A Nonlinear Korn Inequality Based on the Green-Saint Venant Strain Tensor

@article{Musesti2016ANK,
  title={A Nonlinear Korn Inequality Based on the Green-Saint Venant Strain Tensor},
  author={Alessandro Musesti},
  journal={Journal of Elasticity},
  year={2016},
  volume={126},
  pages={129-134}
}
  • A. Musesti
  • Published 23 May 2016
  • Mathematics
  • Journal of Elasticity
A nonlinear Korn inequality based on the Green-Saint Venant strain tensor is proved, whenever the displacement is in the Sobolev space W1,p$W^{1,p}$, p≥2$p\geq 2$, under Dirichlet conditions on a part of the boundary. The inequality can be useful in proving the coercivity of a nonlinear elastic energy. 
View on Springer
arxiv.org
2 Citations
Methods Citations
1

2 Citations

Almost global existence of weak solutions for the nonlinear elastodynamics system with general strain energy

The aim of this paper is to prove the existence of almost global weak solutions for the unsteady nonlinear elastodynamics system in dimension $d=2$ or $3$, for a range of strain energy density…

Almost global existence of weak solutions for the nonlinear elastodynamics system for a class of strain energies

The aim of this paper is to prove the existence of almost global weak solutions for the unsteady nonlinear elastodynamics system in dimension $d=2$ or $3$, for a range of strain energy density…

References

SHOWING 1-7 OF 7 REFERENCES

A nonlinear Korn inequality with boundary conditions and its relation to the existence of minimizers in nonlinear elasticity

A theorem on geometric rigidity and the derivation of nonlinear plate theory from three‐dimensional elasticity

The energy functional of nonlinear plate theory is a curvature functional for surfaces first proposed on physical grounds by G. Kirchhoff in 1850. We show that it arises as a Γ‐limit of…

Linearized Elasticity as Γ-Limit of Finite Elasticity

Linearized elastic energies are derived from rescaled nonlinear energies by means of Γ-convergence. For Dirichlet and mixed boundary value problems in a Lipschitz domain Ω, the convergence of…

Continuity of a Deformation in H1 as a Function of Its Cauchy-Green Tensor in L1

This result has potential applications to nonlinear three-dimensional elasticity, since the stored energy function of a hyperelastic material depends on the deformation gradient field $\bnabla\bTheta$ through the Cauchy-Green tensor.

Three-dimensional elasticity

Part A. Description of Three-Dimensional Elasticity 1. Geometrical and other preliminaries. 2. The equations of equilibrium and the principle of virtual work. 3. Elastic materials and their…

Rigidity and gamma convergence for solid‐solid phase transitions with SO(2) invariance

The singularly perturbed two‐well problem in the theory of solid‐solid phase transitions takes the form $$I_{\varepsilon}[u] = \int\limits^{}_{\Omega} {1 \over {\varepsilon}} W(\nabla u) +…

Bounds for Deformations in Terms of Average Strains