Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites

Dunn, Martin L.; Taya, M.

doi:10.1016/0020-7683(93)90058-f

Cited by 505 publications

(265 citation statements)

References 28 publications

Supporting

Mentioning

255

Contrasting

Unclassified

Order By: Relevance

“…) In formulating the micromechanics theories, it is convenient to adopt matrix notations, which are denoted by bold letters. The matrix equation for predicting the effective moduli of two-phase perfectly bonded fiber-reinforced composites can be written as (for example, refer to Dunn and Taya, 1993) …”

Section: Other Micromechanics Methodsmentioning

confidence: 99%

“…The key assumption made in the dilute approximation is that the interaction among inclusions in the matrix-based composite can be ignored. The strain gradient concentration matrix in the local coordinates can be expressed as (for example, see Dunn and Taya, 1993)…”

Section: Other Micromechanics Methodsmentioning

confidence: 99%

“…The essence of the method is the realizable construction of the final composite from the matrix material through the successive replacement of an incremental volume of the current composite with that of the reinforcement. According to Dunn and Taya (1993), we have…”

Section: Other Micromechanics Methodsmentioning

confidence: 99%

“…The key assumption in the Mori-Tanaka (1973) method is that a single inclusion is embedded in an infinite matrix subjected to an applied remote field equal to the as-yet-unknown averaged strain (stress) field in the matrix. According to Dunn and Taya (1993),…”

Section: Other Micromechanics Methodsmentioning

confidence: 99%

See 3 more Smart Citations

A generalized self-consistent method accounting for fiber section shape

Jiang

Tong

Cheung

2003

International Journal of Solids and Structures

View full text Add to dashboard Cite

A three-phase confocal elliptical cylinder model is proposed for fiber-reinforced composites, in terms of which a generalized self-consistent method is developed for fiber-reinforced composites accounting for variations in fiber section shapes and randomness in fiber section orientation. The reasonableness of the fiber distribution function in the present model is shown. The dilute, self-consistent, differential and Mori-Tanaka methods are also extended to consider randomness in fiber section orientation in a statistical sense. A full comparison is made between various micromechanics methods and with the Hashin and ShtrikmanÕs bounds. The present method provides convergent and reasonable results for a full range of variations in fiber section shapes (from circular fibers to ribbons), for a complete spectrum of the fiber volume fraction (from 0 to 1, and the latter limit shows the correct asymptotic behavior in the fully packed case) and for extreme types of the inclusion phases (from voids to rigid inclusions). A very different dependence of the five effective moduli on fiber section shapes is theoretically predicted, and it provides a reasonable explanation on the poor correlation between previous theory and experiment in the case of longitudinal shear modulus.

show abstract

Section: Other Micromechanics Methodsmentioning

confidence: 99%

Section: Other Micromechanics Methodsmentioning

confidence: 99%

Section: Other Micromechanics Methodsmentioning

confidence: 99%

Section: Other Micromechanics Methodsmentioning

confidence: 99%

See 2 more Smart Citations

A generalized self-consistent method accounting for fiber section shape

Jiang

Tong

Cheung

2003

International Journal of Solids and Structures

View full text Add to dashboard Cite

show abstract

“…Further proposed models such as Mori-Tanaka [90][91][92], the self-consistent scheme [93][94][95][96][97][98], the generalized self-consistent scheme [99][100][101][102][103], and the differential method [104,105] are mainly based on the mean-field approximation [106] and approximate the interaction between the phases. The extension of these models to account for the electroelastic behavior of composite materials was addressed by Dunn and Taya [107]. Further contributions to the self-consistent scheme were made by Nemat-Nasser et al [108] for periodic porous composites, Herve and Zaoui [109] for multilayered spherical inhomogeneities, and by Huang and Hu [110] for aligned elliptical heterogeneities in two-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

190

138

View full text Add to dashboard Cite

The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

show abstract