This sub-contract summarizes work Oates will conduct in collaboration with the PI Taira. Oates will formulate and numerically implement a nonlinear shell and full three dimensional nonlinear solid mechanics finite element models in combination with rate-dependent multi-physics constitutive relations associated with the structure and embedded actuator materials. The goal of this part of the research project is: - Formulation and implementation of A nonlinear structure model that can be accurately and efficiently coupled to high Reynolds number flow solvers, - Constitutive relations that allow integration of advanced nonlinear and hysteretic material laws that include nonlinear viscoelasticity, and a range of field-coupled behavior (e.g., ferroelectricity, magnetostriction, photomechanics, shape memory alloy deformation, etc.). - Uncertainty analysis of the nonlinear structure models and constitutive relations will be quantified using Bayesian statistics to provide an assessment of parameter and model uncertainty as well as propagation of error. Details describing these three research tasks are provided below. An emphasis will be placed on close collaboration with the PI to ensure codes are transferable to the fluid solvers. Further, energy conserved analysis will be conducted to quantify theoretical limits in obtaining enhanced aerodynamic efficiency. This plays an important role in determining integration of functional materials into aircraft control surfaces such as rotorblades. The implementation of a fully coupled FSI model that includes smart structures is expected to advance this field of research that is otherwise costly to conduct experimentally.