The modeling of fracture in solids remains a subject of research interest despite the various techniques developed along the last decades. Essentially, there are two main mathematical descriptions for fracture: the discontinuous approach, where new cracks are described by generating new surfaces to be tracked on the domain; and the continuous approach, where the surface fractures are diffused across a fracture domain and described by one or more continuous variables. Among the continuous approaches, phase field models have been widely used because they are capable of identifying crack initiation and tracking the growth of multiple cracks as well as their orientation, location, merging and bifurcation. We developed a non-variational phase field model that uses a fourth-order degradation tensor as the phase field variable, instead of a set of scalar damage variables. Since this degradation tensor is not directly a damage variable in the model, it is not necessary to choose a degradation function. It is defined as an internal variable whose evolution equation is obtained by thermodynamical arguments in terms of the free-energy and the pseudo-potential of dissipation being considered, directly degrading the elasticity of the material. In this work, we present the main features of our model and how its parameters are adjusted to nucleate and propagate fractures taking into account the failure mechanisms of brittle materials. Results for isotropic and orthotropic materials are presented and compared with experiments.