Penalty force stabilization method for elasto-plastic correspondence models in peridynamics

Zero-energy modes are a challenge in non-ordinary state-based peridynamics. This work extends a penalty force approach to stabilize such models in both elastic and elasto-plastic simulations. The method penalizes nonuniform deformation directly through a tangent-modulus-based correction that adapts to the evolving material state. To evaluate its performance, we introduce two novel zero-energy mode measures — nodal and global nonuniform strain. We compare the method with first- and second-order bond-associated formulations in small and finite strain regimes and assess the influence of power-law, Gaussian, and uniform weight functions. In small strain tests, the penalty force method matches analytical solutions with displacement errors below 10 ⁻⁹ with negligible zero-energy mode measures. In finite strain plasticity, the method converges reliably, reproduces finite element and experimental stress–strain responses, and maintains global displacement errors below 10 ⁻⁴. It shows low sensitivity to the choice of a peridynamic weight function. The penalty force method requires only one deformation gradient evaluation per node, avoids tuning parameters, and suppresses zero-energy artifacts to negligible levels. The results show that it provides a stable and efficient alternative for correspondence-based peridynamic simulations across a wide range of deformation regimes.