2021/12/22 by Marco Valerio d’Agostino, d'Agostino, Marco Valerio, Gianluca Rizzi +9 · 1 citation
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2112.12050
openalex publication_date 2021/12/22 · openalex created_date 2022/05/05 · openalex updated_date 2026/07/28
We consider the classical Mindlin-Eringen linear micromorphic model with a new strictly weaker set of displacement boundary conditions. The new consistent coupling condition aims at minimizing spurious influences from arbitrary boundary prescription for the additional microdistortion field P. In effect, P is now only required to match the tangential derivative of the classical displacement u which is known at the Dirichlet-part of the boundary. We derive the full boundary condition, in adding the missing Neumann condition on the Dirichlet-part. We show existence and uniqueness of the static problem for this weaker boundary condition. These results are based on new coercive inequalities for incompatible tensor fields with prescribed tangential part. Finally, we show that compared to classical Dirichlet conditions on u and P, the new boundary condition modifies the interpretation of the constitutive parameters.