Influence functions for accurate representation of bond deformation in discrete modeling

Continuum-like nonlocal deformation gradients have been constructed based on discrete simulation results. In this paper, the accuracy of the nonlocal deformation gradient based on different influence functions is examined for both representing material point deformation and mapping bonds. A new class of parameterized influence functions that accounts for both bond relative length and angle (with respect to a target bond) is proposed. Numerical example shows great accuracy of the nonlocal deformation gradient using the proposed influence functions in both representing material point deformation and mapping bonds. It is concluded that the proposed influence functions can be used to accurately capture bond-level continuum-like measures.