Damage of a structure under multiaxial dynamic inertial loading: A lumped damage approach

Extracting model parameters from experiments mimicking earthquake loading conditions is of interest to better design civil engineering structures. In the present case, the challenge is to identify the complex response of a notched section of a structure described as a beam assembly, using a complete 3D description that requires a 6 × 6 stiffness matrix for the simple case of an elastic behavior, while here one addresses the presence of a notch or crack which opens or closes along the loading. A shaking table with an earthquake-like motion in one dimension was used to load the structure. The full 3D kinematics of the structure was measured using a pair of high-speed cameras, and stereocorrelation. The displacement field allows the discontinuity of the generalized displacements at the notch root to be characterized. The deduced acceleration field gives access to the generalized forces in the structure, and, in particular, at the notch cross section. Relating generalized forces to generalized displacements discontinuity is the objective of the present study. A POD analysis of either the loading (generalized forces) or response (generalized displacements) gives a natural access of the complexity of loading experienced by the structure. Additionally, the POD analysis provides a direct access to the identification of the local elastic response (independently for the open and closed notch configuration). Identification finally appears as a mere projection of the force signal onto the temporal basis of the displacement or reciprocally. Because of the inertial loading of the structure, a full 3D characterization of the kinematics as enabled by stereocorrelation offers a very simple framework, which is the focus of the present paper, for the identification of elastic properties.