Peridynamic formulations enriched with bond rotation effects

Limited by its fixed effective Poisson's ratio, the bond-based central force peridynamic theory fails to properly describe shear deformation of solids. In this paper, the classical peridynamic theory is enriched with bond rotation effect and reformulated in the thermodynamic framework with emphasis on mathematical derivation of the micro elastic moduli. The macroscopic strain energy of the peridynamic system is completed by involving the local shear stain for both 3D and 2D problems. In each case, the effective elasticity tensor is derived rationally and compared to the results of continuum solid mechanics, which allows relating the micro stiffness parameters to the common macro elastic constants. For validation, numerical tests are performed to assess the prediction of Poisson's ratio. It is shown that the enriched peridynamic model is capable of removing to a large extent the limitation of Poisson's ratio and consistent from the viewpoint of strain homogenization.