On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

Würkner, Mathias; Berger, Harald; Gabbert, Ulrich

doi:10.1016/j.ijengsci.2010.12.016

Cited by 27 publications

(18 citation statements)

References 14 publications

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“…Among the variety of papers dealing with modeling of effective mechanical properties of composites and their experimental verification, the following group of papers in which a coupling between the topology of fibrous reinforcement (or particle) reinforcement and material symmetry of constitutive model describing composite can be distinguished, for instance: Sun and Vaidya [30], Gan et al [9], Liu et al [19], Würkner et al [37], Selvadurai and Nikopour [28] and others.…”

Section: State Of the Artmentioning

confidence: 99%

“…In the recently published paper by Würkner et al [37] the effective elastic modules of the composite formed of isotropic Epoxy matrix and transversely isotropic Graphite fibers are examined for reasonable wide range of volume fraction V f ∈< 0.1 ÷ 0.6 > see also comments in Sect. 3.5.5 of this chapter.…”

Section: State Of the Artmentioning

confidence: 99%

“…3.6a). Such fiber configuration in unidirectional composite is used by Tamma and Avila [32], Würkner et al [37] and others. By contrast, in case of hexagonal symmetry (hexagonal array) fibers are distributed in position of parallel rows equally spaced with distance a but neighboring rows are shifted each to the other with distance a/2 (Fig.…”

Section: Effective Stiffness Matrices Of Unidirectional Composites Chmentioning

confidence: 99%

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Mechanics of Anisotropic Composite Materials

Ganczarski

Hernik

Skrzypek

2015

Mechanics of Anisotropic Materials

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Mechanics of composite materials was in the last decade one of the most rapidly explored engineering area, basically due to huge progress in composite fabrication and use. The main problem referred in this chapter is how to correctly predict averaged effective properties by implementation of numerous homogenization techniques. Useful classification of composites with respect to the format of effective stiffness matrix, based on the analogy between the crystal lattice symmetry and respective configuration of reinforcement in the RUC, is given. Extended section is focused on conventionally used Hill's theorem on upper and lower bounds by Voigt and Reuss' isotropic estimation for approximate determination of stiffness and compliance matrices of anisotropic composite. Consistent application of the Hill theorem to the elements of elastic stiffness or compliance matrices (but not to engineering anisotropy constants) enable to explain some peculiarities of the Poisson ratio diagrams, met in respective bibliography (e.g., Aboudi et al., Micromechanics of Composite Materials, 2013; Sun and Vaidya, Compos. Sci. Technol. 56:171-179, 1996; Gan et al., Int. J. Solids Struct. 37:5097-5122, 2000). The new effective proposal to achieve approximation of the mechanical modules of unidirectionally reinforced composites by the use of hybrid-type rule of weighted average between the Voigt and Reuss upper and lower estimates is proposed. Capability of this averaged interpolation was checked based on selected findings by Gan et al. (Int. J. Solids Struct. 37:5097-5122, 2000) for Boron/Al composite, which show good convergence and enable to treat weighting coefficients as universal ones over the full V f range.

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Section: State Of the Artmentioning

confidence: 99%

Section: State Of the Artmentioning

confidence: 99%

Section: Effective Stiffness Matrices Of Unidirectional Composites Chmentioning

confidence: 99%

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Mechanics of Anisotropic Composite Materials

Ganczarski

Hernik

Skrzypek

2015

Mechanics of Anisotropic Materials

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“…Kar-Gupta and Venkatesh [20] systematically assessed the effects of fibre distribution on the piezoelectric coefficients by comparing 14 different fibre arrangements. Recently, FE and boundary element (BE) methods [21][22][23][24][25][26] have been extensively used in homogenization process, 2 Journal of Engineering for one of the reasons that both FE and BE methods are applicable regardless of the type of inclusion in the unit cell. However, the adoption of numerical methods raises two major issues: one is that results generated from this method are highly meshing dependent The correctness and accuracy can be affected by the modelling and meshing methods selected; another is that the RVE presents continuity in the homogeneous media, which means the deformation of such an element should keep continuous within an element and on the interfacial boundary of any two adjacent elements as well.…”

Section: Introductionmentioning

confidence: 99%

“…Xia et al [28] then indicated that this boundary condition is only valid for normal tractions, whereas the unit cell is not only overconstrained, but also against stress/strain periodicity if shear loading is applied. For the simplicity of application, a modified periodic boundary condition has been derived and used in the work afterwards [16,24,28].…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Effective Properties of 3D Piezoelectric Composites

Qin¹,

Xiao

Lan

2014

Journal of Engineering

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The prediction of the overall effective properties of fibre-reinforced piezocomposites has drawn much interest from investigators recently. In this work, an algorithm used in two-dimensional (2D) analysis for calculating transversely isotropic material properties is developed. Since the finite element (FE) meshing patterns on the opposite areas are the same, constraint equations can be applied directly to generate appropriate load. The numerical results derived using this model have found a good agreement with those in the literature. The 2D algorithm is then modified and improved in such a way that it is valid for three-dimensional (3D) analysis in the case of random distributed shorts and inclusions. Linear interpolation of displacement field is employed to establish constraint equations of nodal displacements between two adjacent elements.

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Numerical homogenization of composite structures with rhombic fiber arrangements

Würkner

Berger

Gabbert

2011

Proc Appl Math and Mech

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A numerical procedure is developed to determine effective material properties of unidirectional fiber reinforced composites with rhombic fiber arrangements. With the assumption of a periodic micro structure a representative volume element (RVE) is considered, where the phases have isotropic or transversely isotropic material characterizations. The interface between the phases is treated as perfect. The procedure handles the primary non‐rectangular periodicity with homogenization techniques based on finite element models. Due to appropriate boundary conditions applied to the RVE elastic effective coefficients are derived. Six different boundary condition states are required to get all coefficients of the stiffness tensor. Results are listed and compared with other publications and good agreements are shown. Furthermore new results are presented, which exhibit the orthotropic behavior of such composites caused by the rhombic fiber arrangement. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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On numerical evaluation of effective material properties for composite structures with rhombic fiber arrangements

Cited by 27 publications

References 14 publications

Mechanics of Anisotropic Composite Materials

Mechanics of Anisotropic Composite Materials

Numerical Simulation of Effective Properties of 3D Piezoelectric Composites

Numerical homogenization of composite structures with rhombic fiber arrangements

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