Engineering › Mechanics of Materials

Composite Material Mechanics

Works Count: 28682

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Description

This cluster of papers focuses on the multi-scale modeling and computational homogenization of heterogeneous materials, particularly emphasizing the size-dependent behavior and elastic properties of nanostructures and composite materials. The research covers topics such as micromechanics, effective properties, and the influence of surface/interface energies on material behavior.

Keywords

Multi-Scale; Heterogeneous Materials; Computational Homogenization; Elastic Properties; Nanostructures; Composite Materials; Size-Dependent Behavior; Micromechanics; Effective Properties; Material Modeling

The Halpin‐Tsai equations: A review

1976-05-01

J. C. Halpin Affdl , J. L. Kardos

Abstract The Halpin‐Tsai equations are based upon the “self‐consistent micromechanics method” developed by Hill. Hermans employed this model to obtain a solution in terms of Hill's “reduced moduli”. Halpin and … Abstract The Halpin‐Tsai equations are based upon the “self‐consistent micromechanics method” developed by Hill. Hermans employed this model to obtain a solution in terms of Hill's “reduced moduli”. Halpin and Tsai have reduced Hermans' solution to a simpler analytical form and extended its use for a variety of filament geometries. The development of these micromechanic's relationships, which form the operational bases for the coniposite analogy of Halpin and Kardos for semi‐crystalline polymers, are reviewed herein.

The elastic field outside an ellipsoidal inclusion

1959-10-27

J. D. Eshelby

The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a … The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a certain surface distribution may be used in place of the biharmonic potential used previously. The elastic field outside an ellipsoidal inclusion or inhomogeneity may be expressed entirely in terms of the harmonic potential of a solid ellipsoid. The solution gives incidentally the velocity field about an ellipsoid which is deforming homogeneously in a viscous fluid. An expression given previously for the strain energy of an ellipsoidal region which has undergone a shear transformation is generalized to the case where the region has elastic constants different from those of its surroundings. The Appendix outlines a general method of calculating biharmonic potentials.

Effective Thermal Conductivity of Composites with Interfacial Thermal Barrier Resistance

1987-06-01

D. P. H. Hasselman , L. F. Johnson

A modification of the original theories of Rayleigh and Maxwell permitted the deriva tion of expressions for the effective thermal conductivity of composites consisting of a continuous matrix phase with … A modification of the original theories of Rayleigh and Maxwell permitted the deriva tion of expressions for the effective thermal conductivity of composites consisting of a continuous matrix phase with dilute concentrations of dispersions with spherical, cylin drical and flat plate geometry with a thermal barrier resistance at the interface between the components.

Theory of mechanical properties of fibre-strengthened materials: I. Elastic behaviour

1964-09-01

R. Hill

Universal Elastic Anisotropy Index

2008-08-01

Shivakumar I. Ranganathan , Martin Ostoja‐Starzewski

Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature … Practically all elastic single crystals are anisotropic, which calls for an appropriate universal measure to quantify the extent of anisotropy. A review of the existing anisotropy measures in the literature leads to a conclusion that they lack universality in the sense that they are non-unique and ignore contributions from the bulk part of the elastic stiffness (or compliance) tensor. Proceeding from extremal principles of elasticity, we introduce a new universal anisotropy index that overcomes the above limitations. Furthermore, we establish special relationships between the proposed anisotropy index and the existing anisotropy measures for special cases. A new elastic anisotropy diagram is constructed for over 100 different crystals (from cubic through triclinic), demonstrating that the proposed anisotropy measure is applicable to all types of elastic single crystals, and thus fills an important void in the existing literature.

Preprocessing and postprocessing for materials based on the homogenization method with adaptive finite element methods

1990-10-01

J. M. Guedes , Noboru Kikuchi

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Elastic properties of reinforced solids: Some theoretical principles

1963-09-01

R. Hill

Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases

1994-09-01

Ce‐Wen Nan

The magnetoelectric effect in composites of piezoelectric and piezomagnetic phases is investigated theoretically. The magnetoelectric effect is totally absent in these two constituent phases, and so it is a new … The magnetoelectric effect in composites of piezoelectric and piezomagnetic phases is investigated theoretically. The magnetoelectric effect is totally absent in these two constituent phases, and so it is a new property of the composites. A generalized theoretical framework based on a Green's function method and perturbation theory is proposed to treat the coupled magnetoelectric behavior in the composites. Explicit relations for determining the effective magnetoelectric effect in the composites are derived, and the different approximate expressions for the magnetoelectric coefficient of the fibrous composites with 1-3 or 3-1 connectivity of phases are given. To illustrate the technique, numerical calculations of the magnetoelectric coefficients of the ${\mathrm{BaTiO}}_{3}$-${\mathrm{CoFe}}_{2}$${\mathrm{O}}_{4}$ composites for various phase compositions and particle shapes are performed. The theoretical estimates are shown to be in agreement with available experimental results, and also show the interesting magnetoelectric behavior of the composites.

Continuum micro-mechanics of elastoplastic polycrystals

1965-04-01

R. Hill

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Solutions for effective shear properties in three phase sphere and cylinder models

1979-08-01

Richard M. Christensen , King Him Lo

Materials with prescribed constitutive parameters: An inverse homogenization problem

1994-09-01

Ole Sigmund

FE2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre SiC/Ti composite materials

2000-03-01

Frédéric Feyel , Jean‐Louis Chaboche

The viscosity of suspensions of rigid spheres

1952-08-01

R. Roscoe

An explanation is given of the dependence of the relative viscosity on the size distribution of the suspended spheres, an effect recently observed by Ward and Whitmore.(1) It is shown … An explanation is given of the dependence of the relative viscosity on the size distribution of the suspended spheres, an effect recently observed by Ward and Whitmore.(1) It is shown theoretically that if the spheres are of very diverse sizes, the relative viscosity is (1 - c)-2.5 for all values of the volume concentration c. For spheres of equal size, the validity of the Einstein expression for the relative viscosity (1 + 2.5c) is restricted to concentrations well below c = 0.05; while for medium and high concentrations the relative viscosity is given by the theoretical expression (1 - 1.35c)-2.5. The use of the latter formula in interpreting measurements on the viscosity of solutions is briefly indicated.

The Elastic Moduli of Fiber-Reinforced Materials

1964-06-01

Zvi Hashin , B. W. Rosen

Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal … Bounds and expressions for the effective elastic moduli of materials reinforced by parallel hollow circular fibers have been derived by a variational method. Exact results have been obtained for hexagonal arrays of identical fibers and approximate results for random array of fibers, which may have unequal cross sections. Typical numerical results have been obtained for technically important elastic moduli.

Materials with structural hierarchy

1993-02-01

Roderic S. Lakes

A Variational Approach to the Theory of the Effective Magnetic Permeability of Multiphase Materials

1962-10-01

Zvi Hashin , S. Shtrikman

Variational theorems are established and applied to the derivation of bounds for the effective magnetic permeability of macroscopically homogeneous and isotropic multiphase materials. For reasons of mathematical analogy the results … Variational theorems are established and applied to the derivation of bounds for the effective magnetic permeability of macroscopically homogeneous and isotropic multiphase materials. For reasons of mathematical analogy the results are also valid for the dielectric constant, electric conductivity, heat conductivity, and diffusivity of such materials. For the case of two-phase materials, the bounds derived are the most restrictive ones that can be given in terms of the phase permeabilities and volume fractions. Comparison of present theoretical results with existing experimental data shows good agreement.

Bounds and self-consistent estimates for the overall properties of anisotropic composites

1977-06-01

J.R. Willis

VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS

1974-10-01

Guy T. Kuster , M. Nafi Toksöz

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and … The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. It is found that the concentration, shapes, and properties of the inclusions are important parameters. A concentration of a fraction of one percent of thin (small aspect ratio) inclusions could affect the compressional and shear velocities by more than ten percent. For both sedimentary and igneous rock models, the calculations for “dry” (i.e.,air‐saturated) and water‐saturated states indicate that the compressional velocities change significantly while the shear velocities change much less upon saturation with water.

Fine phase mixtures as minimizers of energy

1987-01-01

J. M. Ball , Richard D. James

Effective properties of composite materials with periodic microstructure: a computational approach

1999-04-01

Jean‐Claude Michel , Hervé Moulinec , Pierre Suquet

Thermal Expansion Coefficients of Composite Materials Based on Energy Principles

1968-07-01

R. A. Schapery

Bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity. Inequalities between certain approximate and exact … Bounds on effective thermal expansion coefficients of isotropic and anisotropic composite materials consisting of isotropic phases are derived by employing extremum principles of thermoelasticity. Inequalities between certain approximate and exact forms of the potential and complementary energy functionals are first estab lished. These inequalities are then used in conjunction with a new method for minimizing the difference between upper and lower bounds in order to derive volumetric and linear thermal expansion coefficients. Application is made to two- and three-phase isotropic composites and a fiber-reinforced material. It is found for some important cases that the solutions are exact, and take a very simple form. We also show conditions under which the rule-of-mixtures and Turner's equation can be used for thermal expansion coeffi cients. Finally, simple methods for extending all results to viscoelastic composites are indicated.

Physics of inhomogeneous inorganic materials

1993-01-01

Ce‐Wen Nan

Surface stress in solids

1978-01-01

Morton E. Gurtin , A. Ian Murdoch

The Variational Approach to Fracture

2008-01-01

Blaise Bourdin , Gilles A. Francfort , Jean‐Jacques Marigo

The Occurrence of Singularities in the Elastic Frequency Distribution of a Crystal

1953-03-15

Léon Van Hove

It is shown that for a crystal, under the assumption of harmonicity for the interatomic forces and as a consequence of the periodic structure, the frequency distribution function of elastic … It is shown that for a crystal, under the assumption of harmonicity for the interatomic forces and as a consequence of the periodic structure, the frequency distribution function of elastic vibrations has analytic singularities. In the general case, the nature of the singularities depends only on the number of dimensions of the crystal. For a two-dimensional crystal, the distribution function has logarithmically infinite peaks. In the three-dimensional case, the distribution function itself is continuous whereas its first derivative exhibits infinite discontinuities. These results are elementary consequences of a theorem of Morse on the existence of saddle points for functions defined on a torus.

Steady‐State and Multiple Cracking of Short Random Fiber Composites

1992-11-01

Victor C. Li , Christopher K.Y. Leung

This paper analyzes the pseudostrain‐hardening phenomenon of brittle matrix composites reinforced with discontinuous flexible and randomly distributed fibers, based on a cohesive crack‐mechanics approach. The first crack strength and strain … This paper analyzes the pseudostrain‐hardening phenomenon of brittle matrix composites reinforced with discontinuous flexible and randomly distributed fibers, based on a cohesive crack‐mechanics approach. The first crack strength and strain are derived in terms of fiber, matrix, and interface micromechanical properties. Conditions for steady‐state cracking and multiple cracking are found to depend on two nondimensionalized parameters that embody all relevant material micromechanical parameters. The results are therefore quite general and applicable to a variety of composite‐material systems. Phrased in terms of a failure‐mechanism map, various uniaxial load‐deformation behaviors for discontinuous fiber composites can be predicted. The influence of a snubbing effect due to local fiber/matrix interaction for randomly oriented crack‐bridging fibers on the composite properties is also studied.

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Theory of Elasticity and Consolidation for a Porous Anisotropic Solid

1955-02-01

M. A. Biot

The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is … The author's previous theory of elasticity and consolidation for isotropic materials [J. Appl. Phys. 12, 155–164 (1941)] is extended to the general case of anisotropy. The method of derivation is also different and more direct. The particular cases of transverse isotropy and complete isotropy are discussed.

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Bounds and self-consistent estimates for creep of polycrystalline materials

1976-02-10

John W. Hutchinson

A study of steady creep of face centred cubic (f. c. c.) and ionic polycrystals as it relates to single crystal creep behaviour is made by using an upper bound … A study of steady creep of face centred cubic (f. c. c.) and ionic polycrystals as it relates to single crystal creep behaviour is made by using an upper bound technique and a self-consistent method. Creep on a crystallographic slip system is assumed to occur in proportion to the resolved shear stress to a power. For the identical systems of an f. c. c. crystal the slip-rate on any system is taken as γ = α (ז/ז 0 ) n where α is a reference strain-rate, ז is the resolved shear stress and ז 0 is the reference shear stress. The tensile behaviour of a polycrystal of randomly orientated single crystals can be expressed as ∊̄ = α (σ̄/σ̄ 0 ) n where ∊̄ are σ̄ the overall uniaxial strain-rate and stress and σ̄ 0 is the uniaxial reference stress. The central result for an f. c. c. polycrystal in tension can be expressed as σ̄ 0 = h ( n ) ז 0 . Calculated bounds to h ( n ) coincide at one extreme ( n = ∞) with the Taylor result for rigid/perfectly plastic behaviour and at the other ( n = 1) with the Voigt bound for linear viscoelastic behaviour. The self-consistent results, which are shown to be highly accurate for n = 1, agree closely with the upper bound for n ≽ 3. Two types of glide systems are considered for ionic crystals: A-systems, {110} <110>, with γ = α (ז/ז A ) n ; and B-systems, {100} <110>, with γ = α (ז/ז B ) n . The upper bound to the tensile reference stress σ̄ 0 is shown to have the simple form σ̄ 0 ≼ A ( n )ז A + B ( n )ז B ; A ( n ) and B ( n ) are computed for the entire range of n , including the limit n = ∞. Self-consistent predictions are again in good agreement with the bounds for high n . Upper bounds in pure shear are also calculated for both f. c. c. and ionic polycrystals. These results, together with those for tension, provide a basis for assessing the most commonly used stress creep potentials. The simplest potential based on the single effective stress invariant is found to give a reasonably accurate characterization of multiaxial stress dependence.

Elastic moduli of a cracked solid

1976-01-01

Bernard Budiansky , Richard J. O’Connell

A self-consistent mechanics of composite materials

1965-08-01

R. Hill

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Average stress in matrix and average elastic energy of materials with misfitting inclusions

1973-05-01

T. Mori , Kōichi Tanaka

A variational approach to the theory of the elastic behaviour of multiphase materials

1963-03-01

Zvi Hashin , S. Shtrikman

Elastic materials with couple-stresses

1962-01-01

R. A. Toupin

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Orientation Behavior of Fibers in Concentrated Suspensions

1984-04-01

Fransisco Folgar , Charles L. Tucker

A mathematical model is developed to predict the orientation distribution function of rigid fibers in concentrated suspensions. The model contains a phenomenological term to account for interactions between fibers. Predictions … A mathematical model is developed to predict the orientation distribution function of rigid fibers in concentrated suspensions. The model contains a phenomenological term to account for interactions between fibers. Predictions of the model are tested against experiments in simple shear flow, using suspensions of nylon monofilaments in silicone oil. The results compare favorably for steady-state distributions, though the theory predicts a more rapid approach to steady state than actually occurs. The model predicts, and experiments show, that fiber orientation is not reversible when the flow is reversed. The model is useful for predicting the effects of processing on fiber orienta tion in short fiber composites.

The stress system in a suspension of force-free particles

1970-04-29

G. K. Batchelor

The purpose of the paper is to consider in general terms the properties of the bulk stress in a suspension of non-spherical particles, on which a couple (but no force) … The purpose of the paper is to consider in general terms the properties of the bulk stress in a suspension of non-spherical particles, on which a couple (but no force) may be imposed by external means, immersed in a Newtonian fluid. The stress is sought in terms of the instantaneous particle orientations, and the problem of determining these orientations from the history of the motion is not considered. The bulk stress and bulk velocity gradient in the suspension are defined as averages over an ensemble of realizations, these averages being equal to integrals over a suitably chosen volume of ambient fluid and particles together when the suspension is statistically homogeneous. Without restriction on the type of particle or the concentration or the Reynolds number of the motion, the contribution to the bulk stress due to the presence of the particles is expressed in terms of integrals involving the stress and velocity over the surfaces of particles together with volume integrals not involving the stress. The antisymmetric part of this bulk stress is equal to half the total couple imposed on the particles per unit volume of the suspension. When the Reynolds number of the relative motion near one particle is small, a suspension of couple-free particles of constant shape is quasi-Newtonian; i.e. the dependence of the bulk stress on bulk velocity gradient is linear. Two significant features of a suspension of non-spherical particles are (1) that this linear relation is not of the Newtonian form and (2) that the effect of exerting a couple on the particles is not confined to the generation of an antisymmetrical part of the bulk stress tensor. The role of surface tension at the particle boundaries is described. In the case of a dilute suspension the contributions to the bulk stress from the various particles are independent, and the contributions arising from the bulk rate of strain and from the imposed couple are independent for each particle. Each particle acts effectively as a force doublet (i.e. equal and opposite adjoining ‘Stokeslets’) whose tensor strength determines the disturbance flow far from the particle and whose symmetrical and antisymmetrical parts are designated as a stresslet and a couplet. The couplet strength is determined wholly by the externally imposed couple on the particle; but the stresslet strength depends both on the bulk rate of strain and, for a non-spherical particle, on the rate of rotation of the particle relative to the fluid resulting from the imposed couple. The general properties of the stress system in a dilute suspension are illustrated by the specific and complete results which may be obtained for rigid ellipsoidal particles by use of the work by Jeffery (1922).

The Elastic Moduli of Heterogeneous Materials

1962-03-01

Zvi Hashin

Bounds and expressions for the elastic moduli of two or many phase nonhomogeneous materials are obtained by an approximate method based on the variational theorems of the theory of elasticity … Bounds and expressions for the elastic moduli of two or many phase nonhomogeneous materials are obtained by an approximate method based on the variational theorems of the theory of elasticity and on a concentric-spheres model. Theoretical results are in good agreement with experimental results for a two-phase alloy.

On the elastic moduli of some heterogeneous materials

1965-08-01

Bernard Budiansky

Force at a Point in the Interior of a Semi-Infinite Solid

1936-05-01

R. D. Mindlin

A solution of the three-dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi-infinite solid. This … A solution of the three-dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi-infinite solid. This represents the fundamental solution having a singular point in a solid bounded by a plane. From it may be derived, by a known method of synthesis, the solutions for the semi-infinite solid which correspond to the solutions known as nuclei of strain in the solid of indefinite extent.

Determination of the size of the representative volume element for random composites: statistical and numerical approach

2003-05-19

Toufik Kanit , Samuel Forest , Isabelle Galliet +2 more

Micromechanics: Overall Properties of Heterogeneous Materials

1996-06-01

Sia Nemat‐Nasser , M. Lori , S. K. Datta

Part 1 Overall properties of heterogeneous solids: aggregate properties and averaging methods aggregate properties, averaging methods elastic solids with microcavities and microcracks linearly elastic solids, elastic solids with traction-free defects, … Part 1 Overall properties of heterogeneous solids: aggregate properties and averaging methods aggregate properties, averaging methods elastic solids with microcavities and microcracks linearly elastic solids, elastic solids with traction-free defects, elastic solids with micrcavities, elastic solids with microcracks elastic solids with micro-inclusions overall elastic modulus and compliance tensors, examples o elastic solids with elastic micro-inclusions, upper and lower bounds for overall elastic moduli, self-consistent differential and related averaging methods, Eshelby's tensor and related topics solids with periodic microstructure general properties and field equations, overall properties of solids with periodic microstructure, mirror-image decomposition of periodic fields. Part 2 Introduction to basic elements of elasticity theory: foundations geometric foundations, kinematic foundations, dynamic foundations, constitutive relations elastostatic problems of linear elasticity boundary-value problems and extremum principles three-dimensional problems solution of singular problems. Appendix: references.

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Berechnung der Fließgrenze von Mischkristallen auf Grund der Plastizitätsbedingung für Einkristalle .

1929-01-01

A. Reuss

Design of materials with extreme thermal expansion using a three-phase topology optimization method

1997-06-01

Ole Sigmund , S. Torquato

Slender-body theory for particles of arbitrary cross-section in Stokes flow

1970-11-26

G. K. Batchelor

A rigid body whose length (2 l ) is large compared with its breadth (represented by R 0 ) is straight but is otherwise of arbitrary shape. It is immersed … A rigid body whose length (2 l ) is large compared with its breadth (represented by R 0 ) is straight but is otherwise of arbitrary shape. It is immersed in fluid whose undisturbed velocity, at the position of the body and relative to it, may be either uniform, corresponding to translational motion of the body, parallel or perpendicular to the body length, or a linear function of distance along the body length, corresponding to an ambient pure straining motion or to rotational motion of the body. Inertia forces are negligible. It is possible to represent the body approximately by a distribution of Stokeslets over a line enclosed by the body; and then the resultant force required to sustain translational motion, the net stresslet strength in a straining motion, and the resultant couple required to sustain rotational motion, can all be calculated. In the first approximation the Stokeslet strength density F ( x ) is independent of the body shape and is of order μ U ε, where U is a measure of the undisturbed velocity and ε = (log 2 l / R 0 ) −1 . In higher approximations, F ( x ) depends on both the body cross-section and the way in which it varies along the length. From an investigation of the ‘inner’ flow field near one section of the body, and the condition that it should join smoothly with the ‘outer’ flow which is determined by the body as a whole, it is found that a given shape and size of the local cross-section is equivalent, in all cases of longitudinal relative motion, to a circle of certain radius, and, in all cases of transverse relative motion, to an ellipse of certain dimensions and orientation. The equivalent circle and the equivalent ellipse may be found from certain boundary-value problems for the harmonic and biharmonic equations respectively. The perimeter usually provides a better measure of the magnitude of the effect of a non-circular shape of a cross-section than its area. Explicit expressions for the various integral force parameters correct to the order of ε 2 are presented, together with iterative relations which allow their determination to the order of any power of ε. For a body which is ‘longitudinally elliptic’ and has uniform cross-sectional shape, the force parameters are given explicitly to the order of any power of ε, and, for a cylindrical body, to the order of ε 3 .

A new approach to the application of Mori-Tanaka's theory in composite materials

1987-06-01

Y. Benveniste

The Elastic and Thermo-elastic Properties of Composite Media

1956-08-01

Edward H. Kerner

In a continuation of a previous paper, it is shown here how the gross bulk and shear moduli of a composite material consisting of a suspension of grains or a … In a continuation of a previous paper, it is shown here how the gross bulk and shear moduli of a composite material consisting of a suspension of grains or a compact of grains may be deduced. The grains are assumed to be perfectly bonded to the suspending medium or to each other, and are taken to be spheres in the mean. By using an averaging procedure due to Bruggeman, and analysing the effect of a uniform hydrostatic compression and of a uniform tension on an average grain, a pair of de-coupled equations for the gross moduli is found for suspensions. When the suspending medium vanishes and the grains are packed, these equations become coupled and there is exhibited a discontinuity in the gross moduli. The bulk coefficients of linear expansion of the two kinds of composites are found from an analysis of the dilatation and bulk stress for average spherical grains when the composite as a whole is subjected to some small temperature change. All results are free of any limitation on the number of components.

Micromechanics - Overall Properties of Heterogeneous Materials

1993-01-01

Theory of Mixtures

1976-01-01

Ray M. Bowen

A numerical method for computing the overall response of nonlinear composites with complex microstructure

1998-04-01

Hervé Moulinec , Pierre Suquet

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Conduction of Heat in Solids

2016-01-01

D. R. Poirier , G. H. Geiger

Periodic homogenization with finite element method coupling to reliability analysis of metal matrix composites

2025-06-25

Karim Benyahi , Youcef Bouafia , Mohand Said Kachi +1 more | Journal of Reinforced Plastics and Composites

This work concerns the micromechanical modeling of RVE as well as the evaluation of the reliability of MMC materials. We mainly seek to simulate the elastoplastic behavior of composites through … This work concerns the micromechanical modeling of RVE as well as the evaluation of the reliability of MMC materials. We mainly seek to simulate the elastoplastic behavior of composites through a periodic homogenization technique. The macroscopic response for the MMC with different mesh sizes, as well as the influence of the RVE microstructure size are studied under static loading. Based on the results of this study, the proposed approach is able to simulate well the behavior appearance and ductility plateau for percentages ranging from 10% to 30% spheroidal inclusion under static and cyclic loading. On the other hand, for ellipsoidal inclusions, a slight variation can be observed before rupture, which can be explained by the loss of rigidity due to delamination of the inclusions. And for a 5% inclusion percentage, our simulation seems to provide a better estimate of the composite’s behavior than other models proposed in the literature. Then, a reliability approach is coupled to the mechanical model (AL-SIC4.1 MMC) in order to estimate the reliability index. The results demonstrated that the choice of distribution laws of the simulated random variables is made for a significant probability density and by a density curve with more concentrated results.

An edge dislocation interacting with a compressible liquid inclusion of arbitrary shape

2025-06-22

Xu Wang , Peter Schiavone | Archive of Applied Mechanics

Quaternion-Based Dynamic Algorithm for Random Generation of Solid 4D Cylindrical Curves in RVE Modeling

2025-06-21

Sanusi Hamat , Mohamad Ridzwan Ishak , Piaras Kelly +5 more | Composites Communications

Homogenization in hyperelasticity using Empirically Corrected Cluster Cubature (E3C) hyper-reduction

2025-06-20

Stephan Wulfinghoff | Computer Methods in Applied Mechanics and Engineering

Stochastic modeling of mechanical behavior of materials with heterogeneous structure

2025-06-12

V. A. Zimina , I. Yu. Smolin | Russian Physics Journal

Scaling law for eﬀective conductivity of spherical-circular inclusion composites with imperfect interface

2025-06-12

Nguyễn Trung Kiên | Journal of Micromechanics and Microengineering

Abstract A general imperfect interface model for conductivity problem is presented. For this kind, both the local temperature and heat ﬂux are discontinuous at the interface. The present model includes … Abstract A general imperfect interface model for conductivity problem is presented. For this kind, both the local temperature and heat ﬂux are discontinuous at the interface. The present model includes the lowly and highly conducting ones as the particular cases. In contrast to the ideal interface, the eﬀective conductivity of composite containing imperfectly bonded inclusions depends on the size of the particles. This size dependence can be captured through some scaling laws. These ones help to check the suitability of data measurement or numerical calculation for eﬀective conductivity of composite materials having imperfect interface over a wide size range.&#xD;

Comprehensive Analysis of Elastic–Plastic Behavior in Hybrid Metal Matrix Composites with Varied Reinforcement Geometry

2025-06-12

Grzegorz Mieczkowski , Dariusz Szpica , Andrzej Borawski | Materials

This study presents a comprehensive analytical–numerical approach to determining the elastic–plastic properties of Hybrid Metal Matrix Composites (HMMCs), contrasting with prior research that primarily emphasizes elasticity. Using the finite element … This study presents a comprehensive analytical–numerical approach to determining the elastic–plastic properties of Hybrid Metal Matrix Composites (HMMCs), contrasting with prior research that primarily emphasizes elasticity. Using the finite element method (FEM) and elasticity and plasticity theory, we determined key parameters, including Young’s modulus, Poisson’s ratio, yield strength, and ultimate tensile strength. The method, which also accounts for strain-hardening behavior via the Hollomon model, enables precise simulation of HMMC with randomly distributed reinforcement particles of varying shapes and sizes, offering a realistic representation of the composite microstructure. Verification against the literature confirms the accuracy of the approach in reflecting both elastic and plastic behavior, providing essential insights into the material’s full mechanical response, particularly yield strength and strain-hardening properties, aspects rarely explored in depth in existing studies on HMMCs.

Solving the problems of the conductivity of heterogeneous media by the method of the discrete Radon transform

2025-06-11

Mustapha Boukour , Mohammed Rida Derraz , Anass El Mamouni +1 more | Mathematics and Mechanics of Solids

In the framework of periodic homogenization, the Fast Fourier Transform (FFT) homogenization method allows one to formulate the linear conduction problem as an integral equation whose solution can be represented … In the framework of periodic homogenization, the Fast Fourier Transform (FFT) homogenization method allows one to formulate the linear conduction problem as an integral equation whose solution can be represented in Fourier space. In this work, we demonstrate that this solution can also be expressed in real space, with a precise geometrical interpretation. Our homogenization method builds upon a combination of the Discrete Radon Transform proposed by Gelfand, Gindikin, and Graev and a plane and anti-plane vector decomposition in some specific directions. This new combination enables us to efficiently decompose a vector field into two orthogonal subspaces (curl and divergence-free components). Based on this proposed approach, the conduction problem is reduced to an integral equation, where the local fields and subsequently the macroscopic behaviors are expressed as a real series expansion. We introduce an iterative scheme utilizing the finite Radon transform to solve the residual integral equation. In comparison to the FFT-based scheme developed by Moulinec and Suquet, our numerical experiments demonstrate that for certain specific microstructures, our method yields accurate results at significantly lower computational cost.

Surface-driven computational homogenization method for metamaterial beams

2025-06-06

Shuo Li , L.N. Xiao , Yu Zhang +2 more | International Journal of Engineering Science

Deterministic and stochastic analysis of a three phase piezoelectric composite using the coupled PIM-VAM based homogenization framework

2025-06-06

Pandi Pitchai , P. J. Guruprasad | Composite Structures

Multiscale modeling of elasto-plastic behavior for short fiber composites considering interfaces

2025-06-03

Runtian Zhao , Haoyu Shi , Ting Wu +4 more | Composites Part A Applied Science and Manufacturing

Efficient RVE modeling for ellipsoidal particle- and short fiber-hybrid reinforced composites: Novel algorithms for overlap detection and geometric periodicity

2025-06-01

Xingwei Yan , Yang Hu , Yong Xie +1 more | Composite Structures

Experimental and numerical analysis of heat transfer in polymer composites with metallic inclusions using virtual element method

2025-06-01

Sina Tahouni , Mohammad Azhdari , Ghader Rezazadeh +4 more | Materials & Design

Anisotropic elastoplastic behavior and fracture prediction in graphene macro-film: Experiments and modeling

2025-06-01

Haoyu Zheng , Shilin Yan , Xiangyu Xie +4 more | Thin-Walled Structures

Optimal design of triply-periodic minimal surface implants for bone repair

2025-06-01

David Cohen , Julián A. Norato | Structural and Multidisciplinary Optimization

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Multiple scattering of elastic waves in polycrystals

2025-06-01

Anubhav Roy , Christopher M. Kube | Journal of the Mechanics and Physics of Solids

Anti-plane waves in a layered cylindrical piezo-composite structure considering interface model

2025-06-01

Xuan Wang , Feng Jin | Applied Mathematical Modelling

The Ultimate Flexural Strength of Fiber-Reinforced Ceramic Matrix Composite: A Multiscale Approach

2025-05-30

Jacques Lamon | Journal of Composites Science

This paper tackles the important issue of the flexural strength of continuous fiber-reinforced ceramic composite. Estimates of the flexural strength of 2D woven SiC/SiC composite are extracted from symmetric and … This paper tackles the important issue of the flexural strength of continuous fiber-reinforced ceramic composite. Estimates of the flexural strength of 2D woven SiC/SiC composite are extracted from symmetric and asymmetric 3-point bending test results using three independent approaches: (1) the equations of elastic beam theory for homogeneous solids, (2) finite element analysis of the stress state, (3) stress–strain relations in the tensile outer surface of specimens. Furthermore, the flexural strength is predicted from the ultimate tensile strength using a bundle failure model based on the fracture of the critical filament. It is shown that the equation of elastic beam theory significantly overestimates the flexural strength of the 2D SiC/SiC (620 MPa), while the alternate approaches and the predictions from the ultimate tensile strength converged to ≈340 MPa. The variability of strength data was approached using the construction of p-quantile diagrams that provide an unbiased assessment of the normal distribution function. Pertinent Weibull parameters are derived using the first moment equations. Important trends in the effects of the size, stress gradient, tension–flexure relations, strength of critical filament in a tow, and populations of critical flaws are established and discussed.

Three-dimensional Green’s functions for a transversely isotropic elastic bimaterial with viscous interface

2025-05-30

Xu Wang , Peter Schiavone | Acta Mechanica

Influence of the shape and location of orthotropic inclusion on the stress state of anisotropic body under longitudinal shear

2025-05-30

V. S. Kravets , М. P. Savruk , L. Yo. Onyshko +1 more | Materials Science

A Simulative Evaluation of Triply Periodic Minimal Surface Structures in the Context of Elastocaloric Applications

2025-05-29

Michael Fries , Paul Motzki , Dirk Bähre +1 more | Advanced Engineering Materials

Elastocaloric technology is currently the most promising alternative air conditioning technology, in terms of environmental friendliness and efficiency. To optimize an elastocaloric machine in its entity, it is essential to … Elastocaloric technology is currently the most promising alternative air conditioning technology, in terms of environmental friendliness and efficiency. To optimize an elastocaloric machine in its entity, it is essential to research and improve all components, from the material to efficient load concepts. This work is dedicated to the evaluation of triply periodic minimal surface (TPMS) structures for use as heating/cooling element within an elastocaloric machine. TPMS structures have promising properties such as a high surface/volume ratio, which offers great potential for the exchange of generated thermal energy with the environment. They consist of continuous curved surfaces without notches, which act as nucleation points for fatigue cracks under cyclic loading, commonly found in continuous operating cooling devices. The structures Gyroid, Diamond, Schwarz, and FischerKochS are compared by simulating compression tests. The elastocaloric efficiency, defined as the quotient of generated thermal energy and invested mechanical work and the heat exchange potential, are used as evaluation criteria. To illustrate the improvement that can be achieved by using TPMS structures instead of conventional geometries, a tube is used as a comparative geometry. The observed deformation mechanisms are correlated with the results of a geometric analysis to determine optimization strategies for the investigated structures.

Displacement potentials and stress functions: applications to three-dimensional problems

2025-05-23

Martin H. Sadd

Three-dimensional microscopic modeling and property prediction of composite ceramic materials

2025-05-21

Dong Wang , F. Shi , Bo Zhao +3 more

A viscoelastic micromechanical damage model for multiphase porous composites: Model development and application

2025-05-21

Rui Xie , Qing Liu , Mingzhu Qiu +4 more

Microstructure‐Based Numerical Modeling and Experimental Analysis of the Effect of Fiber‐Matrix Separation in Glass‐Reinforced Polyamide‐6 Forged Components

2025-05-20

U. Olaziregi , A. Esnaola , M. Baskaran +4 more

ABSTRACT This study investigates the structural behavior of a glass‐fibe reinforced polyamide‐6 forged part using numerical simulation methods that replicate the microstructure created by the fiber‐matrix separation (FMS) phenomenon. A … ABSTRACT This study investigates the structural behavior of a glass‐fibe reinforced polyamide‐6 forged part using numerical simulation methods that replicate the microstructure created by the fiber‐matrix separation (FMS) phenomenon. A numerical “as‐designed” (idealized) model of a T‐beam loaded in three‐point bending, which assumed uniformly distributed fibers throughout the part, overestimated stiffness and strength of the experimental results by 106% and 86%, respectively. Process‐Property‐Structure‐Performance relationship consideration importance was highlighted in this work. The “as‐manufactured” numerical model, based on the real fiber content in each region studied by microstructural analysis, was validated with experimental three‐point bending tests predicting only 2% of deviation in stiffness. However, fiber distribution can be neglected when modeling strength in “as‐manufactured,” as failure in experimental T‐beams consistently initiated at the fiber‐free tip of the rib and propagated catastrophically through the rib area.

A k-medoids-based partitioned method for computational homogenization of heterogeneous materials

2024-12-31

Modesar Shakoor

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The Haar measure in solid mechanics

2024-10-03

Clément Ecker , Boris Kolev

This article addresses the overlooked but crucial role of the Haar measure in solid mechanics, a concept well-established in mathematical literature but frequently misunderstood by mechanicians. The aim is to … This article addresses the overlooked but crucial role of the Haar measure in solid mechanics, a concept well-established in mathematical literature but frequently misunderstood by mechanicians. The aim is to provide practical insights and methodologies for the application of the Haar measure in various mechanical scenarios. The article begins with an introduction to the Haar measure, underlying its significance and a theoretical foundation for its definition and formulas. Moving beyond mathematical abstraction, the core of the article relies on practical applications, including the computation of the Haar measure for the orthogonal transformations of the 2D and 3D space under several commonly used parametrisations, an application about invariant theory in mechanics and sampling on a group orbit. These applications are presented with practical examples, enabling mechanicians to integrate the Haar measure into their research seamlessly. The article caters to a broad audience, with sections designed for both introductory comprehension and in-depth exploration. Our goal is to equip mechanicians with a valuable tool, bridging the gap between mathematical theory and practical applications in the field of mechanics.

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