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A theoretical model is presented suitable for the description of the damaging
process in brittle materials. The model is based on damage mechanics: it features
two second order symmetric damage tensors, representative of surface damage
induced by tensile and compressive strains activates at different orientations to the
principal strain directions, according to the sign of the principal strain which
attains a damage threshold, and a scalar variable representative of volumetric
damage. In this model, two separate damage variables, one for tension and the
other for compression, allow to model the non-symmetric behaviour and the
unilateral effect. Damage activation is governed by two different loading
functions evolving with nonreciprocal hardening and softening. The capabilities
of the model in describing the mechanical response of material elements subjected
to non-proportional stresses are illustrated.