Mixed dimensional modeling of reinforced structures

Using thin reinforcements is a common way to strengthen structures, as in reinforced concrete for example. From a numerical point of view, dealing with these reinforcements is tedious, because of their diameter which is usually small compared to the characteristic dimensions of the structures, therefore requiring very fine meshes to represent them accurately. In this paper, a new approach allowing to mix a volumic and a lineic modeling of the reinforcements is proposed. Fine meshes with a volumic representation of the reinforcements are used in the zones of interest of the structure, whereas coarser meshes associated to lineic elements are used in the rest of the structure in order to decrease the computing times. A methodology to ensure the transition between both modeling is proposed, so that the results in the zones of interest are similar to the results that would be obtained with a full volumic representation of the reinforcements. The efficiency of the method is illustrated on several examples, involving linear elasticity and plasticity.