Identification of elastic property and loading fields from full-field displacement measurements

A method is introduced to identify simultaneously elastic properties and loading fields from a measured displacement field. Since the mechanical behavior of micro-electro-mechanical systems (MEMS) is governed by surface effects, this type of identification tool is thought to be of major interest. However, increasing the number of parameters to retrieve affects the redundancy necessary for an accurate identification. A finite-element formulation of a distance between measured and statically admissible (SA) displacement fields is shown to be equivalent to a standard least-squares distance to kinematically admissible (KA) fields if the used modeling is suitable. Any deviation from this equivalence is then the signature of a modeling error. Balancing the distance to KA and SA displacement fields allows one to retrieve unknown modeling parameters. This method is detailed on heterogeneous Euler–Bernoulli beams submitted to an unknown loading field and applied to experimental displacement fields of micro-cantilevers obtained with an electrostatic set-up. An elastic property field and a parameterized loading field are then identified, and the quality of the identification is assessed.