Implementation of the Zienkiewicz–Pande Model into a Four-Dimensional Lattice Spring Model for Plasticity and Fracture

Abstract

Plasticity and fracture problems have always been hot topics in numerical methods. In this work, a universal implementation procedure for the elasto-plastic constitutive model is developed in the four-dimensional lattice spring model (4D-LSM), in which the Jaumann stress rate is incorporated to exclude the influence of the rigid rotation in the particle stress, expanding the ability of 4D-LSM to deal with large elastic deformation problems by its own to large plastic deformation problems. As an example, the Zienkiewicz–Pande (ZP) constitutive model is implemented. Several numerical examples are carried out to check the performance of the implemented model. Through a comparison with analytical solutions, available experimental data, and other numerical results, the stability of the developed plastic framework and the correctness of the stress calculation scheme are verified. Meanwhile, numerical results show that the developed code is capable of solving elasto-plastic large deformation problems. With the advantage of 4D-LSM in handling fracture problems, the ability of the embedded model to solve plastic fracture problems is verified with a simple maximum deformation failure criterion.