A quasi-nonlocal coupling method for bond-based peridynamics with classical continuum mechanics

PurposeThe purpose of this paper is to propose a novel quasi-nonlocal coupling of the bond-based peridynamic model with the classical continuum mechanics model to fully take advantage of their merits and be free of ghost forces.Design/methodology/approachThis study reconstructs a total energy functional by introducing a coupling parameter that alters only the nonlocal interactions in the coupling region rather than the whole region and a modified elasticity tensor that affects the local interactions. Then, the consistency of force patch test is enforced in the coupling region to completely eliminate the ghost force in a general energy-based coupling scheme. For a one-dimensional problem, these coupling parameters are further determined through an energy patch test to preserve the energy equivalence or through an l1-regularization. And, for a two- or three-dimensional problem, depending on the existence of a solution to the discretized force patch test, they are determined through an l1-minimization or l1-regularization.FindingsOne- and two-dimensional numerical examples under affine deformation have been conducted to verify the accuracy of the quasi-nonlocal coupling method, which exhibits no ghost force. Moreover, the coupling model can reproduce almost the same deformation behaviors of points near the crack for a cracked plate under tension as that from a pure peridynamic model, the former with a rather low computational cost and an easier application of boundary conditions.Originality/valueThis work is aiming at getting over long-standing ghost force issues in the energy-based coupling scheme. The numerical results from the cracked plate problem are exhibited promising extension to dynamic problems.

On the Effect of Ghost Force in the Quasicontinuum Method: Dynamic Problems in One Dimension

Numerical error caused by “ghost forces” in a quasicontinuum method is studied in the context of dynamic problems. The error in the discrete W1,∞ norm is analyzed for the time scale (ε) and the time scale (1) with ε being the lattice spacing.