**4. Conclusions**

Based on the concept of the EDE, the DEFEM is extended for simulating translational and rotational motions and small deformations of particles.

When the particle contacts other particles, it is assumed that there is a group of EDEs on the outermost boundary element of the particle. The updated Lagrangian finite element method is used to obtain the coupling solution of internal stress and the overall motion of particles in the DEFEM. It is necessary to decompose the overall displacement of particles into three parts: the translational and rotation displacement and the deformation displacement. The concept of template particles is proposed in the whole simulation process, which only moves and rotates without deformation. The translational displacement and rotation displacement of the template particles can be obtained by using the DEM. The difference between the updated coordinates of the particles and the template particles is considered the deformation displacement in the DEFEM. And it is used to calculate the stress distribution of particles and the internal force of the node. Therefore, this method has a wide range of applications, such as the simulation of non-spherical particles.

The accuracy of this method is proved by the software validation. The application of the DEFEM in the particle accumulation process is given. The motion characteristics and deformation of particles are discussed, and the stress distribution and force chain structure in particle accumulation is obtained in this paper. This paper extends the application of the DEFEM in translational and rotational motions of particles with deformations. This new method can also be used to solve multi-physical field coupling problems such as thermal and mechanical coupling in the future.
