An implicit Updated Lagrangian Fragile Points Method with a support domain refinement scheme for solving large deformation problems

Engineering structures may undergo large deformations, but simulating is still challenging for existing numerical methods, for example, the element-based methods struggle from the mesh distortion and the strong form particle-based methods exhibit tensile instability. This article aims on presenting a novel numerical method for large deformation simulations, which is named the implicit Updated Lagrangian Fragile Points Method (ULFPM). The point-based nature of the proposed method ensures immunity to mesh distortion, and its stability is guaranteed by its foundation on weak form formulations. For verifications, the proposed implicit ULFPM has been applied to several large deformation problems. For all the examples, the proposed method is able to provide reliable results with a good agreement with the reference results. Moreover, the implicit ULFPM performs better than the Finite Element Method to some extent for extremely large deformation problems. It is also discussed that the accuracy of the implicit ULFPM is improved significantly by using the support domain refinement scheme. The examples indicate that the proposed method can serve as a reliable tool for predicting the large deformations of structures in engineering practices.