A unifying perspective: the relaxed linear micromorphic continuum

By Patrizio Neff, Ionel-Dumitrel Ghiba, A. Madeo, Luca Placidi, Giuseppe Rosi. Continuum Mechanics and Thermodynamics, 2013

311 citations recorded by the source corpus.

We formulate a relaxed linear elastic micromorphic continuum model with symmetric Cauchy force stresses and curvature contribution depending only on the micro-dislocation tensor. Our relaxed model is still able to fully describe rotation of the microstructure and to predict nonpolar size effects. It is intended for the homogenized description of highly heterogeneous, but nonpolar materials with microstructure liable to slip and fracture. In contrast to classical linear micromorphic models, our free energy is not uniformly pointwise positive definite in the control of the independent constitutive variables. The new relaxed micromorphic model supports well-posedness results for the dynamic and static case. There, decisive use is made of new coercive inequalities recently proved by Neff, Pauly and Witsch and by Bauer, Neff, Pauly and Starke. The new relaxed micromorphic formulation can be related to dislocation dynamics, gradient plasticity and seismic processes of earthquakes. It unifies and simplifies the understanding of the linear micromorphic models.

Subfields: Biomedical Engineering, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/4661210ef81649cd4a67e46f6b4f1b473c4f5111

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Citations in the corpus

Granular micromechanics based micromorphic model predicts frequency band gaps (2015, unknown): “proposed relaxed linear micromorphic model vanishes [46,47].”
Macroscopic Description of Microscopically Strongly Inhomogenous Systems: A Mathematical Basis for the Synthesis of Higher Gradients Metamaterials (2015, unknown): “[13, 20, 22, 27, 12, 8, 23]).”
On some fundamental misunderstandings in the indeterminate couple stress model. A comment on recent papers of A.R. Hadjesfandiari and G.F. Dargush (2016, unknown): “1) = 2μ ‖sym∇u‖(2) + λ [tr(∇u)](2) + μc ‖ skew∇u−A‖(2) + 2μL(2)c ‖curl axl(A)‖(2) for the Cosserat model, where μc ≥ 0 is the (difficult to interpret [38]) Cosserat couple modulus [33].”
Continuum and discrete models for structures including (quasi-) inextensible elasticae with a view to the design and modeling of composite reinforcements (2015, background): “…descriptors in order to account for those phenomena of energy distribution, trapping and flow which were studied – in different contexts – in the papers (Carcaterra, 2002; Carcaterra and Akay, 2004; Culla et al., 2003; Ko et al., 2005; Luongo, 2001; Neff et al., 2013b; Madeo et al., 2013).”