A novel numerical manifold method with derivative degrees of freedom and without linear dependence

A new high-order NMM is described in detail. The derivative degrees of freedom with physical meaning, which have been used in discontinuous deformation analysis (DDA), continue to be employed in the NMM. A new local displacement approximation, whose order is promoted, is suggested for the NMM. The local approximation makes the NMM get rid of the issue of the linear dependence (LD) and makes the NMM possess the substantive characteristic of a continuous stress field at the “star points”. An existing stress post-processing technology, which does not lead to a forfeit of the abovementioned essential characteristic, is reinvented to improve the stress accuracy of the displacement-based method. The recurrence formula of the initial stress matrix is also generalized and revised to adapt to the proposed NMM. Moreover, a simplified inhibition approach is presented to deal with the free expansion (FE) problem of manifold element. Several typical examples are given to demonstrate the effectiveness of the proposed NMM.