Geometrical Nonlinear Extension of Extended Bond-Based Peridynamic Model

Abstract:

The extended bond-based peridynamic （XPD） model resolved the limitation of fixed Poisson’s ratio in the classical model for small deformation problems. In this paper， a novel implementation using the finite deformation formulation is proposed to deal with geometrical nonlinear problems. The rotation of solid is calculated by the polar decomposition of the deformation gradient tensor derived from the least square fitting of the local displacement field. Therefore， the deformed part of the bond deflection can be separated from the general displacements， and then correct large deformation predictions can be obtained by integrating each bond force of the deformed system. Several benchmark studies are presented to demonstrate the predictive ability of the proposed model.

Key words:extended bond-based peridynamic (XPD) model;large deformation;geometrical nonlinearity;polar decomposition