Within the linear Toupin–Mindlin strain gradient elasticity we discuss the well-posedness of the first boundary-value problem, that is, a boundary-value problem with Dirichlet-type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher-order elastic moduli and two inequalities for the Lamé moduli. The conditions are less restrictive than those followed from the positive definiteness of the deformation energy.
Authors
Additional information
- DOI
- Digital Object Identifier link open in new tab 10.1002/zamm.202200474
- Category
- Publikacja w czasopiśmie
- Type
- artykuły w czasopismach
- Language
- angielski
- Publication year
- 2023
