  The Shuttleworth equation: a linear stress-strain relation ubiquitously used
in modeling the behavior of soft surfaces. Its validity in the realm of
materials subject to large deformation is a topic of current debate. Here, we
allow for large deformation by deriving the constitutive behavior of the
surface from the general framework of finite kinematics. We distinguish cases
of finite and infinitesimal surface relaxation preceding an infinitesimal
applied deformation. The Shuttleworth equation identifies as the Cauchy stress
measure in the fully linearized setting. We show that both in finite and
linearized cases, measured elastic constants depend on the utilized stress
measure. In addition, we discuss the physical implications of our results and
analyze the impact of surface relaxation on the estimation of surface elastic
moduli in the light of two different test cases.
