A three-body potential peridynamics frame element analysis

Purpose A peridynamic (PD) frame element is presented to obtain the numerical solutions of the three-body potential (TBP) PD model implicitly within the finite element analysis (FEA) framework. Design/methodology/approach The bond vector described by the TBP PD model is treated as a PD frame element, namely, a TBP PD frame element, due to its mechanical similarity with a frame element in FEA, based on which the element stiffness matrix can be constructed symmetrically. The procedures of storing element connectivity and assembling the global stiffness matrix are completely consistent with those in FEA. And the resulting simultaneous equations can be solved by the robust numerical methods in FEA. Findings For problems under quasi-static loading conditions, the elastic deformation solutions can be implicitly computed by the proposed numerical method immediately and the simulation processes can be continued in the presence of damage evolution by transforming the implicit scheme to an explicit scheme, i.e. the implicit–explicit transition method. Two numerical examples are performed to validate the applicability of the proposed numerical method. Originality/value The study constructs a numerical method for solving the TBP PD model implicitly within the FEA framework, aiming to achieve the solution immediately before the onset of initial failure; therefore, it improves the computational efficiency especially for the problems under quasi-static conditions.