Combined explicit and implicit algorithms for dynamic problems using the numerical manifold method

The efficiency and accuracy are usually regarded as two general indices to check capability of a numerical method with respect to the time integration. The traditional numerical manifold method (NMM) employs implicit scheme to obtain high computational accuracy, but the efficiency is relatively low, especially when the iterations of contacts are involved. In this paper, the temporal coupled explicitimplicit (E-I) algorithm is proposed, in which the time integration schemes, transfer algorithm and contact algorithm are studied, respectively. A few numerical examples are simulated using the proposed coupled algorithms, in which one calibration example is studied with respect to the coupled temporal based on the cover system. The simulated results are well agreement with the implicit and explicit algorithms simulations, but the efficiency is improved evidently. It is predicted that the proposed couple E-I algorithm can be applied for larger scale engineering systems to combine the merits of both the implicit and the explicit algorithms of the NMM.