A coupling extended multiscale finite element and peridynamic method for modeling of crack propagation in solids

Abstract

A coupling extended multiscale finite element and peridynamic method is developed for the quasi-static mechanical analysis of large-scale structures with crack propagation. Firstly, a novel incremental peridynamic (PD) formulation based on the ordinary state-based PD model is derived utilizing the Taylor expansion technique. To combine the high computational efficiency of the EMsFEM and advantages of dealing with discontinuous problems of the PD, a coupling strategy based on the numerical base function is proposed, in which the displacement constraint relationships between the coarse element nodes of the EMsFEM and the material points of the PD among the coupling domain are constructed by the numerical base functions and are represented by a coupling strain energy function using the Lagrange multiplier method. Then, a bilinear softening material model is adopted to describe the damage and failure of the bond, and the incremental-iterative algorithms are applied to obtain the steady-state solutions. Finally, several representative numerical examples are presented, and the results demonstrate the accuracy and efficiency of the proposed coupling method for the quasi-static mechanical analysis of large-scale structures with crack propagation. Comparing with the single EMsFEM and PD method, the present coupling method can reduce much computational cost and well deal with crack problems, simultaneously.