An improved stabilized peridynamic correspondence material model for the crack propagation of nearly incompressible hyperelastic materials

An improved stabilized peridynamic correspondence material model (IS-PD-CMM) is proposed in this paper to simulate the crack propagation of nearly incompressible hyperelastic materials. A shape-associated micromodulus as the correction coefficient (penalty factor) is introduced into the modified force state in the IS-PD-CMM to control the deformation caused by nonuniform deformation vector state. Different from the conventional stabilization method, the penalty factor in the IS-PD-CMM is only related to the material properties and does not require the parameter calibration. In addition, an equivalent strain function is introduced into the IS-PD-CMM as the failure criterion for the nearly incompressible hyperelastic material, where the nonlocal damage of the model is determined by calculating the ratio of bond breakages of material particles. The high accuracy and adaptability of the IS-PD-CMM are demonstrated by three representative examples including the infinitesimal deformation of linear elastic materials and the finite deformation of hyperelastic materials. Finally, the in-plane tensile fracture behavior and the out-of-plane tearing fracture behavior are simulated and analyzed to illustrate the good performance of the IS-PD-CMM in predicting the crack propagation of nearly incompressible hyperelastic materials.