NL-SBFEM: A pure SBFEM formulation for geometrically and materially nonlinear problems

Abstract

In the context of numerical methods for solving partial differential equations, the research presented in this article introduces a pioneering Scaled Boundary Finite Element Method (SBFEM) formulation designed to tackle geometrically and materially nonlinear problems. The novel formulation, named NL-SBFEM, utilizes the deformation gradient and the first Piola–Kirchhoff stress, and is distinguished by its purity as a standalone SBFEM formulation without the need for integration with other numerical methods, thereby preserving all the inherent advantages of SBFEM. This research thoroughly validates the NL-SBFEM, demonstrating its accuracy and reliability when compared to analytical solutions and results obtained using conventional numerical methods. The method accommodates well-established hyperelastic material models while benefits from the ease of integrating new hyperelastic material models within the framework. With its capability to address nonlinear problems, the proposed development can introduce SBFEM as an alternative to FEM in the field of computational biomechanics.