The paper builds a stable variational formulation for the non-ordinary state-based peridynamics (NOSB-PD). Firstly, a new force state vector is reformulated by introducing the first Piola-Kirchhoff stress in continuum mechanics. The consistency of the new governing equation of the proposed pridynamic model and classical continuum mechanics is proved. Secondly, a stable variational formulation of non-ordinary state based peridynamics is developed to unify the boundary conditions in peridynamcis and continuum mechanics. The zero mode oscillations of non-ordinary state based peridynamics is also eliminated by penalty method in numerical implementation. Numerical examples are illustrated to validate the proposed method. Numerical solutions obtained by the proposed method also indicate that the proposed method can well capture the general nonlinear behavior of solid materials.
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