Finite Element Model for Curved Embedded Reinforcement

Abstract

The geometric relations required for an embedded finite element representation of generally curved reinforcing bars or prestressing tendons are developed. For practical reasons, the reinforcing layers are described in global coordinates, independently of the finite element mesh. An inverse mapping procedure is developed to transform global coordinates of points on the reinforcement layer into local natural coordinates in the parent element. The strain field in the layer is discussed, including a bond slip model. The principle of virtual work is used to derive the various element matrices. The procedure is successfully tested, using both regular and irregular meshes, on three test problems: a uniform strain field, and two versions of a quarter ring under external pressure.