The first part of the paper deals with the introduction of a tensorial damage measure. The author generalizes a concept of Y. N. Rabotnov [Creep problems in structural members (1969; Zbl 0184.518)] according to which the damage is characterized by the fraction of the apparent cross- sectional area being occupied by voids and fissures. It is presupposed that in any material point there exist three mutually perpendicular principal directions with assigned cross-sections that exhibit generally different area fractions of damage or ”continuity”, resp. Therefore the linear mapping that relates the vectors of the apparent and the effective area is described by a symmetric tensor of continuity. Thus the corresponding tensors of the Cauchy-stress and the net-stress are related by the same continuity tensor, in a similar manner as the Cauchy-tensor and the first Piola-Kirchhoff-tensor of stress are connected in continuum mechanics.
The second part of the publication presents the construction of constitutive equations relating the strain velocity with the tensors of stress, of continuity and of initial anisotropy. Several more or less intricate response functions are formulated and reduced by the means of representation theory. The suggested concept of damage or continuity tensor has a comprehensible physical base and may surely lead to new results. The development of voids and fissures can be imagined to be accompanied not only by pure stretching of material but by an additional rotation, too. In this more general case the tensor of continuity must be non-symmetric.