scholarly journals Micromechanical modelling of porous viscoelastic composite materials

2018 ◽  
Vol 191 ◽  
pp. 00007
Author(s):  
Mohamed El Kouri ◽  
Abderrahmane Bakkali ◽  
Lahcen Azrar
Keyword(s):  
Effective Properties ◽  
Methodological Approach ◽  
Micromechanical Model ◽  
Mean Field ◽  
Viscoelastic Composite ◽  
Field Techniques ◽  
Viscoelastic Matrix ◽  
Convolution Products ◽  
Viscoelastic Composites ◽  
Effective Behavior

Modelling and predicting the effective behavior of non-ageing viscoelastic composites have attracted the attention of many researchers. Actually, predicting the effective behavior and the macroscopic overall response while taking into account the constituents properties and shape of inclusions as well as their volume fractions is a challenging topic. In this work, porous viscoelastic composites are considered. The porous effect is introduced as a solid voided inclusions embedded in a viscoelastic matrix. The effective behavior is modelled by delayed integropartial differential equations. The resolution of the resulting equations is done through a methodological approach based on the Volterra tensorial products and the dynamic Green‘s tensor. Thus, the localization equations relating the local and the global fields are derived. After that, the Mori-Tanaka mean field micromechanical model assumptions are applied to derive the Mori-Tanaka‘s localization tensor. Once this step is completed, the effective properties are obtained through mean field techniques. The effective properties are given through tensorial convolution products. A numerical algorithm is elaborated for the computation of direct and inverse tensorial convolution products. For the validation of the developed modelling a comparison with Laplace-Carson approach is done.

Evaluation of effective transverse mechanical properties of transversely isotropic viscoelastic composite materials

2011 ◽  
Vol 45 (25) ◽  
pp. 2641-2658 ◽  
Author(s):  
Andrey V. Pyatigorets ◽  
Sofia G. Mogilevskaya
Keyword(s):  
Mechanical Properties ◽  
Effective Properties ◽  
Transversely Isotropic ◽  
Elastic Fibers ◽  
Reinforced Composites ◽  
Viscoelastic Composite ◽  
Viscoelastic Matrix ◽  
Linear Viscoelastic ◽  
Comparison Of The Results ◽  
Benchmark Solutions

A new computational approach for calculation of the effective transverse mechanical properties of unidirectional fiber-reinforced composites with linear viscoelastic matrix and elastic fibers is presented. The approach requires the knowledge of stresses outside a cluster representing the structure of composite in question. The effective properties are found from the assumption that the viscoelastic stresses at the distances far away from the cluster are the same as those from a single equivalent inhomogeneity. The approach directly takes into account the interactions between the inhomogeneities. The comparison of the results with several benchmark solutions reveals the advantages of the developed approach.

Creep Responses of Smart Sandwich Composites at Multiple Length Scales: Experiments and Modeling

2010 ◽  
Vol 133 (1) ◽  
Author(s):  
Anaïs Farrugia ◽  
Charles Winkelmann ◽  
Valeria La Saponara ◽  
Jeong Sik Kim ◽  
Anastasia H. Muliana
Keyword(s):  
Creep Behavior ◽  
Composite Structures ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Foam Core ◽  
Sandwich Beams ◽  
Fiber Reinforced ◽  
Polymer Foam ◽  
Creep Tests ◽  
Unique Challenge

In service, composite structures present the unique challenge of damage detection and repair. Piezoelectric ceramic, such as lead zirconate titanate (PZT), is often used for detecting damage in composites. This paper investigates the effect of embedded PZT crystals on the overall creep behavior of sandwich beams comprising of glass fiber reinforced polymer laminated skins and polymer foam core, which could potentially be used as a damage-detecting smart structure. Uniaxial quasi-static and creep tests were performed on the glass/epoxy laminated composites having several fiber orientations, 0 deg, 45 deg, and 90 deg, to calibrate the elastic and viscoelastic properties of the fibers and matrix. Three-point bending creep tests at elevated temperature (80°C) were then carried out for a number of control sandwich beams (no PZT crystal) and conditioned sandwich beams (with PZT crystals embedded in the center of one facesheet). Lateral deflection of the sandwich beams was monitored for more than 60 h. The model presented in this paper is composed by two parts: (a) a simplified micromechanical model of unidirectional fiber reinforced composites used to obtain effective properties and overall creep response of the laminated skins and (b) a finite element method to simulate the overall creep behavior of the sandwich beams with embedded PZT crystals. The simplified micromechanical model is implemented in the material integration points within the laminated skin elements. Fibers are modeled as linear elastic, while a linearized viscoelastic material model is used for the epoxy matrix and foam core. Numerical results on the creep deflection of the smart sandwich beams show good correlations with the experimental creep deflection at 80°C, thus proving that this model, although currently based on material properties reported at room temperature, is promising to obtain a reasonable prediction for the creep of a smart sandwich structure at high temperatures.

Dynamic Stability of Unidirectional Fiber-Reinforced Viscoelastic Composite Plates

1989 ◽  
Vol 42 (11S) ◽  
pp. S39-S47 ◽  
Author(s):  
N. K. Chandiramani ◽  
L. Librescu
Keyword(s):  
Shear Deformation ◽  
Dynamic Stability ◽  
Stability Problem ◽  
Micromechanical Model ◽  
Shear Deformation Theory ◽  
Constitutive Law ◽  
Fiber Reinforced ◽  
Viscoelastic Composite ◽  
Unidirectional Fiber ◽  
The Stability

This paper deals with a dynamic stability analysis of unidirectional fiber-reinforced composite viscoelastic plates subjected to compressive edge loads. The integrodifferential equations governing the stability problem are obtained by using, in conjunction with a Boltzmann hereditary constitutive law for a 3-D viscoelastic medium, a higher-order shear deformation theory of orthotropic plates. Such a theory incorporates transverse shear deformation, transverse normal stress, and rotatory inertia effects. The solution of the stability problem as considered within this paper concerns the determination of the critical in-plane edge loads yielding the asymptotic instability. Numerical applications, based on material properties derived within the framework of Aboudi’s micromechanical model, are presented and pertinent conclusions concerning the nature of the loss of stability and the influence of various parameters are outlined.

Micromechanics-based analyses of short fiber-reinforced composites with functionally graded interphases

2019 ◽  
Vol 54 (8) ◽  
pp. 1031-1048 ◽  
Author(s):  
Yang Yang ◽  
Qi He ◽  
Hong-Liang Dai ◽  
Jian Pang ◽  
Liang Yang ◽  
...  
Keyword(s):  
Aspect Ratio ◽  
Elastic Properties ◽  
Effective Properties ◽  
Micromechanical Model ◽  
Short Fiber ◽  
Functionally Graded ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Fiber Reinforced ◽  
The Matrix

A micromechanical model for short fiber-reinforced composites (SFRCs) with functionally graded interphases and a systematic prediction scheme to determine the effective properties are presented. The matrix and the fibers are regarded to be linear elastic, isotropic, and homogeneous. Fibers are assumed to be ellipsoids coated perfectly by functionally graded interphases, which is supposed to be formed chemically or physically by the constituents near the interface. First, to analyze the grading interphase effect, layer-wise concept is followed to divide the functionally graded interphases into multi-homogeneous sub-layers. Next, to take the effect of functionally graded interphases into account, a combination of multi-inclusion method and Mori–Tanaka method is applied to predict effective elastic properties of this unidirectional SFRCs with respect to the content and aspect ratio of the inclusions. By employing coordinate transformation, spatially elastic moduli are obtained. Finally, Voigt homogenization scheme is used to obtain the overall, averaged, symmetrical elastic properties of the SFRCs. Numerical examples and analyses demonstrate the applicability of the proposed method and indicate the influences of graded interphase, orientation, and aspect ratio of inclusions as well as properties and contents of the constituents on the overall properties of SFRCs.

scholarly journals Model reduction by mean-field homogenization in viscoelastic composites. I. Primal theory

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200407 ◽  
Author(s):  
Martín I. Idiart ◽  
Noel Lahellec ◽  
Pierre Suquet
Keyword(s):  
Strain Field ◽  
Mean Field ◽  
Inelastic Strain ◽  
Mathematical Structure ◽  
Schwarz Inequality ◽  
Internal Variables ◽  
Legendre Transform ◽  
Time Step ◽  
Legendre Transforms ◽  
Viscoelastic Composites

A homogenization scheme for viscoelastic composites proposed by Lahellec & Suquet (2007 Int. J. Solids Struct. 44 , 507–529 ( doi:10.1016/j.ijsolstr.2006.04.038 )) is revisited. The scheme relies upon an incremental variational formulation providing the inelastic strain field at a given time step in terms of the inelastic strain field from the previous time step, along with a judicious use of Legendre transforms to approximate the relevant functional by an alternative functional depending on the inelastic strain fields only through their first and second moments over each constituent phase. As a result, the approximation generates a reduced description of the microscopic state of the composite in terms of a finite set of internal variables that incorporates information on the intraphase fluctuations of the inelastic strain and that can be evaluated by mean-field homogenization techniques. In this work we provide an alternative derivation of the scheme, relying on the Cauchy–Schwarz inequality rather than the Legendre transform, and in so doing we expose the mathematical structure of the resulting approximation and generalize the exposition to fully anisotropic material systems.

scholarly journals Model reduction by mean-field homogenization in viscoelastic composites. II. Application to rigidly reinforced solids

2020 ◽  
Vol 476 (2242) ◽  
pp. 20200408
Author(s):  
Martín I. Idiart ◽  
Noel Lahellec ◽  
Pierre Suquet
Keyword(s):  
Elastic Moduli ◽  
Solid Phase ◽  
Mean Field ◽  
Free Energy Density ◽  
Companion Paper ◽  
Viscoelastic Solid ◽  
Complex Deformation ◽  
Link Type ◽  
The Mean ◽  
Viscoelastic Composites

The mean-field homogenization scheme proposed by Lahellec & Suquet (2007 Int. J. Solids Struct. 44 , 507–529 ( doi:10.1016/j.ijsolstr.2006.04.038 )) and revisited in a companion paper (Idiart et al . 2020 Proc. R. Soc. A 20200407 ( doi:10.1098/rspa.2020.0407 )) is applied to random mixtures of a viscoelastic solid phase and a rigid phase. Two classes of mixtures with different microstructural arrangements are considered. In the first class the rigid phase is dispersed within the continuous viscoelastic phase in such a way that the elastic moduli of the mixture are given exactly by the Hashin–Shtrikman formalism. In the second class, both phases are intertwined in such a way that the elastic moduli of the mixture are given exactly by the Self-Consistent formalism. Results are reported for specimens subject to various complex deformation programmes. The scheme is found to improve on earlier approximations of common use and even recover exact results under several circumstances. However, it can also generate highly inaccurate predictions as a result of the loss of convexity of the free-energy density. An auspicious procedure to partially circumvent this issue is advanced.

Multiple Surface Cracking and Its Effect on Interface Cracks in Functionally Graded Thermal Barrier Coatings Under Thermal Shock

2003 ◽  
Vol 70 (2) ◽  
pp. 234-245 ◽  
Author(s):  
S. Rangaraj ◽  
K. Kokini
Keyword(s):  
Thermal Shock ◽  
Thermal Barrier Coatings ◽  
Architectural Design ◽  
Effective Properties ◽  
Mean Field ◽  
Functionally Graded ◽  
Analytical Models ◽  
Thermal Barrier ◽  
Thermal Fracture ◽  
Barrier Coatings

The thermal fracture behavior in functionally graded yttria stabilized zirconia–NiCoCrAlY bond coat alloy thermal barrier coatings was studied using analytical models. The response of three coating architectures of similar thermal resistance to laser thermal shock tests was considered. Mean field micromechanics models were used to predict the effective thermoelastic and time-dependent (viscoplastic) properties of the individual layers of the graded thermal barrier coatings (TBCs). These effective properties were then utilized in fracture mechanics analyses to study the role of coating architecture on the initiation of surface cracks. The effect of the surface crack morphology and coating architecture on the propensity for propagation of horizontal delamination cracks was then assessed. The results of the analyses are correlated with previously reported experimental results. Potential implications of the findings on architectural design of these material systems for enhanced thermal fracture resistance are discussed.

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 Analytic Results in (2+1)-Dimensional Finite Temperature LGT

1997 ◽  
Vol 12 (32) ◽  
pp. 5753-5766 ◽  
Author(s):  
M. Billó ◽  
M. Caselle ◽  
A. D'Adda
Keyword(s):  
Monte Carlo ◽  
Effective Action ◽  
Finite Temperature ◽  
Mean Field ◽  
Polyakov Loop ◽  
Critical Coupling ◽  
Dimensional Theory ◽  
Field Techniques ◽  
Large N ◽  
Good Agreement

In a (2 + 1)-dimensional pure LGT at finite temperature the critical coupling for the deconfinement transition scales as βc(nt) = Jcnt + a1, where nt is the number of links in the "timelike" direction of the symmetric lattice. We study the effective action for the Polyakov loop obtained by neglecting the spacelike plaquettes, and we are able to compute analytically in this context the coefficient a1 for any SU(N) gauge group; the value of Jc is instead obtained from the effective action by means of (improved) mean field techniques. Both coefficients have already been calculated in the large N limit in a previous paper. The results are in very good agreement with the existing Monte Carlo simulations. This fact supports the conjecture that, in the (2 + 1)-dimensional theory, spacelike plaquettes have little influence on the dynamics of the Polyakov loops in the deconfined phase.

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