A higher-order stress point method for non-ordinary state-based peridynamics. (August 2020) - Cui, Hao; Li, Chunguang; Zheng, Hong
Highlights: The proposed stress point method does not require any additional parameters. It can be effortlessly applied to various cases without the need for extensive numerical tests to optimize the parameters. The proposed method presents much better accuracy and robustness than other control methods under various weight functions and horizon ratios. It can also mitigate the errors caused by surface effects. The proposed stress point method shows tiny deviations and period elongations in the dynamic calculation. The proposed stress point method is still appropriate to solve the crack propagation and branching problems, since it still leverages the non-local property of the non-ordinary state-based peridynamic. Abstract: A higher-order stress point method for non-ordinary state-based peridynamic (NOSB-PD) is presented. The stress point is interpolated by its adjacent original nodes, where the second-order peridynamic derivatives are determined according to the peridynamic differential operator. By introducing the higher-order derivatives, the proposed stress point method could efficiently suppress the zero-energy mode oscillations. In contrast to other available control methods, the stress point method has better accuracy and stability, and much fewer period elongations in the dynamic calculation. More importantly, the method does not require any additional parameters and it can mitigate the errors arising from the surface effect as well. Furthermore, the proposed method can easily solve the discontinuities problems since it leverages the non-local property of the NOSB-PD. As demonstrated in the last two examples, the phenomena of crack propagation and branching are successfully captured by the proposed stress point method.