Green's functions for the isotropic planar relaxed micromorphic model - concentrated force and concentrated couple

Panos Gourgiotis (1) , Gianluca Rizzi (2) , Peter Lewintan (3) , Davide Bernardini (4) , Adam Sky (5) , Angela Madeo (6) , Patrizio Neff (7)

1 NTUA - National Technical University of Athens [Athens]
2 TU - Technische Universität Dortmund [Dortmund]
3 Universität Duisburg-Essen = University of Duisburg-Essen [Essen]
4 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
5 University of Luxembourg [Luxembourg]
6 M2S - Mécanique des Matériaux et des Structures
7 Universität Duisburg-Essen, Fakultät für Mathematik

We derive the Green's functions (concentrated force and couple in an infinite space) for the isotropic planar relaxed micromorphic model. Since the relaxed micromorphic model particularises into the microstretch, Cosserat (micropolar), couple-stress, and linear elasticity model for certain choices of material parameters, we recover the fundamental solutions in all these cases.

Keywords: generalized continua; fundamental solution; Kelvin-Mindlin problem; concentrated force; concentrated couple; micromorphic continuum; micro-stretch; Cosserat continuum; micropolar continuum; couple stress model; relaxed micromorphic model; gauge invariant dislocation model

Domains: Mathematical Physics [math-ph]

Panos Gourgiotis, Gianluca Rizzi, Peter Lewintan, Davide Bernardini, Adam Sky, et al.. Green's functions for the isotropic planar relaxed micromorphic model - concentrated force and concentrated couple. 2023. ⟨hal-04250494⟩