using a specific additive decomposition\(\psi_{e}={\psi_{e}}^{+}+{\psi_{e}}^{-}\)of the elastic energy
density \(\psi_{e}\), in contrast to Eq.(6), the degradation of only the
positive energy part is allowed herein, whereas the negative part
remains undegraded. The \({\psi_{e}}^{+}\) represents tensile
contributions and \({\psi_{e}}^{-}\) represents compressive
contributions to the stored elastic strain energy. This modification
provides a mechanism for distinguishing states of strain under which
cracks will growth. In Contrafatto29 the trace of the
elastic strain tensor was used as separating interface. This approach
has also been followed by Faria30 and
Ambati31. In such a way the elastic energy takes
different forms according to the sign of the elastic strain
tensor.28