion of models based on the concept of microstructural periodicity. In the final part, two recent unit cell-based models, which continue to evolve, are outlined. First, a homogenization technique called finite-volume direct averaging micromechanics theory is presented as a viable and easily implemented alternative to the mainstream finite-element based asymptotic homogenization of unit cells. The recent incorporation of parametric mapping into this approach has made it competitive with the finite-element method. Then, the latest work based on locally-exact solutions of unit cell problems is described. In this approach, the interior unit cell problem is solved exactly using the elasticity approach. The exterior problem is tackled with a new variational principle that successfully overcomes the non-separable nature of the overall unit cell problem.

242 citations


Journal ArticleDOI
TL;DR: In this article, a review of the state-of-the-art in asymptotic homogenization of composites is presented, by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications.
Abstract: The present paper provides details on the new trends in application of asymptotic homogenization techniques to the analysis of composite materials and thin-walled composite structures and their effective properties. The problems under consideration are important from both fundamental and applied points of view. We review a state-of-the-art in asymptotic homogenization of composites by presenting the variety of existing methods, by pointing out their advantages and shortcomings, and by discussing their applications. In addition to the review of existing results, some new original approaches are also introduced. In particular, we analyze a possibility of analytical solution of the unit cell problems obtained as a result of the homogenization procedure. Asymptotic homogenization of 3D thin-walled composite reinforced structures is considered, and the general homogenization model for a composite shell is introduced. In particular, analytical formulas for the effective stiffness moduli of wafer-reinforced shell and sandwich composite shell with a honeycomb filler are presented. We also consider random composites; use of two-point Pade approximants and asymptotically equivalent functions; correlation between conductivity and elastic properties of composites; and strength, damage, and boundary effects in composites. This article is based on a review of 205 references. DOI: 10.1115/1.3090830

223 citations


Journal ArticleDOI
TL;DR: The multiscale micromechanics model is shown to be able to satisfactorily predict the strength characteristics of different bones from different species, on the basis of their mineral/collagen content, their intercrystalline, intermolecular, lacunar, and vascular porosities, and the elastic and strength properties of hydroxyapatite and (molecules) collagen.

179 citations


Journal ArticleDOI
TL;DR: In this paper, a micromechanics model is developed to assess the impact of the effects of electron hopping and the formation of conductive networks on the electrical conductivity of CNT-polymer nanocomposites.
Abstract: The introduction of carbon nanotubes (CNTs) into nonconducting polymers has been observed to yield orders of magnitude increases in conductivity at very low concentrations of CNTs. These low percolation concentrations have been attributed to both the formation of conductive networks of CNTs within the polymer and to a nanoscale effect associated with the ability of electrons to transfer from one CNT to another known as electron hopping. In the present work, a micromechanics model is developed to assess the impact of the effects of electron hopping and the formation of conductive networks on the electrical conductivity of CNT-polymer nanocomposites. The micromechanics model uses the composite cylinders model as a nanoscale representative volume element where the effects of electron hopping are introduced in the form of a continuum interphase layer, resulting in a distinct percolation concentration associated with electron hopping. Changes in the aspect ratio of the nanoscale representative volume element are used to reflect the changes in nanocomposite conductivity associated with the formation of conductive networks due to the formation of nanotube bundles. The model results are compared with experimental data in the literature for both single- and multi-walled CNT nanocomposites where it is observed that the model developed is able to qualitatively explain the relative impact of electron hopping and nanotube bundling on the nanocomposite conductivity and percolation concentrations.

168 citations


Journal ArticleDOI
TL;DR: In this article, a micromechanical analytical model is proposed to address the problem of stiffness and yield stress prediction in the case of nanocomposites consisting of silica nanoparticles embedded in a polymer matrix.

157 citations


Journal ArticleDOI
TL;DR: In this paper, a model of the unit cell of the textile reinforcement is used to predict damage initiation and crack orientation using Puck's criterion, with good agreement with experimental damage initiation threshold and nonlinear tensile diagrams is found both for loading in fibre and off-axis directions.

156 citations



Journal ArticleDOI
TL;DR: In this article, the accepted version of spiral is added to spiral, Elsevier says ok while mandate is not enforced. 17.17.01.14 KB, 0.00

148 citations


Journal ArticleDOI
TL;DR: In this paper, the early-age stiffness and strength evolution of cement paste is studied in the framework of continuum micromechanics, based on a self-consistent scheme.
Abstract: Early-age stiffness and strength evolution of cement paste is studied in the framework of continuum micromechanics. Based on the self-consistent scheme, elastic and strength properties are upscaled from the scale of several micrometers up to the scale of several hundreds or thousands of micrometers. Four material phases are considered: clinker, hydration products, water and air. We assign a spherical geometry to clinker grains and pores, while we investigate both spherical and acicular (needle-type) shapes as geometrical representation of the micrometer-sized hydration products. As regards macroscopic poromechanical boundary conditions, two extreme cases are considered: drained conditions and sealed conditions, respectively. These choices allow for studying the influence of (i) the morphological representation of hydrates, and of (ii) the bulk stiffness of water, on the micromechanical prediction of early-age behavior of cement paste, including setting and the hydration-dependent evolutions of both elastic stiffness and uniaxial compressive strength. The newly proposed strength model is based on a von Mises-type elastic limit criterion for individual hydrates. Corresponding deviatoric stress peaks within hydrates are estimated through quadratic stress averages. In this way, the micromechanical strength criterion is formulated in terms of macroscopic loading (stresses or strains, respectively). Model-predicted elasticity and strength evolutions are compared with data from experimental testing of cement pastes with water–cement ratios ranging from 0.35 to 0.60. Satisfactory agreement between model predictions and experiments allows for two conclusions: the morphology of hydrates significantly influences micromechanics-based elastic stiffness estimates of cement paste particularly at very early ages, whereas elastic properties of mature cement paste can be estimated reliably on the basis of both spherical or acicular shaped hydrates. The development of a reliable strength model, however, requires consideration of hydrates as non-spherical particles, no matter what age of cement paste is considered.

Journal ArticleDOI
TL;DR: An overview of methods of the mathematical modeling of deformation, damage and fracture in fiber reinforced composites is presented in this paper, where the models are classified into five main groups: shear lag-based, analytical models, fiber bundle model and its generalizations, fracture mechanics based and continuum damage mechanics based models and numerical continuum mechanical models.

Journal ArticleDOI
TL;DR: In this article, a micromechanics-based approach to the strength properties of composite materials with a Drucker-Prager matrix in the situation of non-associated plasticity is described.
Abstract: The present paper describes a micromechanics-based approach to the strength properties of composite materials with a Drucker–Prager matrix in the situation of non-associated plasticity. The concept of limit stress states for such materials is first extended to the context of homogenization. It is shown that the macroscopic limit stress states can theoretically be obtained from the solution to a sequence of viscoplastic problems stated on the representative elementary volume. The strategy of resolution implements a non-linear homogenization technique based on the modified secant method. This procedure is applied to the determination of the macroscopic strength properties and plastic flow rule of materials reinforced by rigid inclusions, as well as for porous media. The role of the matrix dilatancy coefficient is in particular discussed in both cases. Finally, finite element solutions are derived for a porous medium and compared to the micromechanical predictions.

Journal ArticleDOI
TL;DR: In this paper, the strength of a composite consisting of 40% NaOH/Na 2 SO 3 treated hemp fibre, polypropylene and 4% MAPP was evaluated by means of mathematical modelling and mechanical testing.
Abstract: The strength of a composite consisting of 40 wt% NaOH/Na 2 SO 3 treated hemp fibre, polypropylene and 4 wt% MAPP was evaluated by means of mathematical modelling and mechanical testing Interfacial shear strength, single fibre tensile strength and fibre length distribution within the composite were obtained, and theoretical composite strengths were determined by means of the Modified Rule of Mixtures and Bowyer–Bader models The experimentally obtained composite tensile strength of 505 MPa was found to be one-third of the theoretical strength determined by means of the Bowyer–Bader model, and this difference was thought to be mainly due to the non-axial planar-random orientation of the fibres within the composite

Journal ArticleDOI
TL;DR: In this article, the shear strength properties of unsaturated granular materials with capillary effects were investigated based on discrete element simulations and micromechanical calculations, and the results showed a nonlinear evolution of the cohesion with the water content.

Journal ArticleDOI
TL;DR: In this article, an analytical micromechanical model for kink-band formation in an unidirectional fiber-reinforced composite is developed based on the equilibrium of an imperfect fibre laterally supported by an elasto-plastic matrix.

Journal ArticleDOI
TL;DR: In this paper, a micromechanics model for aging basic creep of early-age concrete is proposed, where the authors formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste and another related to concrete.
Abstract: We propose a micromechanics model for aging basic creep of early-age concrete. Therefore, we formulate viscoelastic boundary value problems on two representative volume elements, one related to cement paste (composed of cement, water, hydrates, and air), and one related to concrete (composed of cement paste and aggregates). Homogenization of the “nonaging” elastic and viscoelastic properties of the material’s contituents involves the transformation of the aforementioned viscoelastic boundary value problems to the Laplace-Carson (LC) domain. There, formally elastic, classical self-consistent and Mori-Tanaka solutions are employed, leading to pointwisely defined LC-transformed tensorial creep and relaxation functions. Subsequently, the latter are back-transformed, by means of the Gaver-Wynn-Rho algorithm, into the time domain. Temporal derivatives of corresponding homogenized creep and relaxation tensors, evaluated for the current maturation state of the material (in terms of current volume fractions of cem...

Journal ArticleDOI
TL;DR: The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach the desired values for biomaterial stiffness or strength.
Abstract: Hydroxyapatite (HA) biomaterials production has been a major field in biomaterials science and biomechanical engineering. As concerns prediction of their stiffness and strength, we propose to go beyond statistical correlations with porosity or empirical structure-property relationships, as to resolve the material-immanent microstructures governing the overall mechanical behavior. The macroscopic mechanical properties are estimated from the microstructures of the materials and their composition, in a homogenization process based on continuum micromechanics. Thereby, biomaterials are envisioned as porous polycrystals consisting of HA needles and spherical pores. Validation of respective micromechanical models relies on two independent experimental sets: biomaterial-specific macroscopic (homogenized) stiffness and uniaxial (tensile and compressive) strength predicted from biomaterial-specific porosities, on the basis of biomaterial-independent ("universal") elastic and strength properties of HA, are compared with corresponding biomaterial-specific experimentally determined (acoustic and mechanical) stiffness and strength values. The good agreement between model predictions and the corresponding experiments underlines the potential of micromechanical modeling in improving biomaterial design, through optimization of key parameters such as porosities or geometries of microstructures, in order to reach the desired values for biomaterial stiffness or strength.

Journal ArticleDOI
TL;DR: In this article, a unit-cell micromechanics model is presented to predict the effective Young's modulus of open-cell nanoporous materials, incorporating the effects of surface energy and residual surface stress on the effective elastic property of nanoporous material.
Abstract: The mechanical properties of a nanoporous material depend not only on its porosity but also on its characteristic sizes of microstructure, e.g., the average sizes of ligaments. Classical continuum mechanics models cannot interpret this type of size dependence. We here present a unit-cell micromechanics model to predict the effective Young’s modulus of open-cell nanoporous materials. The theory of surface elasticity is adopted to incorporate the effects of surface energy and residual surface stress on the effective elastic property of nanoporous materials. This model can reasonably elucidate the relevant experimental results.

Journal ArticleDOI
TL;DR: In this article, the effects of the martensite phase on the failure mode and ductility of dual-phase (DP) steels were investigated using a micromechanics-based finite element method.
Abstract: The effects of the mechanical properties of the martensite phase on the failure mode and ductility of dual-phase (DP) steels are investigated using a micromechanics-based finite element method. Actual microstructures of DP steels obtained from scanning electron microscopy (SEM) are used as representative volume elements (RVEs) in the finite element calculations. Ductile failure of the RVE is predicted as plastic strain localization during the deformation process. Systematic computations are conducted on the RVE to quantitatively evaluate the influence of the martensite mechanical properties and volume fraction on the macroscopic mechanical properties of DP steels. These properties include the ultimate tensile strength (UTS), ultimate ductility, and failure modes. The computational results show that, as the strength and volume fraction of the martensite phase increase, the UTS of DP steels increases, but the UTS strain and failure strain decrease. In addition, shear-dominant failure modes usually develop for DP steels with lower martensite strengths, whereas split failure modes typically develop for DP steels with higher martensite strengths. The methodology and data presented in this article can be used to tailor DP steel design for its intended purposes and desired properties.

Journal ArticleDOI
TL;DR: In this article, the effect of the statistical variability of fiber strengths, viscosity of the polymer matrix as well as the interaction between the damage processes in matrix, fibers and interface are investigated numerically.

Journal ArticleDOI
TL;DR: Hu et al. as discussed by the authors developed an accurate and computationally efficient homogenization-based continuum plasticity-damage (HCPD) model for macroscopic analysis of ductile failure in porous ductile materials containing brittle inclusions.
Abstract: This paper develops an accurate and computationally efficient homogenization-based continuum plasticity-damage (HCPD) model for macroscopic analysis of ductile failure in porous ductile materials containing brittle inclusions. Example of these materials are cast alloys such as aluminum and metal matrix composites. The overall framework of the HCPD model follows the structure of the anisotropic Gurson–Tvergaard–Needleman (GTN) type elasto-plasticity model for porous ductile materials. The HCPD model is assumed to be orthotropic in an evolving material principal coordinate system throughout the deformation history. The GTN model parameters are calibrated from homogenization of evolving variables in representative volume elements (RVE) of the microstructure containing inclusions and voids. Micromechanical analyses for this purpose are conducted by the locally enriched Voronoi cell finite element model (LE-VCFEM) [Hu, C., Ghosh, S., 2008. Locally enhanced Voronoi cell finite element model (LE-VCFEM) for simulating evolving fracture in ductile microstructures containing inclusions. Int. J. Numer. Methods Eng. 76(12), 1955–1992]. The model also introduces a novel void nucleation criterion from micromechanical damage evolution due to combined inclusion and matrix cracking. The paper discusses methods for estimating RVE length scales in microstructures with non-uniform dispersions, as well as macroscopic characteristic length scales for non-local constitutive models. Comparison of results from the anisotropic HCPD model with homogenized micromechanics shows excellent agreement. The HCPD model has a huge efficiency advantage over micromechanics models. Hence, it is a very effective tool in predicting macroscopic damage in structures with direct reference to microstructural composition.

Journal ArticleDOI
TL;DR: In this paper, strength of materials based approach was used for determination of effective coupled thermo-electro-mechanical (TEM) properties of piezoelectric fiber reinforced composite (PFRC).

Journal ArticleDOI
TL;DR: In this paper, a review of the time dependent viscoelastic behaviour of wood is presented under constant and cyclic climatic conditions, separately, focusing on results obtained in recent years on the behaviour of thin wood tissues, single fibres, thermo-visco-elasticity of wood, influence of hemicelluloses and the modelling of the effect of transient moisture at the molecular level on the mechanical response.
Abstract: Wood, like all polymeric materials, shows viscoelastic behaviour. The time dependent behaviour of wood depends on material anisotropy, temperature, moisture and stresses. To predict the behaviour of wood, numerous mathematical models have been developed largely relying on experimental results. In this paper, time dependent viscoelastic behaviour of wood is reviewed under constant and cyclic climatic conditions, separately. More emphasis is given on results obtained in recent years on the behaviour of thin wood tissues, single fibres, thermo-viscoelasticity of wood, influence of hemicelluloses and the modelling of the effect of transient moisture at the molecular level on the mechanical response.

Journal ArticleDOI
TL;DR: Finite element analysis was used to predict the compressive impact response of low-density closed-cell polyethylene and polystyrene foams, and the predicted yield stresses were close to experimental data, for a range of foam densities as mentioned in this paper.

Journal ArticleDOI
TL;DR: A finite element based micromechanical model has been developed for analyzing and characterizing the microstructural as well as homogenized mechanical response of brain tissue under large deformation and it was found that axon undulation has significant impact on the stiffness and on how stresses were distributed between the axon and the matrix.
Abstract: A finite element based micromechanical model has been developed for analyzing and characterizing the microstructural as well as homogenized mechanical response of brain tissue under large deformation. The model takes well-organized soft tissue as a fiber-reinforced composite with nonlinear and anisotropic behavior assumption for the fiber as well as the matrix of composite matter. The procedure provides a link between the macroscopic scale and microscopic scale as brain tissue undergoes deformation. It can be used to better understand how macroscopic stresses are transferred to the microstructure or cellular structure of the brain. A repeating unit cell (RUC) is created to stand as a representative volume element (RVE) of the hyperelastic material with known properties of the constituents. The model imposes periodicity constraints on the RUC. The RUC is loaded kinematically by imposing displacements on it to create the appropriate normal and shear stresses. The homogenized response of the composite, the average stresses carried within each of the constituents, and the maximum local stresses are all obtained. For each of the normal and shear loading scenarios, the impact of geometrical variables such as the axonal fiber volume fraction and undulation of the axons are evaluated. It was found that axon undulation has significant impact on the stiffness and on how stresses were distributed between the axon and the matrix. As axon undulation increased, the maximum stress and stress in the matrix increased while the stress in the axons decreased. The axon volume fraction was found to have an impact on the tissue stiffness as higher axon volume fractions lead to higher stresses both in the composite and in the constituents. The direction of loading clearly has a large impact on how stresses are distributed amongst the constituents. This micromechanics tool provides the detailed micromechanics stresses and deformations, as well as the average homogenized behavior of the RUC, which can be efficiently used in mechanical characterization of brain tissue.

Journal ArticleDOI
TL;DR: In this article, the effects of loading conditions on the macroscale response of granular materials have been studied extensively using experimental methods and it is relatively straightforward to quantify the variations in material macroresponse using continuum constitutive equations.
Abstract: It is well known that all three principal stresses play a role in the stress-strain-strength-volume response of solids and granular materials, yet conventional triaxial compression tests and direct shear tests are typically used for the determination of design parameters for granular materials, even when field conditions may be plane strain (e.g., behind a long retaining wall). The effects of loading conditions on the macroscale response of granular materials have been studied extensively using experimental methods and it is relatively straightforward to quantify the variations in material macroresponse using continuum constitutive equations. However, these methods provide relatively little insight into the driving micromechanics that govern macroscale behavior, particularly in soils that fail via regions of high localized strain (e.g., shear banding). Thus, it is desirable to develop a set of models that reproduce the expected macroscopic behavior and allow insight into the governing microscale mechanics...

Journal ArticleDOI
TL;DR: In this article, a micromechanical model is presented by combining a continuum damage model and a discrete damage model within the framework of a finite element code, where debonding of particle/matrix interface was modeled by the viscoelastic cohesive zones considering damage irreversibility.


Journal ArticleDOI
TL;DR: In this article, a 3D micromechanical study has been performed in order to investigate local damage in UD composite materials under transverse and longitudinal tensile loading, in particular, the influence of non-uniform distribution of fibres in RVEs with a hexagonal packing array and the effects of thermal residual stresses has been investigated.
Abstract: A three dimensional (3D) micromechanical study has been performed in order to investigate local damage in UD composite materials under transverse and longitudinal tensile loading. In particular, the influence of non-uniform distribution of fibres in RVEs (representative volume element) with a hexagonal packing array and the effects of thermal residual stresses has been investigated. To examine the effect of inter-fibre spacing and residual stress on failure, a study based on the Maximum Principal Stress failure criterion and a stiffness degradation technique has been used for damage analysis of the unit cell subjected to mechanical loading. Results indicate a strong dependence of damage onset and its evolution from the fibres position within the RVE. Predicted mechanical properties, damage initiation and evolution are also clearly influenced by the presence of residual stress.