Constitutive behavior is generally recognized to be the dominant property in the analysis, design, or understanding of advanced materials — from inorganic structural materials to proteins. How a complex system of atoms and electrons responds to applied stresses, stimuli, and foreign agents is a fundamental concern in dealing with a wide range of biological and physical phenomena. For example, the breakdown of bone in genetic disease, the tearing of tendon due to injuries, the damage of DNA due to UV irradiation, or the structural response of a composite in an airplane are all processes requiring a knowledge of appropriate constitutive relations. Validated predictive models — the development of constitutive relations rooted in quantum and atomistic simulations and capable of describing the key functional properties — provide an opportunity to transform analysis and design in settings such as these.
Variational formulation of three-dimensional viscous free-surface flows — Natural imposition of surface-tension boundary-conditions
LW Ho & AT Patera. International Journal for Numerical Methods in Fluids, 13(6):691-698, 1991.