Vol 54, No 5-6 (2002)

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Energy-based limit conditions for transversally isotropic solids

K. Kowalczyk, J. Ostrowska-Maciejewska

Arch. Mech. 54 (5-6), 497-523, 2002



Using an example of transversal isotropy, the limit condition having an energy interpretation for anisotropic bodies proposed by J. Rychlewski [11] has been illustrated. Transversal isotropy is characterized by the highest degree of symmetry, for which the spherical tensor is not any more the eigenstate of the compliance tensor C. In the case when the spectral decomposition of the compliance tensor C is taken as a main energy-orthogonal decomposition, the limit condition representing a generalization of the Maxwell-Huber-Mises condition is obtained. For a prescribed form of the limit tensor H, the Mises condition is presented in the form of a sum of elastic energies corresponding to uniquely defined energy-orthogonal parts of stress with certain weights, representing the limiting values of those energies. The effect of Burzyński's condition on the form of anisotropy and on the limit condition is discussed. Experimental tests are proposed which could be useful in determining the physical parameters describing the transversal isotropy.

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