On Korn's first inequality with non-constant coefficients

By Patrizio Neff. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 2002

104 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/1799e931ca0578705fd9430236a26f16bd81d54f

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In Biomedical Engineering

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

Optimal BV estimates for a discontinuous Galerkin method for linear elasticity (2004, unknown): “For fixed F̂, the quadratic expression is uniformly positive (generalized Korn’s second inequality, see [20]) such that ∥∥F̂−T∇ũTn + ∇ũnF̂−1∥∥20,Ω + ∥∥ũn∥∥20,Ω ≥ C(F̂)∥∥ũn∥∥21,Ω (3.”
Discontinuous Galerkin methods for non‐linear elasticity (2006, background): “It remains to prove equation (61), which cannot be strictly obtained from the results in [25], because F is not continuous in B0.”
Korn's First Inequality with variable coefficients and its generalization (2003, methodology): “Technische Universität Darmstadt, FB Mathematik, AG6, Schloßgartenstraße 7, 64289 Darmstadt, Germany E-mail : pompe@mathematik.tu-darmstadt.de (Received May 20, 2002)”
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): “From linearized elasticity we have Korn’s inequality [30], that is”
Dynamic problems for metamaterials: Review of existing models and ideas for further research (2014, methodology): “deeper insights in the analytical aspects (Neff, 2002; Neff, Münch, 2008; Neff, Pompe, 2013).”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, background): “It is possible to also cite some studies which consider visco-elastic continuum theories with damage (see [127– 131]) for microscopically granular or discrete systems, as for instance [132–137], or other studies of phenomena involving multiscale coupling (see e.g. [138]).”