Modeling of brittle fracture in thick plates subjected to transient dynamic loads using a hybrid phase field model

In this work, we propose a hybrid phase field model for the brittle fracture analysis of thick plates subjected to transient dynamic loads. Shear deformation effects which play important role on the behavior of thick plates are captured by using Reddy’s third-order shear deformation theory. The proposed model preserves the linearity of the elastic equilibrium equation within the staggered solution approach and ensures the evolution of damage due to the tensile part of the strain energy. The governing equations of motion of the proposed model are derived by seeking the minimization of the free energy functional. These governing equations are solved in a finite element framework using a staggered solution algorithm. The proposed model is compared with the model with no tension–compression split. Both these models show different mechanical response of thick plates. Using numerical examples, the efficiency of the proposed model in predicting the nucleation and propagation of damage in thick plates subjected to transient dynamic loads is presented.