AbstractThis work is motivated by the current numerical limitation in multiscale simulation of ductile fracture processes at scale down to the microstructure size and aims to overcome the difficulties in 3D complicated mesh generation and locally extremely large strain analysis (local mesh distortion). The proposed ‘conforming local meshfree approximation’ directly and exactly satisfies displacement compatibility on a non‐conforming assembly mesh. Local meshfree nodes, which can be freely placed and move on a finite element mesh, describe local large deformation. The improved accuracy on non‐conforming mesh, the exactness in geometry representation on a structured mesh, and the good tolerance to mesh distortion are demonstrated by numerical examples. Copyright © 2010 John Wiley & Sons, Ltd.