Thermodynamically Consistent Variational Approach for Modeling Brittle Fracture in Thick Plates by a Hybrid Phase Field Model

Abstract

In this work, we propose a thermodynamically consistent phase-field model for the brittle fracture analysis of thick plates. A hybrid model, which is fast and accurate, is proposed for the phase-field modeling of fracture in thick plates. Reddy’s third-order shear deformation theory (TSDT) has been employed to capture the transverse shear deformation effects in thick plates. Governing equations are derived by seeking the minimization of the free-energy functional. A staggered solution algorithm with arc length control is used to solve the governing equations within the finite element framework. The nucleation and propagation of cracks in the thick plates subjected to uniformly distributed load is presented. The mechanical response corresponding to phase-field models based on both the classical plate theory and TSDT has been compared for the case of thick plates and a significant difference between these two models is observed. Parametric studies have been carried out to illustrate the effects of boundary conditions, shear deformation, and the mesh size.