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The paraboloid failure surface for the general orthotropic material

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Summary

It has been established that the elliptic paraboloid failure criterion (EPFC) is a potential means of describing the yielding and failure behavior of transversely isotropic (transtropic) materials presenting also strength differential effects along all principal stress axes. The cases studied correspond to symmetric forms of loading which are parallel to the principal strength directions of the material.

In this paper the general case of an orthotropic material not presenting any kind of strength symmetry was encountered. It has been shown that an elloptic parabloid surface may continue to represent the failure surface of such materials. However the symmetry of this surface relatively to the principal diagonal plane containing the strong σ3-axis and the bisector of the two remaining axes is destroyed. For these materials the elliptic paraboloid is leaning toward the intermediate strength σ2-axis and the angle of inclination of the plane of symmetry of the paraboloid with the σ1σ2-plane depends on the difference in strengths between the σ2- and σ1-axes. The characteristic properties of the inclined paraboloid were studied and important differences between the inclined and the symmetric surfaces were established. Examples with orthotropic polymers and composites were included exemplifying the characteristic properties of orthotropic materials.

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  1. Department of Engng. Sciences, Athens National Technical University, P. O. Box 77 230, GR-175-10, Athens, Greece

    P. S. Theocaris

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  1. P. S. Theocaris
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Theocaris, P.S. The paraboloid failure surface for the general orthotropic material. Acta Mechanica 79, 53–79 (1989). https://doi.org/10.1007/BF01181480

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