A bond-based peridynamic model for geometrically exact beams

Abstract

A bond-based peridynamic model is established for geometrically exact beams under Simo-Reissner hypothesis. In the framework of the special Euclidean group, a set of nonlocal deformation measures are obtained from the relative position of two cross-sectional centroids and the relative rotation of cross-sectional frames. These measures capture the tension, shearing, bending and torsion of the bond, providing accurate descriptions under conditions of uniform material strains. The peridynamic strain energy density is formulated accordingly. Linear momentum and angular momentum equations are derived from Hamilton’s principle. Several static and dynamic numerical examples are provided to verify the proposed model. The damage analysis capability of the model is exemplified in capturing the dynamic fragmentation of beams.