2023/11/03 by Stefanie Heyden, Heyden, Stefanie, Nicolas Bain +1 · 1 citation
Engineering · #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Physical sciences #Soft Condensed Matter (cond-mat.soft) #Structural Analysis and Optimization
paper · pdf · doi:10.48550/arxiv.2311.01896
openalex publication_date 2023/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.