On a concept of directional damage gradient in transversely isotropic materials

Of interest in this paper is the description of damage evolution in anisotropic materials where it is mainly observed that damage is in general strongly influenced by the anisotropy itself. More specifically, transversely isotropic materials such as unidirectional fibre-reinforced composites and sedimentary rocks are under focus. The approach we use is based on continuum damage mechanics where the damage gradient quantity is involved. In this work, this latter is oriented toward privileged directions where damage will most probably propagate. This task is accomplished by adopting the integrity-basis formulation where the directional damage gradient is embedded and, otherwise, allows for a neat decomposition of the material response into directional, transverse, and pure shear contributions. This offers an appealing framework where damage characterization can be easily formulated. Damage can be chosen to be governed by transverse strains, by in-plane pure shear strains, or by both of them. One can then speak, respectively, of a mode-I, mode-II, or mixed I/II damage mechanisms if use is made of the terminology adopted in fracture mechanics. On the numerical side, an algorithmic design is proposed for an easy implementation within the context of the finite element method. A set of numerical examples is then presented to explore qualitatively the potential of the proposed framework.