A comprehensive unit cell model: a study of coupled effects in piezoelectric 1–3 composites

Pettermann, H.E.; Suresh, S.

doi:10.1016/s0020-7683(99)00224-3

Cited by 117 publications

(64 citation statements)

References 26 publications

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“…From Fig. (3), it is seen that the results are different between square array and hexagonal array, some reasons for this behavior has been discussed by Pettermann and Suresh [7]. It is also seen that the results predicted by the GSCM are almost in exact agreement with those for the hexagonal array predicted by the present method.…”

Section: Examples and Analysissupporting

confidence: 60%

Study on Electro-Magneto-Elastic Fiber Composites with Periodically Distributed Reinforced Phases Under Antiplane Deformation Mode and its Applications

Xing-li¹,

Hou²,

Xu³

2011

TOMSJ

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Abstract:The response of electro-magneto-elastic long fiber composites containing periodically distributed reinforced phases under antiplane shear load coupled with inplane electromagnetic load, which lead to the antiplane deformation mode, is dealt with. There are three different electro-magneto-elastic materials in the unit cell (3-phase model), a rigorous analytical method is developed by using the generalized eigenstrains concept integrated with the doubly quasiperiodic Riemann boundary value problem theory. The expressions of electro-magneto-elastic fields in each phase of composites are obtained. As an important application of the presented solution, the effective electro-magneto-elastic moduli are predicted by using the average field theorem and compared with the results derived from the generalized self-consistent method.

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Section: Examples and Analysissupporting

confidence: 60%

Study on Electro-Magneto-Elastic Fiber Composites with Periodically Distributed Reinforced Phases Under Antiplane Deformation Mode and its Applications

Xing-li¹,

Hou²,

Xu³

2011

TOMSJ

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“…[406][407][408][409] for magnetomechanical problems, Refs. [410][411][412][413][414][415][416] for electromechanical problems, and Refs. [417] and [418] for hydromechanical problems, see also Refs.…”

Section: Beyond Purely Elastic Problemsmentioning

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

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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.

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“…According to numerical homogenization, a unit cell is explicitly solved and the resulting average quantities are then used for the determination of the parameters of a macroscopic constitutive law [4,5].…”

Section: Introductionmentioning

confidence: 99%

A multi-scale computational method including contact for the analysis of damage in composite materials

Drosopoulos

Wriggers

Stavroulakis

2014

Computational Materials Science

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A comprehensive unit cell model: a study of coupled effects in piezoelectric 1–3 composites

Cited by 117 publications

References 26 publications

Study on Electro-Magneto-Elastic Fiber Composites with Periodically Distributed Reinforced Phases Under Antiplane Deformation Mode and its Applications

Study on Electro-Magneto-Elastic Fiber Composites with Periodically Distributed Reinforced Phases Under Antiplane Deformation Mode and its Applications

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

A multi-scale computational method including contact for the analysis of damage in composite materials

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