A neural network peridynamic method for modeling rubber-like materials

Abstract

Peridynamic (PD) is a powerful tool for simulating the large deformation and failure process of many types of materials. However, its use in modeling rubber-like materials is limited due to the complex constitutive nature of the material, and low efficiency and numerical oscillation caused by PD. To address this issue, a neural network (NN) non-ordinary state-based peridynamics (NOSB PD) method is developed to model the large deformation and failure behavior of rubber-like materials. This method is free of the zero-energy modes, and can significantly improve the computational efficiency. Unlike the traditional NOSB PD method that formulates the force density vector based on the deformation gradient, this method uses a deep NN to map the bond related quantities to the force density vector. The accuracy and efficiency of the proposed method are demonstrated through a series of numerical examples. Additionally, this method can be applied to various hyperelastic materials for which analytical constitutive models exist.