Sensitivity analysis in kinematically incompatible models

A natural question that arises when working with the so-called kinematically incompatible models is about the positioning of the internal artificial boundary that splits the domain of analysis into the sub-domains for which the different, incompatible, models are established. Although the experience in modeling might provide an ad hoc solution to such matter it may also draw misleading conclusions. Here, the sensitivity analysis furnishes a systematic and reliable framework to study the impact of the positioning of the artificial boundary over the solution of the problem. In this sense, the present work is concerned with the sensitivity analysis of the variational formulation corresponding to the kinematically incompatible models when the boundary over which the incompatibility between the models takes place is changed. Assuming the presence of a discontinuity in the fields over a given interface between two incompatible models, this analysis allows to measure the sensitivity of a given cost functional when the location of such interface is changed. The application for which this analysis is envisaged is to assess the correctness, or incorrectness, in the definition of the positioning of such coupling interface between dimensionally-heterogeneous domains. Also, some numerical results are provided to give numerical evidence of the usefulness of the present tool.