A modified axisymmetric ordinary state-based peridynamics with shear deformation for elastic and fracture problems in brittle solids

Although axisymmetric problems are neither the plane stress nor plane strain problems, they can be solved in the two-dimensional (2-D) domain for convenience. In this paper, a modified axisymmetric ordinary state-based peridynamic model considering the shear deformation for linear elastic solids is proposed. By subtracting the rigid body rotation part from the total deformation, the shear deformation of a bond is considered. The bond force density vector is derived indirectly by equalizing the PD energy density and the classical strain energy density. The fictitious density in adaptive dynamic relaxation (ADR) method is derived. Two new damage criterions based on the maximum stretch/deviatoric strain are proposed. Several axisymmetrically three-dimensional (3-D) numerical examples are performed in the computational domains, where the present numerical results are compared with the existing analytical solutions, the classical finite element numerical results and axisymmetric ordinary state-based peridynamic results. The numerical results demonstrate this proposed method can simulate the initiation and propagation of cracks very well under the axisymmetrical conditions, and it has more accuracy than axisymmetric ordinary state-based peridynamic model.