A mathematical framework of high-order surface stresses in three-dimensional configurations
Tungyang Chen (National Cheng Kung University), Min-Sen Chiu (National Cheng Kung University)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Wed 9:00 - 10:30
MacMillan 117
The mathematical behavior of a curved interface between two different solid phases with surface or interface stress effects is often described by the generalized Young-Laplace (YL) equations. The generalized YL equation can be derived by considering force equilibrium of a thin interphase with membrane stresses along the interface. In this work we present a refined mathematical framework by incorporating the high-order surface or interface stresses between two neighboring media in three dimensions. The high-order interface stresses are resulting from the non-uniform surface stress across the layer thickness, and thereby effectively inducing a bending effect. In the formulation the deformation of the thin interphase is approximated by the Kirchhoff-Love assumption of thin shell. The stress equilibrium conditions are fulfilled by consideration of balance for forces as well as stress couples. By simple geometric expositions, we derive in explicit forms the stress jump conditions for high-order surface stresses. In illustrations, the bending behavior of nanoplates with high-order stresses is examined, and is compared with the results by the conventional YL equation. We note that the framework of high-order surface stress is analogous to that of Cosserat media.