Showing papers on "Micromechanics published in 2011"

The micromechanics of three-dimensional collagen-I gels

Abstract: We study the micromechanics of collagen-I gel with the goal of bridging the gap between theory and experiment in the study of biopolymer networks. Three-dimensional images of fluorescently labeled collagen are obtained by confocal microscopy, and the network geometry is extracted using a 3D network skeletonization algorithm. Each fiber is modeled as an elastic beam that resists stretching and bending, and each crosslink is modeled as torsional spring. The stress–strain curves of networks at three different densities are compared with rheology measurements. The model shows good agreement with experiment, confirming that strain stiffening of collagen can be explained entirely by geometric realignment of the network, as opposed to entropic stiffening of individual fibers. The model also suggests that at small strains, crosslink deformation is the main contributer to network stiffness, whereas at large strains, fiber stretching dominates. As this modeling effort uses networks with realistic geometries, this analysis can ultimately serve as a tool for understanding how the mechanics of fibers and crosslinks at the microscopic level produce the macroscopic properties of the network. © 2010 Wiley Periodicals, Inc. Complexity 16: 22-28, 2011 © 2011 Wiley Periodicals, Inc.

Micromechanical analysis of fuzzy fiber reinforced composites

Abstract: A novel fuzzy fiber reinforced composite (FFRC) reinforced with zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is proposed. The distinct constructional feature of this composite is that the uniformly aligned CNTs are radially grown on the surface of carbon fibers. Analytical models based on the mechanics of materials approach and the Mori–Tanaka method are derived to estimate the effective elastic constants of this proposed FFRC. The values of the effective elastic properties of this composite are estimated with and without considering an interphase between the CNT and the polymer matrix. It has been found that the transverse effective properties of this composite are significantly improved due to the radial growing of CNTs on the surface of carbon fiber. The effective properties are also found to be sensitive to the CNT diameter.

A micromechanical study on the effect of intra-ply properties on transverse shear fracture in fibre reinforced composites

Abstract: A micromechanics damage model is presented which examines the influence of intra-ply properties on the transverse shear deformation of a carbon fibre/epoxy composite. It was found that while thermal residual stress influenced the initial location of damage in the microstructure, its influence on the overall shear response was less pronounced. The fibre–matrix interface strength was found to control transverse shear strength, while the interface fracture energy had marked effect on the strain to failure and the interaction of damage mechanisms during fracture. It was also found that regions of low fibre volume fraction, such as areas near the ply boundary, were more susceptible to yielding due to the lack of reinforcement in these regions. The micromechanical model developed shows similar behaviour to in situ experimental observations and could thus prove useful in determining optimum constituent properties allowing for increased interlaminar shear strength of fibre reinforced composite laminates.

Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

Abstract: A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

The nanogranular origin of friction and cohesion in shale—A strength homogenization approach to interpretation of nanoindentation results

Abstract: An inverse micromechanics approach allows interpretation of nanoindentation results to deliver cohesivefrictional strength behavior of the porous clay binder phase in shale. A recently developed strength homogenization model, using the Linear Comparison Composite approach, considers porous clay as a granular material with a cohesive-frictional solid phase. This strength homogenization model is employed in a Limit Analysis Solver to study indentation hardness responses and develop scaling relationships for indentation hardness with clay packing density. Using an inverse approach for nanoindentation on a variety of shale materials gives estimates of packing density distributions within each shale and demonstrates that there exists shale-independent scaling relations of the cohesion and of the friction coefficient that vary with clay packing density. It is observed that the friction coefficient, which may be interpreted as a degree of pressure-sensitivity in strength, tends to zero as clay packing density increases to one. In contrast, cohesion reaches its highest value as clay packing density increases to one. The physical origins of these phenomena are discussed, and related to fractal packing of these nanogranular materials. Copyright 2010 John Wiley & Sons, Ltd.

Multiscale mass-spring models of carbon nanotube foams

Abstract: This article is concerned with the mechanical properties of dense, vertically aligned CNT foams subject to one-dimensional compressive loading. We develop a discrete model directly inspired by the micromechanical response reported experimentally for CNT foams, where infinitesimal portions of the tubes are represented by collections of uniform bi-stable springs. Under cyclic loading, the given model predicts an initial elastic deformation, a non-homogeneous buckling regime, and a densification response, accompanied by a hysteretic unloading path. We compute the dynamic dissipation of such a model through an analytic approach. The continuum limit of the microscopic spring chain defines a mesoscopic dissipative element (micro-meso transition) which represents a finite portion of the foam thickness. An upper-scale model formed by a chain of non-uniform mesoscopic springs is employed to describe the entire CNT foam. A numerical approximation illustrates the main features of the proposed multiscale approach. Available experimental results on the compressive response of CNT foams are fitted with excellent agreement.

A micromechanics-based thermodynamic formulation of isotropic damage with unilateral and friction effects

Abstract: This paper is devoted to micromechanical modeling of isotropic damage in brittle materials . The damaged materials will be considered as heterogeneous media composed of solid matrix weakened by isotropically distributed microcracks . The original contribution of the present work is to provide a proper micromechanical thermodynamic formulation for damage-friction modeling in brittle materials with the help of Eshelby’s solution to matrix-inclusion problems. The elastic and plastic strain energy involving unilateral effects will be fully determined. The condition of microcrack opening–closure transition will be determined in both strain-based and stress-based forms. The effect of spatial distribution of microcracks will also be taken into account. Further, the damage evolution law is formulated in a sound thermodynamic framework and inherently coupled with frictional sliding . As a first phase of validation, the proposed micromechanical model is finally applied to reproduce basic mechanical responses of ordinary concrete in compression tests.

Continuum Damage Mechanics of Materials and Structures

Abstract: Continuum damage mechanics of materials and structures: present and future. Essential damage mechanics - bridging the scales. Microstructure evolution, state variable models, damage mechanics and bounding theorems. Discrete versus continuum damage mechanics: a probabilistic perspective. Damage micromechanics modelling of discontinuous reinforced composites. Continuum damage mechanics applied to quasi-brittle materials. An anisotropic damage theory and unilateral effects: applications to laminates and to three-and four-dimensional composites. Introduction to continuum damage mechanics. Continuum damage modelling for concrete structures in dynamic situations. Interface damage mechanics: application to delamination. Computational methods for delamination and fracture in composites. Size effect theory and its application to fracture of fiber composites and sandwich plates.

The effect of inclusion waviness and waviness distribution on elastic properties of fiber-reinforced composites

Abstract: In this study we investigated the effects of inclusion waviness and its distribution to the effective composite stiffness. Different waviness conditions were analyzed: uniform waviness with variable inclusion orientation or aspect ratio, and uniform aspect ratio with variable waviness. The inclusion waviness was found to have a greater effect on tensile moduli and shear modulus for unidirectional composites; however, if the inclusions are either randomly dispersed or partially aligned, the degree of waviness effect was smaller. The elastic moduli were also over-estimated if inclusion aspect ratio or waviness followed symmetric distributions. In addition, the waviness distribution effect was larger when larger inclusion waviness was introduced in a composite. The lack of fiber waviness distribution assumption was found to lead to inaccurate composite stiffness predictions, especially for composite with higher fiber volume fraction. We also demonstrated the inclusion waviness effects on the tensile modulus of carbon nanotube-reinforced composites. The results showed that the disparity between theoretical predictions and experimental data could be due to different inclusion waviness conditions.

Micromechanical multiscale model for alkali activation of fly ash and metakaolin

Abstract: The process of alkali activation of fly ash and metakaolin is examined in the view of micromechanics. Elasticity is predicted via semi-analytical homogenization methods, using a combination of intrinsic elastic properties obtained from nanoindentation, evolving volume fractions and percolation theory. A new quantitative model for volume fraction is formulated, distinguishing the evolution of unreacted aluminosilicate material, solid gel particles of N-A-S-H gel, and open porosity, which is partially filled with the activator. The stiffening of N-A-S-H gel is modeled by increasing the fraction of solid gel particles. Their packing density and intrinsic elasticity differ in N-A-S-H gels synthesized from both activated materials. Percolation theory helps to address the quasi-solid transition at early ages and explains a long setting time and the beneficial effect of thermal curing. The low ability of N-A-S-H gel to bind water chemically explains the high porosity of Ca-deficient activated materials. Micromechanical analysis matches well the elastic experimental data during the activation and elucidates important stages in the formation of the microstructure.

Homogenization of elastic–plastic periodic materials by FVDAM and FEM approaches – An assessment

Abstract: The standard computational approach for the homogenization of elastic–plastic response of periodic materials is the finite-element method. Amongst the emerging alternatives, the finite-volume direct averaging micromechanics (FVDAM) theory has shown promise. Herein, we present a systematic comparison of the predictive capabilities of both approaches in the context of two technologically important material systems, each of which exhibits interesting plasticity-driven local and global responses in its own right, which have not been well-documented. This comparison is conducted for the first time on the same footing using an in-house developed finite-element code which closely mimics the homogenization framework, displacement field approximation and unit cell discretization employed by the parametric FVDAM theory. A new stress measure is introduced which highlights the fundamental differences in the variational-based and direct averaging-based solution approaches employed by the two methods. The comparison provides firm support for the parametric FVDAM theory’s ability to capture highly localized plasticity effects in different classes of heterogeneous materials, which lead to interesting and technologically important phenomena at the homogenized scale.

A variational formulation for the incremental homogenization of elasto-plastic composites

Abstract: This work addresses the micro–macro modeling of composites having elasto-plastic constituents. A new model is proposed to compute the effective stress–strain relation along arbitrary loading paths. The proposed model is based on an incremental variational principle (Ortiz, M., Stainier, L., 1999. The variational formulation of viscoplastic constitutive updates. Comput. Methods Appl. Mech. Eng. 171, 419–444) according to which the local stress–strain relation derives from a single incremental potential at each time step. The effective incremental potential of the composite is then estimated based on a linear comparison composite (LCC) with an effective behavior computed using available schemes in linear elasticity. Algorithmic elegance of the time-integration of J2 elasto-plasticity is exploited in order to define the LCC. In particular, the elastic predictor strain is used explicitly. The method yields a homogenized yield criterion and radial return equation for each phase, as well as a homogenized plastic flow rule. The predictive capabilities of the proposed method are assessed against reference full-field finite element results for several particle-reinforced composites.

A Micromechanics Finite-Strain Constitutive Model of Fibrous Tissue.

Abstract: Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation, i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress–strain relation and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress–strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.

Complete determination of elastic moduli of interpenetrating metal/ceramic composites using ultrasonic techniques and micromechanical modelling

Abstract: The complete stiffness matrices of several metal/ceramic composites were analysed using the complementary ultrasonic spectroscopic techniques ultrasound phase spectroscopy (UPS) and resonant ultrasound spectroscopy (RUS). Three different aluminum/alumina composites having complex interpenetrating architectures were studied: a composite based on freeze-cast ceramic preform, a composite based on open porous ceramic preform obtained by pyrolysis of cellulose fibres, and a composite based on discontinuous fibre preform. Six of the nine independent elastic constants describing orthotropic elastic anisotropy were pre-determined by ultrasound phase spectroscopy and used as initial guess input for resonant ultrasound spectroscopy analysis, making the final results of all nine elastic constants more reliable. In all cases, consistent and reproducible results are obtained. Finally the experimental results were compared with effective elastic constants calculated using micromechanical modelling and a good correspondence between both is obtained.

Eshelby's tensor fields and effective conductivity of composites made of anisotropic phases with Kapitza's interface thermal resistance

Abstract: Eshelby's results and formalism for an elastic circular or spherical inhomogeneity embedded in an elastic infinite matrix are extended to the thermal conduction phenomenon with a Kapitza interface thermal resistance between matrix and inclusions. Closed-form expressions are derived for the generalized Eshelby interior and exterior conduction tensor fields and localization tensor fields in the case where the matrix and inclusion phases have the most general anisotropy. Unlike the relevant results in elasticity, the generalized Eshelby conduction tensor fields and localization tensor fields inside circular and spherical inhomogeneities are shown to remain uniform even in the presence of Kapitza's interface thermal resistance. With the help of these results, the size-dependent overall thermal conduction properties of composites are estimated by using the dilute, Mori–Tanaka, self-consistent and generalized self-consistent models. The analytical estimates are finally compared with numerical results delivered ...

A study on effect of mineral additions on the mechanical, thermal, and structural properties of poly(butylene terephthalate) (PBT) composites

Abstract: Fillers play a major role in determining the properties and behavior of polymer composites. In this study a series of polybutylene terephthalate composites are fabricated using mica and talc particles as filler materials. The effects of these two different minerals on the mechanical, thermal and structural properties of composites are investigated. Comparative analysis shows that both the fillers have different effect on tensile strength and elongation at break. The experimental results when compared with theoretical predictions reveal high level of interfacial interaction in both the composite systems. The interaction parameter B derived using Pukanszky equation is found to be higher in mica filled composites which is in agreement with its better mechanical response. Microscopic observation by SEM reveals that both fillers exhibit different fracture micromechanics leading to different reinforcing effects in PBT.

A Burger Model for the Effective Behavior of a Microcracked Viscoelastic Solid

Abstract: This article aims at the determination of the effective behavior of a microcracked linear viscoelastic solid Due to the nonlinearity of the strain concentration in the cracks, the latter cannot be derived directly from a combination of the correspondence theorem with the Eshelby-based homogenization schemes The proposed alternative approach is based on the linear relationship between the macroscopic strain and the local displacement discontinuity across the crack An approximation of the effective behavior in the framework of a Burger model is derived analytically

Prediction of the cohesive strength for numerically simulating composite delamination via CZM-based FEM

Abstract: The cohesive strength is an important parameter in numerically modeling composite delamination via CZM (cohesive zone model) based FEM. A micromechanical model is proposed to predict the cohesive strength based on the periodic RVE technique. A periodic displacement boundary condition has been presented on the assumption that the RVE is orthotropic in the sense of overall response. The cohesive strengths of T700/QY8911 and AS4/PEEK laminates at various fibers cross-angles are gained by FEM. With the predicted cohesive strengths the FEM simulations on Mixed-Mode bending (MMB) and seven-point bending test are presented, and the results are in fair agreement with experimental observation.