Ceramics-Silikáty 47 (1) 1-7 (2003)

EFFECTIVE ELASTIC PROPERTIES OF ALUMINA-ZIRCONIA COMPOSITE CERAMICS - PART 1. RATIONAL CONTINUUM THEORY OF LINEAR ELASTICITY

W. Pabst, E. Gregorová

In this first paper of a series on the effective elastic properties of alumina-zirconia composite ceramics the theoretical framework in which these properties arise, the linear theory of elasticity, is presented in an unconventional way. A rational continuum approach is chosen, but without the formal details necessary for a mathematically strict formulation. Using a referential (Lagrangian) formulation as long as useful, the constitutive equation for the stress tensor is derived for isotropic as well as for anisotropic materials. Particular emphasis is laid on the distinction between the (geometrical) linearization of the kinematic measures (strain tensors) and the (physical) linearization of the constitutive equation (material model). Recent results occurring in the literature are mentioned. Some standard textbook formulae are recalled for the purpose of easy reference in the subsequent papers of this series.

Keywords: Alumina-zirconia composite ceramics, Effective elastic properties, Linear elasticity, Rational mechanics.