A novel Newmark-based method applied to an anisotropic damage phase field model

Resumo

We present an anisotropic phase field model for fracture that uses a fourth-order tensor field to describe
the damage that degrades the material’s elasticity. The governing equations were obtained based on the use of the
principle of virtual power (PVP), the balance of energy and the Clausius-Duhem inequality for the entropy. Small
deformation isothermal case was considered. A failure criteria is also presented to define fracture and to establish a
numerical criterion for damage irreversibility. The model was implemented using the finite element method (FEM)
for the case of plane stress. Results are presented using two time integration methods for the motion equation: the
standard and a modified Newmark method. The backward Euler method was used for the damage equation. Time
efficiency and accuracy of results were compared for both Newmark methods.