20,577 research outputs found
On near-cloaking for linear elasticity
We make precise some results on the cloaking of displacement fields in linear
elasticity. In the spirit of transformation media theory, the transformed
governing equations in Cosserat and Willis frameworks are shown to be
equivalent to certain high contrast small defect problems for the usual Navier
equations. We discuss near-cloaking for elasticity systems via a regularized
transform and perform numerical experiments to illustrate our near-cloaking
results. We also study the sharpness of the estimates from [H. Ammari, H. Kang,
K. Kim and H. Lee, J. Diff. Eq. 254, 4446-4464 (2013)], wherein the convergence
of the solutions to the transmission problems is investigated, when the Lam\'e
parameters in the inclusion tend to extreme values. Both soft and hard
inclusion limits are studied and we also touch upon the finite frequency case.
Finally, we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloak.Comment: 7 figures, 7 tables; Note that the earlier version of this preprint
was titled 'Some results in near-cloaking for elasticity systems'. This new
version of the manuscript has also seen some major upgrade. We have added a
new section on 'Cloaking parameters and isotropic approximation'. In there,
we propose an approximate isotropic cloak algorithm for a symmetrized
Cosserat cloa
Equilibrated tractions for the Hybrid High-Order method
We show how to recover equilibrated face tractions for the hybrid high-order
method for linear elasticity recently introduced in [D. A. Di Pietro and A.
Ern, A hybrid high-order locking-free method for linear elasticity on general
meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1-21], and prove that these
tractions are optimally convergent
Real wave propagation in the isotropic relaxed micromorphic model
For the recently introduced isotropic relaxed micromorphic generalized
continuum model, we show that under the assumption of positive definite energy,
planar harmonic waves have real velocity. We also obtain a necessary and
sufficient condition for real wave velocity which is weaker than
positive-definiteness of the energy. Connections to isotropic linear elasticity
and micropolar elasticity are established. Notably, we show that strong
ellipticity does not imply real wave velocity in micropolar elasticity, while
it does in isotropic linear elasticity
- …