A Versatile Micromechanical Model for Estimating the Effective Properties of Isotropic Composite Materials

2009 ◽  
Vol 614 ◽  
pp. 255-260
Author(s):  
Qi Chang He ◽  
H. Le Quang
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Characteristic Parameter ◽  
Effective Medium ◽  
Inclusion Type ◽  
Composite Sphere ◽  
Host Matrix ◽  
Shear Moduli ◽  
Isotropic Composite

This work is concerned with a versatile and efficient model for estimating the effective moduli of isotropic composites consisting of isotropic phases whose microstructure may be of matrix-inclusion type, disordered or intermediate. This extended version of generalized self-consistent model (GSCM) is built by inserting a composite sphere embedded in an infinite unknown effective medium has the core made of the unknown effective medium and coated by the constituent phases. The volume fraction of the constituent phases in this composite sphere is the characteristic parameter of the relevant microstructure. By imposing the an energy equivalency condition, the equations thus obtained to estimate the effective bulk and shear moduli involve the microstructural parameter which turns out to be capable of describing in some sense how far a microstructure is from the host matrix/inclusion morphology

scholarly journals Nonlinear buckling of CNT-reinforced composite toroidal shell segment surrounded by an elastic medium and subjected to uniform external pressure

2018 ◽  
Vol 40 (3) ◽  
pp. 285-301
Author(s):  
Hoang Van Tung ◽  
Pham Thanh Hieu
Keyword(s):  
Carbon Nanotubes ◽  
Elastic Medium ◽  
Volume Fraction ◽  
Effective Properties ◽  
Micromechanical Model ◽  
External Pressure ◽  
Toroidal Shell ◽  
Nonlinear Load ◽  
Uniform External Pressure ◽  
Reinforced Composite

Buckling and postbuckling behaviors of Toroidal Shell Segment (TSS) reinforced by single-walled carbon nanotubes (SWCNT), surrounded by an elastic medium and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes (CNTs) are reinforced into matrix phase by uniform distribution (UD) or functionally graded (FG) distribution along the thickness direction. Effective properties of carbon nanotube reinforced composite (CNTRC) are estimated by an extended rule of mixture through a micromechanical model. Governing equations for TSSs are based on the classical thin shell theory taking into account geometrical nonlinearity and surrounding elastic medium. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to obtain nonlinear load-deflection relation from which buckling loads and postbuckling equilibrium paths are determined. The effects of CNT volume fraction, distribution types, geometrical ratios and elastic foundation on the buckling and postbuckling behaviors of CNTRC TSSs are analyzed and discussed.

scholarly journals Effective properties of particulate nano-composites including Steigmann–Ogden model of material surface

2021 ◽  
Author(s):  
Lidiia Nazarenko ◽  
Henryk Stolarski ◽  
Holm Altenbach
Keyword(s):  
Volume Fraction ◽  
Effective Properties ◽  
Surface Effects ◽  
Particulate Composites ◽  
Material Surface ◽  
Effective Moduli ◽  
Nano Particle ◽  
Shear Moduli ◽  
Conditional Moments ◽  
Theoretical Predictions

AbstractThe objective of this work is inclusion of the Steigmann-Ogden interface in the Method of Conditional Moments to investigate the influence of surface effects on the effective properties of random particulate composites. The particular focus is centered on accounting for the surface bending stiffness. To this end, the notion of the energy-equivalent inhomogeneity developed for Gurtin–Murdoch interface is generalized to include the surface bending contribution. The crucial aspect of that generalization is identification of the formula defining energy associated with the surface bending. With the help of that formula, the real nano-particle and its surface are replaced by equivalent inhomogeneity with properties incorporating the surface effects. Closed-form expressions for the effective moduli of a composite with a matrix and randomly distributed spherical inhomogeneities are derived. The normalized shear moduli of nanoporous material as a function of void volume fraction is analyzed and evaluated in the context of other theoretical predictions.

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

Polymers ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 2990 ◽  
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.

Thermomechanical nonlinear buckling of pressure-loaded carbon nanotube reinforced composite toroidal shell segment surrounded by an elastic medium with tangentially restrained edges

2018 ◽  
Vol 233 (9) ◽  
pp. 3193-3207 ◽  
Author(s):  
Pham Thanh Hieu ◽  
Hoang Van Tung
Keyword(s):  
Carbon Nanotubes ◽  
Carbon Nanotube ◽  
Elastic Medium ◽  
Volume Fraction ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Toroidal Shell ◽  
Nonlinear Buckling ◽  
Nonlinear Load ◽  
Reinforced Composite

Buckling and postbuckling behaviors of toroidal shell segment reinforced by single-walled carbon nanotubes, surrounded by an elastic medium, exposed to a thermal environment and subjected to uniform external pressure are investigated in this paper. Carbon nanotubes are reinforced into matrix phase by uniform distribution or functionally graded distribution along the thickness direction. Material properties of constituents are assumed to be temperature dependent, and the effective properties of carbon nanotube reinforced composite are estimated by extended mixture rule through a micromechanical model. Governing equations for toroidal shell segments are based on the classical thin shell theory taking into account geometrical nonlinearity, surrounding elastic medium, and varying degree of tangential constraints of edges. Three-term solution of deflection and stress function are assumed to satisfy simply supported boundary condition, and Galerkin method is applied to derive nonlinear load–deflection relation from which buckling loads and postbuckling equilibrium paths are determined. Analysis shows that tangential edge restraints have significant effects on nonlinear buckling of carbon nanotube reinforced composite toroidal shell segments. In addition, the effects of carbon nanotube volume fraction, distribution types, geometrical ratios, elastic foundation, and thermal environments on the buckling and postbuckling behaviors of carbon nanotube reinforced composite toroidal shell segments are analyzed and discussed.

Mathematical Model of the Effective Properties of a Fiber Reinforced Composite with a Linearly Graded Transition Zone

2010 ◽  
Vol 38 (4) ◽  
pp. 286-307
Author(s):  
Carey F. Childers
Keyword(s):  
Mathematical Model ◽  
Transition Zone ◽  
Effective Properties ◽  
Local Stress ◽  
Stress And Strain ◽  
Fiber Reinforced ◽  
Strain Fields ◽  
Shear Moduli ◽  
Fiber Reinforced Composite ◽  
Reinforced Composite

Abstract Tires are fabricated using single ply fiber reinforced composite materials, which consist of a set of aligned stiff fibers of steel material embedded in a softer matrix of rubber material. The main goal is to develop a mathematical model to determine the local stress and strain fields for this isotropic fiber and matrix separated by a linearly graded transition zone. This model will then yield expressions for the internal stress and strain fields surrounding a single fiber. The fields will be obtained when radial, axial, and shear loads are applied. The composite is then homogenized to determine its effective mechanical properties—elastic moduli, Poisson ratios, and shear moduli. The model allows for analysis of how composites interact in order to design composites which gain full advantage of their properties.

Elasticity of colloidal gels: structural heterogeneity, floppy modes, and rigidity

Soft Matter ◽  
2021 ◽  
Author(s):  
D. Zeb Rocklin ◽  
Lilian C Hsiao ◽  
Megan E Szakasits ◽  
Michael J Solomon ◽  
Xiaoming Mao
Keyword(s):  
Coordination Number ◽  
Volume Fraction ◽  
Structural Parameters ◽  
Structural Heterogeneity ◽  
Colloidal Gels ◽  
Shear Moduli ◽  
Rheological Measurements

Rheological measurements of model colloidal gels reveal that large variations in the shear moduli as colloidal volume-fraction changes are not reflected by simple structural parameters such as the coordination number,...

scholarly journals An Intrinsic Material Tailoring Approach for Functionally Graded Axisymmetric Hollow Bodies Under Plane Elasticity

2021 ◽  
Author(s):  
Hassan Mohamed Abdelalim Abdalla ◽  
Daniele Casagrande
Keyword(s):  
Optimization Problem ◽  
Volume Fraction ◽  
Minimum Principle ◽  
Equivalent Stress ◽  
Micromechanical Model ◽  
Plane Elasticity ◽  
Functionally Graded ◽  
Pontryagin Minimum Principle ◽  
Volume Fractions ◽  
Material Tailoring

AbstractOne of the main requirements in the design of structures made of functionally graded materials is their best response when used in an actual environment. This optimum behaviour may be achieved by searching for the optimal variation of the mechanical and physical properties along which the material compositionally grades. In the works available in the literature, the solution of such an optimization problem usually is obtained by searching for the values of the so called heterogeneity factors (characterizing the expression of the property variations) such that an objective function is minimized. Results, however, do not necessarily guarantee realistic structures and may give rise to unfeasible volume fractions if mapped into a micromechanical model. This paper is motivated by the confidence that a more intrinsic optimization problem should a priori consist in the search for the constituents’ volume fractions rather than tuning parameters for prefixed classes of property variations. Obtaining a solution for such a class of problem requires tools borrowed from dynamic optimization theory. More precisely, herein the so-called Pontryagin Minimum Principle is used, which leads to unexpected results in terms of the derivative of constituents’ volume fractions, regardless of the involved micromechanical model. In particular, along this line of investigation, the optimization problem for axisymmetric bodies subject to internal pressure and for which plane elasticity holds is formulated and analytically solved. The material is assumed to be functionally graded in the radial direction and the goal is to find the gradation that minimizes the maximum equivalent stress. A numerical example on internally pressurized functionally graded cylinders is also performed. The corresponding solution is found to perform better than volume fraction profiles commonly employed in the literature.

Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory

2021 ◽  
pp. 109963622199386
Author(s):  
Hessameddin Yaghoobi ◽  
Farid Taheri
Keyword(s):  
Shear Deformation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Sheet Thickness ◽  
Analytical Investigation ◽  
Sandwich Plates ◽  
Simply Supported ◽  
Vibration Stability ◽  
Shear Deformation Plate Theory

An analytical investigation was carried out to assess the free vibration, buckling and deformation responses of simply-supported sandwich plates. The plates constructed with graphene-reinforced polymer composite (GRPC) face sheets and are subjected to mechanical and thermal loadings while being simply-supported or resting on different types of elastic foundation. The temperature-dependent material properties of the face sheets are estimated by employing the modified Halpin-Tsai micromechanical model. The governing differential equations of the system are established based on the refined shear deformation plate theory and solved analytically using the Navier method. The validation of the formulation is carried out through comparisons of the calculated natural frequencies, thermal buckling capacities and maximum deflections of the sandwich plates with those evaluated by the available solutions in the literature. Numerical case studies are considered to examine the influences of the core to face sheet thickness ratio, temperature variation, Winkler- and Pasternak-types foundation, as well as the volume fraction of graphene on the response of the plates. It will be explicitly demonstrated that the vibration, stability and deflection responses of the sandwich plates become significantly affected by the aforementioned parameters.

Transformation Textures in Unstable Austenitic Steel

2002 ◽  
Vol 125 (1) ◽  
pp. 12-17 ◽  
Author(s):  
R. Kubler ◽  
M. Berveiller ◽  
M. Cherkaoui ◽  
K. Inal
Keyword(s):  
Martensitic Transformation ◽  
Volume Fraction ◽  
Micromechanical Model ◽  
Slip Rate ◽  
Transformation Strain ◽  
Dislocation Motion ◽  
Lattice Spin ◽  
Two Phases ◽  
The One ◽  
Elastic Plastic Materials

During the martensitic transformation in elastic-plastic materials, the local transformation strain as well as the plastic flow inside austenite are strongly related with the crystallographic orientation of the austenitic lattice. Two mechanisms involved in these materials, i.e., plasticity by dislocation motion and martensitic phase formation are coupled through kinematical constraints so that the lattice spin of the austenitic grains is different from the one due to classical slip. In this work, the lattice spin ω˙eA of the austenitic grains is related with the slip rate on the slip systems of the two phases, γ˙A and γ˙M, the evolution of the martensite volume fraction f˙ and the overall rotation rate Ω˙ of the grains. This new relation is integrated in a micromechanical model developed for unstable austenite in order to predict the evolution of the austenite texture during TRansformation Induced Plasticity (TRIP). Results for the evolution of the lattice orientation during martensitic transformation are compared with experimental data obtained by X-ray diffraction on a 304 AISI steel.

scholarly journals Recovery of inclusion separations in strongly heterogeneous composites from effective property measurements

2011 ◽  
Vol 468 (2139) ◽  
pp. 784-809 ◽  
Author(s):  
Chris Orum ◽  
Elena Cherkaev ◽  
Kenneth M. Golden
Keyword(s):  
Inverse Spectral Problem ◽  
Algebraic Curves ◽  
Volume Fraction ◽  
Adjoint Operator ◽  
Effective Property ◽  
Host Matrix ◽  
Separation Parameter ◽  
Property Data ◽  
Transformation Structure ◽  
Parameter Values

An effective property of a composite material consisting of inclusions within a host matrix depends on the geometry and connectedness of the inclusions. This dependence may be quite strong if the constituents have highly contrasting properties. Here, we consider the inverse problem of using effective property data to obtain information on the geometry of the microstructure. While previous work has been devoted to recovering the volume fractions of the constituents, our focus is on their connectedness—a key feature in critical behaviour and phase transitions. We solve exactly a reduced inverse spectral problem by bounding the volume fraction of the constituents, an inclusion separation parameter and the spectral gap of a self-adjoint operator that depends on the geometry of the composite. We present a new algorithm based on the Möbius transformation structure of the forward bounds whose output is a set of algebraic curves in parameter space bounding regions of admissible parameter values. These results advance the development of techniques for characterizing the microstructure of composite materials. As an example, we obtain inverse bounds on the volume fraction and separation of the brine inclusions in sea ice from measurements of its effective complex permittivity.

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