Projection vs. relaxation of adjacent bulk deformation for surface modeling: Theoretical and numerical aspects. (September 2021)

• Record Type: Journal Article
• Authors: Sievers, Christian; Mosler, Jörn; Kurzeja, Patrick
• Is Part Of: International journal of solids and structures. Volume 226/227(2021)
• Publication Date: 2021-09
• Subjects: Surface modeling -- Projection -- relaxation -- Finite element implementation -- Variational principles; Mechanics, Applied -- Periodicals; Structural analysis (Engineering) -- Periodicals; Elastic solids -- Periodicals; Mécanique appliquée -- Périodiques; Constructions, Théorie des -- Périodiques; Solides élastiques -- Périodiques; Elastic solids; Mechanics, Applied; Structural analysis (Engineering); Periodicals; 624.18
• DOI: 10.1016/j.ijsolstr.2021.111084
• Languages: English
• ISSNs: 0020-7683

Abstract

Abstract: Motivated by a strong coupling between bulk and surface physics, we present two approaches to derive continuum surface models from the three-dimensional, adjacent bulk deformation: projection and relaxation. In contrast to conventional ad hoc models, properties like the surface stress are consistently derived from a hyperelastic thermodynamic potential. While the projection approach captures classical in-plane stresses, the relaxation approach can further relax normal-normal and normal-shear coupling. A projection onto the surface is indeed always a relaxation if anisotropy is superficial, but not vice versa . The distinct behavior of projection and relaxation is theoretically discussed and highlighted by specific examples. Numerical implementation in a finite-element framework is subsequently elaborated. Its performance is illustrated by isotropic and anisotropic surface energies of a free cube and a beam under tension. Finally, both projection and relaxation constitute valuable alternatives to conventional surface models in terms of physics, geometry and computation.