An implicit non ordinary state based peridynamics with stabilised correspondence material model for finite deformation analysis

This paper is devoted to the development of a stabilised implicit non-ordinary state-based peridynamics approach. We propose a geometrically nonlinear implicit approach focusing on quasi-static analyses. Since the construction of the Jacobian matrix is the most time-consuming step in conducting this nonlinear analysis, we formulate an analytical expression based on the equation of motion of non-ordinary state-based peridynamics to ensure optimum convergence of the global residual force. The implicit formulation can adopt fairly large time increments, making it a good choice for analyses of finite deformation. Another important extension presented in this paper is the modification of the correspondence material model to remove zero-energy mode instabilities and reduce the spurious oscillations, as proposed by Silling (2017). The derivative of the additional stabilisation term with respect to displacement is …