Fracture Simulation Using an Elasto-Viscoplastic Virtual Internal Bond Model With Finite Elements

A virtual internal bond (VIB) model for isotropic materials has been recently proposed by Gao (Gao, H., 1997, “Elastic Waves in a Hyperelastic Solid Near its Plane Strain Equibiaxial Cohesive Limit,” Philos. Mag. Lett. 76, pp. 307–314) and Gao and Klein (Gao, H., and Klein, P., 1998, “Numerical Simulation of Crack Growth in an Isotropic Solid With Randomized Internal Cohesive Bonds,” J. Mech. Phys. Solids 46(2), pp. 187–218), in order to describe material deformation and fracture under both static and dynamic loading situations. This is made possible by incorporating a cohesive type law of interaction among particles at the atomistic level into a hyperelastic framework at the continuum level. The finite element implementation of the hyperelastic VIB model in an explicit integration framework has also been successfully described in an earlier work by the authors. This paper extends the isotropic hyperelastic VIB model to ductile materials by incorporating rate effects and hardening behavior of the material into a finite deformation framework. The hyperelastic VIB model is formulated in the intermediate configuration of the multiplicative decomposition of the deformation gradient framework. The results pertaining to the deformation, stress-strain behavior, loading rate effects, and the material hardening behavior are studied for a plate with a hole problem. Comparisons are also made with the corresponding hyperelastic VIB model behavior.