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

Abstract

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.

References in corpus (20)

• A unifying perspective: the relaxed linear micromorphic continuum
• Wave propagation in relaxed micromorphic continua: modelling metamaterials with frequency band-gaps
• On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush
• Real wave propagation in the isotropic relaxed micromorphic model
• Maxwell meets Korn: A New Coercive Inequality for Tensor Fields with Square-Integrable Exterior Derivative
• Stress channelling in extreme couple-stress materials Part I: Strong ellipticity, wave propagation, ellipticity, and discontinuity relations
• Size-effects of metamaterial beams subjected to pure bending: on boundary conditions and parameter identification in the relaxed micromorphic model
• The gauge theory of dislocations: static solutions of screw and edge dislocations
• A new view on boundary conditions in the Grioli-Koiter-Mindlin-Toupin indeterminate couple stress model
• Unfolding engineering metamaterials design: relaxed micromorphic modeling of large-scale acoustic meta-structures
• Korn inequalities for incompatible tensor fields in three space dimensions with conformally invariant dislocation energy
• Analytical solutions of the cylindrical bending problem for the relaxed micromorphic continuum and other generalized continua (including full derivations)
• Nečas-Lions lemma revisited: An $L^p$-version of the generalized Korn inequality for incompatible tensor fields
• Primal and mixed finite element formulations for the relaxed micromorphic model
• Stress channelling in extreme couple-stress materials Part II: Localized folding vs faulting of a continuum in single and cross geometries
• Optimal incompatible Korn-Maxwell-Sobolev inequalities in all dimensions
• Metamaterial shields for inner protection and outer tuning through a relaxed micromorphic approach
• $L^p$-versions of generalized Korn inequalities for incompatible tensor fields in arbitrary dimensions with $p$-integrable exterior derivative
• $L^p$-trace-free generalized Korn inequalities for incompatible tensor fields in three space dimensions
• A global higher regularity result for the static relaxed micromorphic model on smooth domains

Cited by in corpus (2)

• A computational approach to identify the material parameters of the relaxed micromorphic model
• Yet another best approximation isotropic elasticity tensor in plane strain