Implementation of a new strain split to model unilateral contact within the phase field method

A new orthogonal decomposition of strain tensor into compressive/tensile parts is implemented in
the phase eld model to maintain the physical crack propagation behavior. An e cient operator split
scheme with the introduction of projection tensors is proposed to facilitate the numerical implementation
of the new spectral decomposition. Formulations of the present failure model accounting the unilateral
contact condition are given analytically and explicitly, which implies an extremely robust computational
model. In particular, compared to the existing models, the present framework is general, which can
be applied to all possible elastic behavior, such as isotropic, orthotropic, and totally anisotropic
elastic material. A detailed comparison of fracture response predicted by the present models with the
literature approaches is then provided. It is shown that orthogonal decomposition is able to simulate
various failure scenarios. Especially, this formulation shows a very remarkably prediction compared to
experimental observation for the case of compression load.