Finite element method of bond-based peridynamics and its ABAQUS implementation

Abstract Based on the principle of minimum potential energy, the peridynamic finite element method (PDFEM) is presented, in which the peridynamic (PD) multi-bond element stiffness matrix and the unbalanced force vector are established. An adjusting technique of PD element stiffness matrix is introduced to realize sharing of physical information at joint points between PD elements and classical continuum mechanics (CCM) elements in a unified finite element framework. Applying PDFEM, a new PD element type can be developed through UEL subroutine in ABAQUS to model fracture and damage in the light of PD theory and couple PD grids with CCM meshes. The numerical examples illustrate the availability of PDFEM in ABAQUS, which opens up the prospect of application of peridynamics to practical engineering analysis.