A modified numerical manifold method for simulation of finite deformation problem

Abstract

• False solutions have been found when modeling finite deformation problems using the original NMM. • A new numerical manifold method for simulation of finite deformation is proposed. • The proposed method eliminates the errors caused by large rotation and large strain in the original NMM. With many people contributing to its modifications and advancements, the numerical manifold method (NMM) is now recognized as an efficient tool to solve the continuum–discontinuum coupling problem in geotechnical engineering. However, false solutions have been found when modeling finite deformation problems using the original NMM. Based on the finite deformation theory, a modified version of NMM is derived from the weak form of conservation of momentum and the corresponding traction boundary condition. By taking the dual cover system as the displacement approximation, the governing equations of the modified NMM are formulated. A comparison of the governing equations of the original NMM and modified NMM illustrates the reason that the original NMM is not suitable for simulation of finite deformation problems. Three numerical examples are investigated to verify the capability of proposed method to predict static and dynamic finite deformation response. Numerical results show that the modified NMM eliminates the errors caused by large rotation and large strain, and obtains a good agreement with analytical solutions and the finite element method.