On weak solutions of boundary value problems within the surface elasticity of Nth order. Issue 3 (24th January 2021)

• Record Type: Journal Article
• Authors: Eremeyev, Victor A.; Lebedev, Leonid P.; Cloud, Michael J.
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 101:Issue 3(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-01-24
• Subjects: nonlocal elasticity -- strain gradient elasticity -- surface elasticity -- weak solution; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202000378
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to N th order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution. In order to characterize the smoothness of such solutions, certain energy functional spaces of Sobolev type are introduced. Compared with the solutions obtained in classical linear elasticity, weak solutions for solids with surface stresses are smoother on the boundary; more precisely, a weak solution belongs to H 1 ( V ) ∩ H N ( S s ) where S s ⊂ S ≡ ∂ V and V ⊂ R 3 . Abstract : A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to N th order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution.….