A stable non-ordinary state-based peridynamic model for laminated composite materials

Non-ordinary state-based peridynamics (NOSBPD) has instability issue due to zero-energy modes during nodal integration. A zero-energy mode controlling scheme of NOSBPD for laminated composite materials is derived by using the linearized bond-based peridynamics, which forms a stable force state formulation corresponding to the non-uniform deformation. The proposed controlling scheme does not include any controlling parameter to avoid the complex parametric adjustment. A critical stretch continuously varying with the angle between fiber and bond directions is further proposed for the failure analysis of laminated composite materials with arbitrary fiber angles. The improved NOSBPD model adopts the explicit integration method to solve static problems. Several numerical examples are conducted to validate the proposed scheme suppressing the oscillation caused by zero-energy modes.