Damage-augmented nonlocal lattice particle method for fracture simulation of solids

Fracture of solids, particularly for ductile metallic materials, typically involves elastoplastic deformation and associated damaging processes. This paper proposes a general damage-augmented nonlocal lattice particle method (LPM) to model this coupled behavior. The concept of interchangeability between particle-wise and bond-wise properties in LPM is first introduced and validated. It is shown that tensors can naturally represent material state variables, which is rarely seen in most lattice methods. A tensor-based return-mapping algorithm based on implicit integration is thus implemented to simulate J2 plasticity. Next, the damage-augmented LPM is proposed to properly simulate the material deterioration by combining LPM with a nonlocal damage evolution rule. The proposed method can handle the brittle fracture and pure elastoplastic deformation and simulate ductile fracture phenomena with moderately large time steps. The particle-size/lattice dependency issues of macroscopic mechanical responses are reduced under the proposed framework. Numerical examples of predicting the elastoplastic behavior of engineering structures with/without damage and fracture are provided. Several conclusions and limitations of the proposed method are also discussed.