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The Quarterly Journal of Mechanics and Applied Mathematics 2004 57(4):571-582; doi:10.1093/qjmam/57.4.571
© 2004 by Oxford University Press
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Laminations in planar anisotropic linear elasticity

Sergio Gutiérrez*

( Departamento de Matemática, Pontificia Universidad Católica de Chile, casilla 306, Santiago 22, Chile )

We explicitly compute the effective elasticity tensor obtained by laminating two anisotropic strongly elliptic linearly elastic materials. Assuming the extra symmetry needed for hyperelasticity, we prove that for any non-semi-very strongly elliptic material (that is, with elasticity tensor not positive semidefinite), one can select an isotropic very strongly elliptic material, such that the effective tensor created by laminating these materials, if it exists, is not even strongly elliptic, corresponding then to a highly unstable material.

Received 27 September 2002. Revised 7 March 2003.

* <sgutierr{at}mat.puc.cl>


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