Fracture analysis of hyperelastic membrane using bond-associated non-ordinary state-based peridynamics

Abstract

In this paper, a non-ordinary state-based peridynamics model (NOSB PD) has been proposed to simulate the large deformation and failure analysis of hyperelastic membranes. To account for the curving horizon of the membrane, a non-local membrane theory has been developed by approximating it as a flat surface and applying the plane stress assumption locally. Thus, the membrane structure is simulated using a single layer of material points, which simplifies implementation, improves efficiency, and avoids volume locking. The Gent model has been employed to simulate the hyperelastic material constitutively, as it has an elegant mathematical framework and can achieve the entire range of stretches. Furthermore, Bond-associate NOSB PD is utilized to overcome zero-energy modes without affecting the material properties. A modification has been addressed to overcome the boundary effect by adding a complementary force density to the boundary nodes. The accuracy of large deformation and incompressibility of the developed models are verified by the corresponding finite element analyses. Finally, the proposed method is demonstrated by presenting some benchmark examples, and the results illustrate the accuracy and efficiency of the proposed method for the large deformation, fracture, and off-plane tearing analyses of hyperelastic membranes.