A Deformation-Based Peridynamic Model: Theory and Application

This study presents a peridynamic model formulated using the micromodulus function and bond deformation. The model is derived by establishing energy equivalence between a modified virtual internal bond (VIB) and a peridynamic bond. To address surface effects in peridynamics, a stress-based correction method utilizing nodal stress is introduced, enhancing the model’s numerical accuracy. The model was implemented using an in-house Cython code and validated through the following numerical examples: a plate under traction, a plate with a hole under displacement boundary conditions, a uniaxial compression test on granite with a deformation-based mixed-mode bond failure criterion, and a comparison with an existing strain-based peridynamic model. For the plate under traction, the deformation-based method performed similarly to the strain-based model in the loading direction and better in the unloaded direction. The stress concentration obtained from the proposed model (240 MPa) near the hole in the rectangular plate simulation differed from FEM (252 MPa) by 4.7%. The granite test predicted a UCS of 111.88 MPa and a Young’s modulus of 20.67 GPa, with errors of 0.1% and 1.57%, respectively, compared to the experimental data.