Embedding structures in continua: linear models and finite element discretizations

Abstract: This work describes models and numerical approximations that describe the mechanical behavior of deformable continua with embedded structural members, such as rigid bodies, beams, shells, etc. The continuum formulation extends an idea first presented in the context of the Arlequin method and constrains the kinematics of the two types of bodies to be compatible in the energy sense. In the article, we exploit the shared similarities of all structural theories to introduce a general framework for energetically coupling the latter with continua. In addition, we show that the problems, as well as their finite element approximations, are well-posed. Numerical examples of bodies with inclusions, fibers, and embedded surfaces are provided to illustrate the generality and robustness of the approach.