A variational approach to embed 1D beam models into 3D solid continua

•Novel embedded beam models enabling the fully lateral coupling between 1D beam and 3D solid.•Beam and solid discretizations are fully independent each other.•Rigorous treatment of the theoretical aspects related to the lateral beam/solid interactions.•Good performance of the proposed EBM results. This contribution presents the variational foundations for the embedding of Euler–Bernoulli beams into 3D solid continua. The Embedded Beam Model (EBM) explicitly incorporates the geometry of the beam/solid interaction interface. This is achieved by introducing a displacement compatibility constraint along the entire beam/solid interaction surface, devised to model the adherence between two models, which posses different kinematical descriptions. The paper especially focuses on the theoretical aspects related to the lateral beam/solid interactions. The proposed variational model yields the Euler-Lagrange equations for the coupled problem, which are not standard because of the occurrence of interaction forces due to the kinematical constraints prescribed at the beam/solid coupling interface. Numerical strategies, based on the Finite Element Method (FEM), are proposed to handle the variational formulation at the discrete level. These numerical approaches feature no limitations regarding mesh generation for the solid domain and full coupling between beam degrees of freedom and solid kinematics is obtained in the present model. The proposed formulation is validated against the so-called Direct Numerical Simulation approach. The good performance of the proposed EBM strategy provides a solid groundwork for future improvements, yielding a methodology with strong potential for the analysis of reinforced structures.