Micromechanics-based Analysis Research Articles

Correction to: Micromechanics-based analysis of PVA–ECC after thermal exposure

Correction to: Micromechanics-based analysis of PVA–ECC after thermal exposure

Micromechanics-based analysis of PVA–ECC after thermal exposure

Micromechanics-based analysis of PVA–ECC after thermal exposure

Micromechanics-based reliability analysis method for laminated composite structures

This paper proposes an improved reliability analysis method for composite structures. A new uncertainty model is introduced to quantify the uncertainty in the elastic properties and strength characteristics of the constituents. A multi-scale analysis procedure is developed to link scales in elastic properties, and solve the mechanical responses of all scales. A set of limit state functions are defined, corresponding to the failure modes of intralaminar constituents’ failure and interlaminar delamination. First-order reliability method presents good convergence and accuracy of reliability estimation. Numerical cases are studied to demonstrate the validity and improvements of the proposed method.

Joining of AlN and Al with Compositional Graded Layer by Centrifugal Mixed-Powder Method

In this study, joining of AlN and Al with compositional graded layer is made by centrifugal mixed-powder method (CMPM). The mixed-powder of AlN particles and Al particles is inserted into a spinning mold with bulk-shaped AlN, and then molten Al is poured into the spinning mold with the mixed-powder and bulk-shaped AlN. As a result, the molten Al penetrates into the space between the mixed-powder by the centrifugal force, and at the same time, the Al particles can be melted by heat from the molten Al. Then AlN and Al can be joined with compositional graded layer after solidification. Micromechanics-based analysis is also employed to understand the thermal stress relaxation by the compositional graded layer.

Micromechanics-based Analysis of Effect of Internal Structure on Creep Anisotropy of Asphalt Concrete

In order to investigate the effect of internal structure on creep anisotropy of asphalt concrete (AC), a three-dimensional (3D) micromechanical model was developed using discrete element method. The digital AC specimen composed of coarse aggregates, asphalt mastic and air voids was generated. The corresponding micromechanical models among the interactions of microscale components of digital AC specimen were assigned. The microscale viscoelastic parameters were obtained from laboratory dynamic shear test. Simulation of uniaxial creep tests were conducted on a number of cubic digital AC specimens with different aggregate orientations and sphericity. It was observed that the longer projected length of aggregates in loading direction, the smaller the creep strain is. The creep strain of AC was much smaller in the major axis direction of aggregate orientation as compared with the minor one. The creep anisotropy of AC became obvious with decreasing aggregate sphericity, especially when projected length of aggregates varied greatly in different directions.

Elastoplastic behavior of the metal matrix nanocomposites containing carbon nanotubes: A micromechanics-based analysis

The elastoplastic behavior of aluminum (Al) nanocomposites reinforced with aligned carbon nanotubes (CNTs) is characterized using a unit cell micromechanical model. The interphase zone caused by the chemical reaction between CNT and Al matrix is included in the analysis. To attain the elastoplastic stress–strain curve of the nanocomposites, the successive approximation method together with the von Mises yield criterion is employed. The effects of several important factors including the volume fraction and diameter of CNT, material properties, and size of interphase on the elastoplastic stress–strain curve of the nanocomposites during uniaxial tension are studied. The results indicate that the interphase characteristics significantly affect the elastoplastic behavior of the CNT-reinforced Al nanocomposites. It is also found that the yield stress of the nanocomposites rises with increasing CNT volume fraction or decreasing CNT diameter. Besides, the elastoplastic stress–strain curve of the CNT-reinforced Al nanocomposites is presented for multiaxial tension. The initial yield envelopes of the nanocomposites under longitudinal–transverse biaxial tension are provided too. Comparison between the elastic results of the present model with those of other available micromechanical analyses shows a very good agreement.

Nonlinear finite element analysis of fibre-reinforced polymer/concrete joints

The objective of this research work is to simulate the interfacial shear response of fibre-reinforced polymer/concrete joints using a micromechanics-based concrete approach. The M4 version of the microplane concrete theory is coded in FORTRAN and implemented as a parallel user-defined subroutine into the commercial finite element software package ADINA. This article first focuses on three-dimensional nonlinear micromechanics-based finite element analyses. Then, validations are carried out using experimental results of 40 fibre-reinforced polymer/concrete joints. The objective is to assess the accuracy of the microplane approach to represent the interfacial shear behaviour of the fibre-reinforced polymer/concrete joints as an alternative to implementing interface elements. At the end of this article, numerical comparisons are presented between the predictions using a phenomenological concrete constitutive law adopted in the software package (with a smeared crack model) and the micromechanics-based analysis (microplane theory) to simulate the concrete behaviour.

Micromechanics-Based Analysis of the Effect of Aggregate Homogeneity on the Uniaxial Penetration Test of Asphalt Mixtures

AbstractBased on the microstructure-based discrete-element method (DEM), this study aims to investigate the effect of vertical aggregate homogeneity, i.e., aggregate homogeneity in vertical cross sections, on the uniaxial penetration test of asphalt mixtures. An aggregate homogeneity index, which can be used to evaluate aggregate homogeneity in a two-dimensional (2D) cross section, was briefly introduced. The vertical aggregate distribution was evaluated by the index. Microstructure-based discrete-element modeling of a uniaxial penetration test was accomplished by a discrete-element program called particle flow code in two dimensions. The effect of vertical aggregate homogeneity on penetration strengths regarding a uniaxial penetration test was simulated by the DEM. The obtained results were verified by uniaxial penetration testing. Results show that the effect of vertical aggregate homogeneity on penetration strengths can be numerically simulated by the microstructure-based DEM. The penetration strengths...

Nonlinear finite element analysis of ultra-high-performance fiber-reinforced concrete beams

A nonlinear finite element analysis was performed to simulate the flexural behaviors of ultra-high-performance fiber-reinforced concrete beams. For this, two different tension-softening curves obtained from micromechanics-based analysis and inverse analysis were incorporated. For micromechanics-based analysis, two-dimensional and three-dimensional random fiber orientations were assumed to obtain the fiber-bridging curve, and a softening curve of matrix in ultra-high-performance fiber-reinforced concrete was used. The use of tension-softening curves obtained from inverse analysis and micromechanics-based analysis using two-dimensional random fiber orientation exhibited fairly good agreement with the experimental results, whereas the use of tension-softening curve from micromechanics-based analysis using three-dimensional random fiber orientation underestimated the experimental results.

Combining material and model pedigree is foundational to making ICME a reality

AbstractWith the increased emphasis on reducing the cost and time to market of new materials, the need for analytical tools that enable the virtual design and optimization of materials throughout their processing-internal structure-property-performance envelope, along with the capturing and storing of the associated material and model information across its life cycle, has become critical. This need is also fueled by the demands for higher efficiency in material testing; consistency, quality, and traceability of data; product design; engineering analysis; as well as control of access to proprietary or sensitive information. Fortunately, materials information management systems and physics-based multiscale modeling methods have kept pace with the growing user demands. Herein, recent efforts to identify best practices associated with these user demands and key principles for the development of a robust materials information management system will be discussed. The goals are to enable the connections at various length scales to be made between experimental data and corresponding multiscale modeling toolsets and, ultimately, to enable ICME to become a reality. In particular, the NASA Glenn Research Center efforts towards establishing such a database (for combining material and model pedigree) associated with both monolithic and composite materials as well as a multiscale, micromechanics-based analysis toolset for such materials will be discussed.

Shear stiffness of granular material at small strains: does it depend on grain size?

The shear stiffness of granular material at small strain levels is a subject of both theoretical and practical interest. This paper poses two fundamental questions that appear to be interrelated: (a) whether this stiffness property is dependent on particle size; and (b) whether the effect of testing method exists in terms of laboratory measurements using resonant column (RC) and bender element (BE) tests. For three uniformly graded types of glass beads of different mean sizes (0·195 mm, 0·920 mm and 1·750 mm), laboratory tests were conducted at a range of confining stresses and void ratios, using an apparatus that incorporates both RC and BE functions and thus allows reliable and insightful comparisons. It is shown that the small-strain stiffness, determined by either the RC or BE tests, does not vary appreciably with particle size, and it may be practically assumed to be size independent. The laboratory experiments also indicate that the BE measurements of small-strain stiffness are comparable to the corresponding RC measurements, with differences of less than 10%. Furthermore, the BE measurements for fine glass beads are found to be consistently higher than the RC measurements, especially at large stress levels, whereas this feature becomes less evident for medium-coarse glass beads, and eventually diminishes for coarse glass beads. The study indicates that the characteristics of output signals in BE tests can be largely affected by the frequency of the input signal, the mean particle size of the material and the confining stress level, and that these factors are interrelated. Improper interpretation of wave signals may lead to shear stiffness measurements that are unreasonably low, either showing a substantial increase with particle size or showing the opposite. A micromechanics-based analysis assuming the Hertz–Mindlin contact law is presented to offer an understanding of the size effect from the grain scale.

A micromechanics-based analysis of effects of square and hexagonal fiber arrays in fibrous composites using DQEM

Abstract A micromechanics-based model is presented to predict stress and strain fields and overall elastic properties of a unidirectional (UD) fiber reinforced composite. The differential quadrature element method (DQEM) is formulated for the generalized plane strain assumption and used to obtain solution of the governing partial differential equations of the problem. The cubic serendipity shape functions are used to convert the solution domain to a proper rectangular domain and the new version of the governing equations and boundary conditions are also derived. Two types of representative volume elements (RVEs), e.g. square and hexagonal fiber array packing are considered to represent the real composite. Fully bonded fiber–matrix interface condition is considered and the displacement continuity and traction reciprocity are properly imposed to the interface. Application of the DQEM to the problem leads to an over-determined system of linear equations mainly due to the particular periodic boundary conditions of the RVEs. The Least-squares technique is then employed to obtain solutions for the resulted over-determined system of equations. Numerical results are in excellent agreement with the available analytical and finite element studies. However discrepancies are found between results of the two RVEs. The presented model can provide highly accurate results with very small number of elements and grid points within each element. In addition, the model shows advantages over conventional analytical models for less simplifying assumptions related to the geometry of the RVE.

A Closed-Form Solution for the Eshelby Tensor and the Elastic Field Outside an Elliptic Cylindrical Inclusion

From the analytical formulation developed by Ju and Sun [1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574], it is seen that the exterior point Eshelby tensor for an ellipsoid inclusion possesses a minor symmetry. The solution to an elliptic cylindrical inclusion may be obtained as a special case of Ju and Sun’s solution. It is noted that the closed-form expression for the exterior-point Eshelby tensor by Kim and Lee [2010, “Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion,” ASME Trans. J. Appl. Mech., 77, p. 024503] violates the minor symmetry. Due to the importance of the solution in micromechanics-based analysis and plane-elasticity-related problems, in this work, the explicit analytical solution is rederived. Furthermore, the exterior-point Eshelby tensor is used to derive the explicit closed-form solution for the elastic field outside the inclusion, as well as to quantify the elastic field discontinuity across the interface. A benchmark problem is used to demonstrate a valuable application of the present solution in implementing the equivalent inclusion method.

Micromechanics-based analysis for predicting asphalt concrete modulus

The elastic modulus of asphalt concrete (AC) is an important material parameter for pavement design. The prediction and determination of elastic modulus, however, largely depends on laboratory tests which cannot reflect explicitly the influence of the microstructure of AC. To this end, a micromechanical model based on stepping scheme is adopted. Consideration is given to the influence of interfacial debonding and interlocking effect between the aggregates and asphalt mastic using the concept of effective bonding. Tests on asphalt mixture with various microstructures are conducted to verify the proposed approach. It is shown that the prediction is generally in agreement with experimental results. Parameters affecting the elastic modulus of AC are also discussed in light of the proposed method.

Discrete element simulations of direct shear specimen scale effects

This paper presents a study of the micromechanics of granular materials as affected by the direct shear test scale using the discrete element method (DEM). Parametric studies were conducted to investigate the effects of specimen length and height scales (in relation to the particle size) on the bulk material shear strength and shear banding behaviour in the direct shear test. A mesh-free strain calculation method previously developed by the authors was used to capture and visualise the evolution of strain localisation inside the direct shear box. Simulation results show that the maximum shear strength measured at the model boundaries increases with decreasing specimen length scale and increasing specimen height scale. Micromechanics-based analysis indicates that the local and global aspects of fabric change and failure are the major mechanisms responsible for the specimen scale effect. Global failure along the primary shear band prevails when the specimen length scale and length to height aspect ratio are small, while progressive failure becomes more likely when the specimen length scale and aspect ratio become larger. Further quantifications of the specimen scale effects on the macroscopic behaviour of granular materials rely on the fundamental understanding of quantitative relationships between material fabric, anisotropy and bulk strength.

Closed Form Solution of the Exterior-Point Eshelby Tensor for an Elliptic Cylindrical Inclusion

With the help of the I-integrals expressed by Mura (1987, Micromechanics of Defects in Solids, 2nd ed., Martinus Nijhoff, Dordrecht) and the outward unit normal vector introduced by Ju and Sun (1999, “A Novel Formulation for the Exterior-Point Eshelby’s Tensor of an Ellipsoidal Inclusion,” ASME Trans. J. Appl. Mech., 66, pp. 570–574), the closed form solution of the exterior-point Eshelby tensor for an elliptic cylindrical inclusion is derived in this work. The proposed closed form of the Eshelby tensor for an elliptic cylindrical inclusion is more explicit than that given by Mura, which is rough and unfinished. The Eshelby tensor for an elliptic cylindrical inclusion can be reduced to the Eshelby tensor for a circular cylindrical inclusion by letting the aspect ratio of the inclusion α=1. The closed form Eshelby tensor presented in this study can contribute to micromechanics-based analysis of composites with elliptic cylindrical inclusions.

Towards a non-linear micromechanics-based analysis for particulate composites

A non-classical multiscale modelling for viscoelastic particulate composites has been proposed by Nadot-Martin et al. [Nadot-Martin C, Trumel H, Dragon A. Morphology-based homogenization for viscoelastic particulate composites: Part I: Viscoelasticity sole. Eur. J. Mech. A/Solids 2003;22:89–106]. It is based on the geometrical and kinematical framework advanced first by Christoffersen [Christoffersen J. Bonded granulates. J. Mech. Phys. Solids 1983;31:55–83] in the context of linear elastic constituents and presents an interesting alternative with respect to more widely employed self-consistent like methods. Its specific feature consists in accounting for a specific multiple-grains-and-matrix-layers related microstructural morphology characterizing highly filled composites. Salient textural features of the aggregate can be preserved via homogenization put forward. The viscoelastic homogenization, performed in [Nadot-Martin C, Trumel H, Dragon A. Morphology-based homogenization for viscoelastic particulate composites: Part I: Viscoelasticity sole. Eur. J. Mech. A/Solids 2003;22:89–106], was realized in the small strain context. The present study aims at extending the methodology into the finite deformation range thus making it applicable for a class of assemblies containing highly deformable elastomeric matrix. As the first stage of geometrically non-linear scale transition, the non-hereditary, hyperelastic behaviour of constituents is considered. After specific formal developments, numerical solutions for particular (regular) microstructure and loading paths show the feasibility of the procedure and its advantages, notably accessibility of estimated local fields.

Micromechanics-Based Analysis of Stiffness Anisotropy in Asphalt Mixtures

The mechanical behavior of many bound granular materials, such as asphalt mixtures, is anisotropic in nature. However, the majority of the current mechanical tests and analytical models for asphalt mixtures are based on the assumption of isotropic material properties. This study investigates the stiffness anisotropy of asphalt mixtures using micromechanics-based models. The models’ parameters are obtained by quantifying the internal structure anisotropy in terms of the preferred orientation of longest axes and contact normals of aggregates. Image analysis techniques are used to conduct the internal structure measurements. The orientations of the longest axes are found to be easier to measure, and better descriptors of anisotropy, than the contact normals. Finite-element analyses of the internal structure are also used to provide insight into the mixture stiffness anisotropy. The mixture properties are selected to represent a wide range of temperatures. The stiffness in the horizontal direction is shown to be as high as 30% more than the stiffness in the vertical direction. The stiffness anisotropy decreases with a decrease in the mixture temperature. The finite-element results are shown to have very good correlation with the results of the micromechanics model derived based on the orientation of the longest axes of aggregates.

Micromechanics-Based Predictive Model for Compressively Loaded Angle-Ply Composite Laminates

A micromechanics-based analysis to predict damage initiation in compressively loaded symmetric angle-ply laminates is described. The e nite element method in conjunction with the commercial code Abaqus is used to solve the governing system of equations. The results obtained for the predictions are compared against a set of experimental results previously made available for AS4/3502 symmetric angle-ply laminates. A unie ed model that captures damage initiation and that describes failure mode transition as a function of ply angle is reported. The prediction of the model is found to compare favorably against the experimental data.

A micromechanics-based analysis for tailoring glass-fiber-reinforced thermoplastic laminates with near-zero coefficients of thermal expansion

This paper presents an attempt at tailoring fiber composite laminates with near-zero coefficients of thermal expansion (CTEs) in one particular in-plane direction by using conventional low-cost glass fibers. Specifically, laminates of symmetric and balanced ± θ angle-ply lay-ups in a glass/polypropylene system have been examined. An absolute strain-measurement technique utilizing a scanning laser extensometer has been applied to experimental determination of the ply-angle dependence of the laminate in-plane thermal expansion behavior in the range from room temperature to 120°C at a heating/cooling rate of 0.5°C/min. A preliminary analysis based on the classical thin-laminate theory predicts near-zero CTE values at θ of around 30° but experimentally, a laminate with θ≈30° shows an average CTE value of about −8×10 −6/K. To evaluate this discrepancy in a quantitative manner, a refined analysis based on a well-accepted ‘mean-field’ micromechanics formulation has been developed, taking into account a possible inelastic effect caused by creep of the matrix material. A set of closed-form expressions for the laminate effective in-plane CTEs is obtained, and experimental data are thereby reasonably assessed.