Elasticity Theory of Composites

Willis, J. R.

doi:10.1016/b978-0-08-025443-2.50025-2

Cited by 58 publications

(47 citation statements)

References 53 publications

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“…A fundamental question in heterogeneous media (4) We denote I: the macroscopic stress tensor and (J the stress tensor in Y.…”

Section: Equilibrium Equation In the Representative Elementary Volumementioning

confidence: 99%

“…x (1 -y) 4 (14x 2 -14x + 3)-16 The Young's modulus is equal to 210,000 MPa and the Poisson's ratio to 0.2 (plane stress hypothesis). Figure 2 shows the accuracy between the numerical results and the analytical solution given by eqns (81 ), (82).…”

Section: Validation Testsmentioning

confidence: 99%

“…Different approaches have been explored by many authors [1][2][3][4][5] to determine the elastic behaviour of composite materials. A large class of material could be considered as periodic.…”

Section: Introductionmentioning

confidence: 99%

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Wavelet-Galerkin method for periodic heterogeneous media

Dumont

1996

Computers & Structures

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Abstract-This paper is devoted to a new algorithm to compute the local and overall response of a composite. The local elastic problem is discretized by a Galerkin-wavelet method. Details are given to compute the terms of the matrix and of the right hand side. The local solution is selected by a viscosity method. The solution with average equal to zero is chosen. Due to the form of the wavelet bases, the macroscopic coefficients are computed directly from the wavelet coefficients of the solution. Numerical examples are presented. Comparisons are made with analytic solutions and with finite element computations.

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“…A fundamental question in heterogeneous media (4) We denote I: the macroscopic stress tensor and (J the stress tensor in Y.…”

Section: Equilibrium Equation In the Representative Elementary Volumementioning

confidence: 99%

Section: Validation Testsmentioning

confidence: 99%

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Wavelet-Galerkin method for periodic heterogeneous media

Dumont

1996

Computers & Structures

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“…Many bounds partially describing the set of effective elasticity tensors have been derived [1,8,9,13,14,16,17,19,20,25,29,33,40]. This list is by no means complete and selected reviews of the literature include [5,6,12,18,31,41,42]. Composite materials can be anisotropic and can exhibit crystallographic symmetries.…”

Section: Introductionmentioning

confidence: 99%

Bounds and perturbation series for incompressible elastic composites with transverse isotropic symmetry

Lipton

1992

J Elasticity

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The effective elastic behavior of a transversely isotropic composite made from two incompressible elastic materials is examined. The set of all effective elasticity tensors for transversely isotropic finite rank laminar microstructures is described. The extremal property of this class of microstructures is used to derive a new more precise characterization of the set of effective shear moduli.The perturbation series for the effective elasticity tensor is considered. An explicit formula for the second order perturbation tensor is derived. We describe precisely the set of tensors that correspond to all second order perturbations consistent with transverse isotropy. We apply analytic methods [cf. 27] to show that all second order perturbation tensors are realized by finite rank laminar microstructures.

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“…They have long been an object of study by physicists and materials scientists; selective reviews of the extensive literature include [14,22,68,69,72]. More recently, the study of effective moduli has attracted the attention of a growing community of mathematicians as well.…”

Section: Introductionmentioning

confidence: 99%

U.S. Army Research Office Workshop on Smart Materials, Structures and Mathematical Issues Held in Blacksburg, Virginia on 15-16 September 1988

Rogers¹

1989

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Elasticity Theory of Composites

Cited by 58 publications

References 53 publications

Wavelet-Galerkin method for periodic heterogeneous media

Wavelet-Galerkin method for periodic heterogeneous media

Bounds and perturbation series for incompressible elastic composites with transverse isotropic symmetry

U.S. Army Research Office Workshop on Smart Materials, Structures and Mathematical Issues Held in Blacksburg, Virginia on 15-16 September 1988

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