A bond-augmented stabilized method for numerical oscillations in non-ordinary state-based peridynamics

Abstract

Non-ordinary state-based peridynamics has been widely used due to its capability to combine non-local theory with conventional material models. However, it suffers from numerical oscillations in calculations. The fundamental reason is that the approximate deformation gradient causes the non-unique mapping between deformation states and force states. To address this issue, the present work utilizes the penalty function method to reformulate the deformation gradient for each individual bond. The force state corresponding to a single bond is then constructed based on this newly developed bond-augmented deformation gradient in the framework of least action principle. This bond-augmented force state has a strong dependence on the deformation of that particular bond, thus well resolving the non-unique mapping issue. The resulting bond-augmented stabilized method does not introduce an additional local bond-associated horizon or extra force state termed as that in the previous studies and does not require tedious parameter adjustments. Numerical results show that the proposed bond-augmented stabilized method can significantly remove numerical oscillations and have good accuracy and convergence. Moreover, the proposed bond-augmented stabilized method is also proved to readily capture crack paths.