Finite element implementation of virtual internal bond model for simulating crack behavior

The virtual internal bond (VIB) model has been recently proposed to describe material deformation and failure under both static and dynamic loading. The model is based on the incorporation of a cohesive type law in a hyperelastic framework, and is capable of fracture simulation as a part of the constitutive formulation. However, with an implicit integration scheme, difficulties are often encountered in the finite element implementation of the VIB model due to possible negative eigenvalues of the stiffness matrix. This paper describes the implementation of an explicit integration scheme of the VIB model. Issues pertaining to the implementation, such as mesh size and shape dependence, loading rate dependence, crack initiation and growth characteristics, and solution time are examined. Both quasi-static and dynamic loading cases have been studied. The experimental validation of the VIB model has been done by calibrating the model parameters using the experimental data of Andrews and Kim [Mech. Mater. 29 (1988) 161]. The simulations using the VIB model are shown to agree well with the experimental observations.