A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to account for the reinforcements, while still being able to capture complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.