Heyden Stefanie, Bain Nicolas
ETH Zürich, Institute for Building Materials, 8093 Zürich, Switzerland.
Universite Claude Bernard Lyon 1, CNRS, Institut Lumière Matière, UMR5306, F-69100, Villeurbanne, France.
Soft Matter. 2024 Jul 17;20(28):5592-5597. doi: 10.1039/d4sm00078a.
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.
一种广泛用于模拟软表面行为的线性应力-应变关系。其在大变形材料领域的有效性是当前争论的话题。在此，我们通过从有限运动学的一般框架推导表面的本构行为来考虑大变形。我们区分了在微小施加变形之前有限和无限小表面松弛的情况。沙特尔沃思方程在完全线性化的情况下被确定为柯西应力度量。我们表明，在有限和线性化情况下，测量的弹性常数都取决于所使用的应力度量。此外，我们讨论了结果的物理含义，并根据两个不同的测试案例分析了表面松弛对表面弹性模量估计的影响。
