A ZERO-ENERGY MODE CONTROL METHOD OF NON-ORDINARY STATE-BASED PERIDYNAMICS

Non-ordinary state-based peridynamics suffers from zero-energy mode due to nodal integration. Instabilities of displacement, stress and strain fields are induced and they will affect the computational precision or even ruin the results. Thus, the zero-energy mode needs to be suppressed. However, so far there are no effective zero-energy mode control methods. To address this issue, this work proposes a general and high efficient control method. The specific form of the elastic coefficient tensor corresponding to the nonuniform part of deformation is proposed according to linearized bond-based peridynamic theory in which the difference of micromodulus of different bonds is considered. The force state incorporated by nonuniform deformation is derived through minimum potential principle. The stabilized force state is arrived at by adding the nonuniform force state to the peridynamic force state. The linearlized bond-based peridynamics based stabilized correspondence material model is established and applied to the simulation of the elastic properties and damage process of the plate with a circular hole and the three point bend specimen. The numerical results indicate that the proposed model is effective for controlling zero-energy mode in non-ordinary state-based peridynamics. In comparison with existing zero-energy mode control methods, it has definite physical meaning and the complicated process of adjusting parameters is avoided. Hence, the computational efficiency is evidently improved.