Identification of residual stresses in multi-layered arterial wall tissues using a variational framework

In this context, a conceptual variational framework for the development of residual stress estimation tools is proposed. Particularly, a variational formulation for the characterization of residual deformations and the associated stresses in arterial walls, based on full displacement field measurements of the vessel, is presented. Considering as known data the material parameters characterizing the behavior of the tissue and a set of arterial wall configurations at equilibrium with well defined pressure loads, we propose a cost functional that measures the mechanical imbalance caused by the lack of knowledge of residual stresses. In this manner, the characterization of residual stresses becomes a problem of minimizing such cost functional. Three numerical examples are presented highlighting the potential of the proposed approach. Among these examples, the characterization of residual stresses in a cylindrical geometry representing a three-layered aorta artery is performed.