Numerical modelling of compressible hyperelasticity via smoothed state-based peridynamics

A simply and effective method, smoothed state-based peridynamics, is proposed to simulate the large deformation and fracture behaviors of general compressible hyperelasticity. The proposed method is developed from the state-based peridynamics, which can be defined directly from the given classical model by a corresponding deformation gradient. The handling way of modelling general hyperelastic material through the proposed method is described detailedly in this paper. The compressible Neo-Hookean model, density solution and other numerical technology are investigated. Some popular benchmark problems of hyperelasticity are solved successfully, including the Inflation of a hollow spherical ball, compressed cuboid, pinched cylinder and the elastomer fracture problems.