Abstract
The overall behaviour of a damaged viscoplastic material under axisymmetric loading is addressed in this paper. A linear viscous matrix containing aligned spheroidal cavities is first considered. Its overall behaviour is estimated by means of a differential scheme. The damage-induced morphological anisotropy, due to the shape of the voids, is then analyzed. It is shown to be significant even at low volume fractions of cavities ( ƒ < 0.05 ), when the latter are prolate or oblate. These results are then used to predict the behaviour of a nonlinear viscous matrix containing aligned spheroidal cavities, by means of a variational principle proposed by Ponte Castañeda (1991). Two types of nonlinear matrix behaviour are considered: a power law corresponding to metal forming at moderate strain rates and a linear law with nonzero intercept suited to high strain rates.The constitutive equations of such nonlinear damaged materials have been used in a companion paper in order to study the influence of matrix compressibility on the growth of a spheroidal cavity during straining.
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