A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process

This paper presents a non-ordinary state-based peridynamic formulation that can be applied to the metal machining analysis. The new formulation is first derived by utilizing the technique of mixed local/nonlocal gradient approximations to enforce the contact and essential boundary conditions associated in modeling the machining process. A stabilized peridynamic force vector state is then introduced to suppress the zero-energy modes which show up as the result of particle integration of the state-based peridynamic formulation. The introduction of the stabilized peridynamic force vector state eliminates the need of an estimation of the force–spring-like bond forces and leads to a consistent computation of peridynamic equations of motion using a general constitutive model. Finally, a continuum damage model is incorporated into the present state-based peridynamic formulation together with a decomposed stabilized approximate deformation gradient based on a neighbor particle reconstruction scheme to model the ductile metal failure and to maintain a well-defined geometric mapping in finite deformation. Three numerical benchmarks are analyzed to demonstrate the effectiveness and regularization of the present method for simulating the metal machining process.