Effective Moduli of Solids With Cavities of Various Shapes

Effective elastic properties of solids with cavities of various shapes are derived in two approximations: the approximation of non-interacting cavities and the approximation of the average stress field (Mori-Tanaka’s scheme); the latter appears to be appropriate when mutual positions of defects are random. We construct the elastic potential of a solid with cavities. Such an approach covers, in a unified way, cavities of various shapes and any mixture of them. No degeneracies (or a need in a special limiting procedure) arise when cavities shrink to cracks. It also provides a unified description of both isotropic and anisotropic effective properties and recovers results available in the literature for special cases. Elastic potentials dictate the choice of proper parameters of cavity density. These parameters depend on defect shapes. Even in the case of random orientations, the isotropic overall properties cannot be characterized in terms of porosity alone; for elliptical holes, for example, a second parameter - “eccentricity” - is needed.

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Determination of effective properties of granite rock: A numerical investigation

MRS Advances ◽

10.1557/adv.2018.498 ◽

2018 ◽

Vol 3 (37) ◽

pp. 2159-2168

Author(s):

Rehema Ndeda ◽

S. E. M Sebusang ◽

R. Marumo ◽

Erich O. Ogur

Keyword(s):

Elastic Properties ◽

Close Agreement ◽

Effective Properties ◽

Volume Element ◽

The Finite Element Method ◽

Effective Elastic Properties ◽

Spherical Inclusions ◽

Periodic Microstructures ◽

Crack Profile

ABSTRACTMacroscopic strength of the rock depends on the behavior of the micro constituents, that is, the minerals, pores and crack profile. It is important to determine the effect of these constituents on the overall behavior of the rock. This study seeks to estimate the effective elastic properties of granite using the finite element method. A representative volume element (RVE) of suitable size with spherical inclusions of different distribution is subjected to loading and the effective elastic properties determined. The results are compared to those obtained from analytical methods. The elastic properties are obtained in both the axial and transverse direction to account for anisotropy. It is observed that there is congruence in the results obtained both analytically and numerically. The method of periodic microstructures exhibits close agreement with the numerical results.

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Probability of Debonding and Effective Elastic Properties of Particle-Reinforced Composites

Journal of Mechanics ◽

10.1017/jmech.2017.4 ◽

2017 ◽

Vol 33 (6) ◽

pp. 789-796 ◽

Cited By ~ 4

Author(s):

L. C. Bian ◽

W. Liu ◽

J. Pan

Keyword(s):

Elastic Properties ◽

Effective Properties ◽

Effective Elastic Modulus ◽

Reinforced Composites ◽

Effective Elastic Properties ◽

Linear Elastic ◽

Mechanics Model ◽

Equivalent Inclusion ◽

Particle Reinforced Composites ◽

Good Agreement

AbstractIn this paper, the effective properties of particle-reinforced composites with a weakened interphase are investigated. The particle and interphase are regarded as an equivalent-inclusion, and the interphase zone around the particle is modeled as a linear elastic spring layer. A modified micro-mechanics model is proposed to obtain the effective elastic modulus. Moreover, a statistical debonding criterion is proposed to characterize the varying probability of the evolution of interphase debonding. Numerical examples are considered to illustrate the effect of imperfect interphases on the effective properties of particle-reinforced composites. It is found that the effective elastic properties obtained in the present work are in a good agreement with the existing data from the literatures.

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Digital rock physics and laboratory considerations on a high-porosity volcanic rock

10.5194/egusphere-egu2020-6706 ◽

2020 ◽

Author(s):

Laura L. Schepp ◽

Benedikt Ahrens ◽

Martin Balcewicz ◽

Mandy Duda ◽

Mathias Nehler ◽

...

Keyword(s):

Thermal Conductivity ◽

Elastic Properties ◽

Effective Properties ◽

Rock Physics ◽

Numerical Results ◽

High Porosity ◽

Effective Elastic Properties ◽

Digital Rock Physics ◽

Digital Rock ◽

Laboratory Investigations

Microtomographic imaging techniques and advanced numerical simulations are combined by digital rock physics (DRP) to obtain effective physical material properties. The numerical results are typically used to complement laboratory investigations with the aim to gain a deeper understanding of physical processes related to transport (e.g. permeability and thermal conductivity) and effective elastic properties (e.g. bulk and shear modulus). The present study focuses on DRP and laboratory techniques applied to a rock called reticulite, which is considered as an end-member material with respect to porosity, stiffness and brittleness of the skeleton. Classical laboratory investigations on effective properties, such as ultrasonic transmission measurements and uniaxial deformation experiments, are very difficult to perform on this class of high-porosity and brittle materials.Reticulite is a pyroclastic rock formed during intense Hawaiian fountaining events. The open honeycombed network has a porosity of more than 80 % and consists of bubbles that are supported by glassy threads. The natural mineral has a strong analogy to fabricated open-cell foams. By comparing experimental with numerical results and theoretical estimates we demonstrate the potential of digital material methodology with respect to the investigation of porosity, effective elastic properties, thermal conductivity and permeabilityWe show that the digital rock physics workflow, previously applied to conventional rock types, yields reasonable results for a high-porosity rock and can be adopted for fabricated foam-like materials. Numerically determined effective properties of reticulite are in good agreement with the experimentally determined results. Depending on the fields of application, numerical methods as well as theoretical estimates can become reasonable alternatives to laboratory methods for high porous foam-like materials.

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Micromechanical modeling of 3D printable interpenetrating phase composites with tailorable effective elastic properties including negative Poisson's ratio

Journal of Micromechanics and Molecular Physics ◽

10.1142/s2424913017500151 ◽

2017 ◽

Vol 02 (04) ◽

pp. 1750015 ◽

Cited By ~ 6

Author(s):

L. Ai ◽

X.-L. Gao

Keyword(s):

Elastic Properties ◽

Effective Properties ◽

Matrix Material ◽

Micromechanical Model ◽

Micromechanical Modeling ◽

Tetragonal Symmetry ◽

Geometrical Parameters ◽

Fe Model ◽

Effective Elastic Properties ◽

Interpenetrating Phase Composites

3D printable two-phase interpenetrating phase composites (IPCs) are designed by embedding a 3D periodic re-entrant lattice structure (as the reinforcing phase) in a matrix phase. These IPCs display the cubic or tetragonal symmetry. A micromechanical model is developed to evaluate effective elastic properties of the IPCs. Effective Young's moduli, shear moduli and Poisson's ratios (PRs) of each IPC are determined from the effective stiffness and compliance matrices of the composite, which are obtained through a homogenization analysis using a unit cell-based finite element (FE) model incorporating periodic boundary conditions. The FE simulation results are also compared with those based on various analytical bounding techniques in micromechanics, including the Voigt–Reuss, Hashin–Shtrikman, and Tuchinskii bounds. The effective properties of the IPC can be tailored by adjusting five geometrical parameters, including two strut lengths, two re-entrant angles and one strut diameter, and elastic properties of the two constituent materials. The numerical results reveal that IPCs with a negative PR can be generated by using a compliant matrix material and large re-entrant angles. In addition, it is found that the two re-entrant angles can greatly affect other effective elastic properties of the IPC: the effective shear modulus can be enhanced, while the effective Young's modulus can be enhanced or compromised with the increase of the re-entrant angles. Furthermore, it is seen that by adjusting one of the two re-entrant angles or one of the two strut lengths, the material symmetry exhibited by the IPC can be changed from cubic to tetragonal.

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Aluminum Matrix Composites with Weak Particle Matrix Interfaces: Effective Elastic Properties Investigated Using Micromechanical Modeling

Materials ◽

10.3390/ma14206083 ◽

2021 ◽

Vol 14 (20) ◽

pp. 6083

Author(s):

Aharon Farkash ◽

Brigit Mittelman ◽

Shmuel Hayun ◽

Elad Priel

Keyword(s):

Elastic Properties ◽

Effective Properties ◽

Aluminum Matrix ◽

Unit Cell ◽

Micromechanical Modeling ◽

Aluminum Matrix Composites ◽

Matrix Composites ◽

Element Analysis ◽

Effective Elastic Properties ◽

The Impact

The impact of weak particle-matrix interfaces in aluminum matrix composites (AMCs) on effective elastic properties was studied using micromechanical finite-element analysis. Both simplified unit cell representations (i.e., representative area or volume elements) and “real” microstructure-based unit cells were considered. It is demonstrated that a 2D unit cell representation provides accurate effective properties only for strong particle-matrix bond conditions, and underpredicts the effective properties (compared to 3D unit cell computations) for weak interfaces. The computations based on real microstructure of an Al–TiB2 composite fabricated using spark plasma sintering (SPS) show that, for weak interfaces, the effective elastic properties under tension are different from those obtained under compression. Computations show that differences are the result of the local stress and strain fields, and contact mechanics between particles and the matrix. Preliminary measurements of the effective elastic properties using the ultrasonic pulse-echo technique and compression experiments support the trends observed in computational analysis.

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Modeling of the Effective Elastic Properties of Multifunctional Carbon Nanocomposites Due to Agglomeration of Straight Circular Carbon Nanotubes in a Polymer Matrix

Journal of Applied Mechanics ◽

10.1115/1.4024414 ◽

2013 ◽

Vol 81 (2) ◽

Cited By ~ 8

Author(s):

Chetan Shivaputra Jarali ◽

Somaraddi R. Basavaraddi ◽

Björn Kiefer ◽

Sharanabasava C. Pilli ◽

Y. Charles Lu

Keyword(s):

Carbon Nanotubes ◽

Elastic Properties ◽

Elastic Moduli ◽

Volume Fraction ◽

Effective Properties ◽

Transverse Isotropy ◽

Effective Elastic Moduli ◽

Effective Elastic Properties ◽

The Matrix ◽

Nanotube Composites

In the present study, the effective elastic properties of multifunctional carbon nanotube composites are derived due to the agglomeration of straight circular carbon nanotubes dispersed in soft polymer matrices. The agglomeration of CNTs is common due to the size of nanotubes, which is at nanoscales. Furthermore, it has been proved that straight circular CNTs provide higher stiffness and elastic properties than any other shape of the nanofibers. Therefore, in the present study, the agglomeration effect on the effective elastic moduli of the CNT polymer nanocomposites is investigated when circular CNTs are aligned straight as well as distributed randomly in the matrix. The Mori–Tanaka micromechanics theory is adopted to newly derive the expressions for the effective elastic moduli of the CNT composites including the effect of agglomeration. In this direction, analytical expressions are developed to establish the volume fraction relationships for the agglomeration regions with high, and dilute CNT concentrations. The volume of the matrix in which there may not be any CNTs due to agglomeration is also included in the present formulation. The agglomeration volume fractions are subsequently adopted to develop the effective relations of the composites for transverse isotropy and isotropic straight CNTs. The validation of the modeling technique is assessed with results reported, and the variations in the effective properties for high and dilute agglomeration concentrations are investigated.

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Global Sensitivity Analysis for the Polymeric Microcapsules in Self-Healing Cementitious Composites

Polymers ◽

10.3390/polym12122990 ◽

2020 ◽

Vol 12 (12) ◽

pp. 2990 ◽

Cited By ~ 1

Author(s):

Shuai Zhou ◽

Yue Jia ◽

Chong Wang

Keyword(s):

Sensitivity Analysis ◽

Elastic Properties ◽

Global Sensitivity Analysis ◽

Volume Fraction ◽

Effective Properties ◽

Micromechanical Model ◽

Cementitious Composites ◽

Self Healing ◽

Effective Elastic Properties ◽

Global Sensitivity

Cementitious composites with microencapsulated healing agents are appealing due to the advantages of self-healing. The polymeric shell and polymeric healing agents in microcapsules have been proven effective in self-healing, while these microcapsules decrease the effective elastic properties of cementitious composites before self-healing happens. The reduction of effective elastic properties can be evaluated by micromechanics. The substantial complicacy included in micromechanical models leads to the need of specifying a large number of parameters and inputs. Meanwhile, there are nonlinearities in input–output relationships. Hence, it is a prerequisite to know the sensitivity of the models. A micromechanical model which can evaluate the effective properties of the microcapsule-contained cementitious material is proposed. Subsequently, a quantitative global sensitivity analysis technique, the Extended Fourier Amplitude Sensitivity Test (EFAST), is applied to identify which parameters are required for knowledge improvement to achieve the desired level of confidence in the results. Sensitivity indices for first-order effects are computed. Results show the volume fraction of microcapsules is the most important factor which influences the effective properties of self-healing cementitious composites before self-healing. The influence of interfacial properties cannot be neglected. The research sheds new light on the influence of parameters on microcapsule-contained self-healing composites.

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Effect of Carbon Nanotube Waviness on the Elastic Properties of the Fuzzy Fiber Reinforced Composites

Journal of Applied Mechanics ◽

10.1115/1.4007722 ◽

2013 ◽

Vol 80 (2) ◽

Cited By ~ 32

Author(s):

S. I. Kundalwal ◽

M. C. Ray

Keyword(s):

Elastic Properties ◽

Carbon Fibers ◽

Polymer Matrix ◽

Effective Properties ◽

Analytical Models ◽

Fiber Reinforced ◽

Effective Elastic Properties ◽

Mechanics Of Materials ◽

Reinforced Composite ◽

Walled Carbon Nanotubes

A fuzzy fiber reinforced composite (FFRC) reinforced with wavy zig-zag single-walled carbon nanotubes (CNTs) and carbon fibers is analyzed in this study. The distinct constructional feature of this composite is that the wavy CNTs are radially grown on the surface of carbon fibers. To study the effect of the waviness of CNTs on the elastic properties of the FFRC, analytical models based on the mechanics of materials (MOM) approach is derived. Effective elastic properties of the FFRC incorporating the wavy CNTs estimated by the MOM approach have been compared with those predicted by the Mori–Tanaka (MT) method. The values of the effective elastic properties of this composite are estimated in the presence of an interphase between the CNT and the polymer matrix which models the nonbonded van dar Waals interaction between the CNT and the polymer matrix. The effect of waviness of CNTs on the effective properties of the FFRC is investigated when the wavy CNTs are coplanar with two mutually orthogonal planes. The results demonstrate that the axial effective elastic properties of the FFRC containing wavy CNTs can be improved over those of the FFRC with straight CNTs.

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Effective elastic properties of one-dimensional hexagonal quasicrystal composites

Applied Mathematics and Mechanics ◽

10.1007/s10483-021-2778-8 ◽

2021 ◽

Vol 42 (10) ◽

pp. 1439-1448

Author(s):

Shuang Li ◽

Lianhe Li

Keyword(s):

Composite Materials ◽

Explicit Expression ◽

Elastic Properties ◽

Function Method ◽

Volume Fraction ◽

Effective Properties ◽

Elliptic Cylinder ◽

One Dimensional ◽

Special Cases ◽

Analytical Expressions

AbstractThe explicit expression of Eshelby tensors for one-dimensional (1D) hexagonal quasicrystal composites is presented by using Green’s function method. The closed forms of Eshelby tensors in the special cases of spheroid, elliptic cylinder, ribbon-like, penny-shaped, and rod-shaped inclusions embedded in 1D hexagonal quasicrystal matrices are given. As an application of Eshelby tensors, the analytical expressions for the effective properties of the 1D hexagonal quasicrystal composites are derived based on the Mori-Tanaka method. The effects of the volume fraction of the inclusion on the elastic properties of the composite materials are discussed.

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On the Mechanical Behavior of the Orthotropic Cord-Rubber Composite

Tire Science and Technology ◽

10.2346/1.2167223 ◽

1976 ◽

Vol 4 (4) ◽

pp. 219-232 ◽

Cited By ~ 2

Author(s):

Ö. Pósfalvi

Keyword(s):

Mechanical Behavior ◽

Uniaxial Tension ◽

Elastic Properties ◽

Large Deformations ◽

Virtual Work ◽

Poisson's Ratio ◽

Principle Of Virtual Work ◽

Effective Elastic Properties ◽

Rubber Composite ◽

Mooney Equation

Abstract The effective elastic properties of the cord-rubber composite are deduced from the principle of virtual work. Such a composite must be compliant in the noncord directions and therefore undergo large deformations. The Rivlin-Mooney equation is used to derive the effective Poisson's ratio and Young's modulus of the composite and as a basis for their measurement in uniaxial tension.

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