64 citations · 146 across the 27 of their papers we have counts for
33 papers
Korn and Poincaré-Korn inequalities for thin domains in
Davit Harutyunyan
We prove Korn's first inequalities with and without boundary conditions in () in -regular thin domains with Lipschitz thickness boundaries with a cons…
On weighted rigidity estimates for bulk and thin domains
Davit Harutyunyan, Andre. M. Rodrigues
This work is concerned with weighted Geometric Rigidity Estimates and Korn's first inequalities in bulk and thin domains. We consider weights, that are a nonnegative power of the d…
Rank-one convexity, polyconvexity, and extremality for three-dimensional elasticity tensors in various symmetry classes
Davit Harutyunyan, Gagik Amirkhanyan
It has been known that, for quadratic functions, quasiconvexity equals rank-one convexity but need not equal polyconvexity. While there is an explicit characterization of polyconve…
5G-Enabled Smart Manufacturing -- A booklet by 5G-SMART
Leefke Grosjean, Krister Landernäs, Berna Sayrac +6
In this booklet the most important learnings and key results of 5G-SMART in the area of smart manufacturing are summarized.
On the fractional Korn inequality in bounded domains: Counterexamples to the case
Davit Harutyunyan, Hayk Mikayelyan
The validity of Korn's first inequality in the fractional setting in bounded domains has been open. We resolve this problem by proving that in fact Korn's first inequality holds in…
The buckling load of cylindrical shells under axial compression depends on the cross-section curvature
Davit Harutyunyan, Andre Martins Rodrigues
It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimen…
A hint on the localization of the buckling deformation at vanishing curvature points on thin elliptic shells
Davit Harutyunyan
The general theory of slender structure buckling by Grabovsky and Truskinovsky [\textit{Cont. Mech. Thermodyn.,} 19(3-4):211-243, 2007], (later extended in [\textit{Journal of Nonl…
On the extreme rays of the cone of quasiconvex quadratic forms: Extremal determinats vs extremal and polyconvex forms
Davit Harutyunyan, Narek Hovsepyan
This work is concerned with the study of the extreme rays of the convex cone of quasiconvex quadratic forms (denoted by ). We characterize quadratic forms $…
The sharp Korn interpolation and second inequalities in thin domains
Davit Harutyunyan
In the present paper we extend the Korn interpolation and second inequalities in thin domains, proven in [\ref{bib:Harutyunyan.4}], to the space for any A…
A note on the extreme points of the cone of quasiconvex quadratic forms with orthotropic symmetry
Davit Harutyunyan
We study the extreme points of the cone of quasiconvex quadratic forms with linear elastic orthotropic symmetry. We prove that if the determinant of the acoustic matrix of the asso…
The asymptotically sharp Korn interpolation and second inequalities for shells
Davit Harutyunyan
We consider shells in three dimensional Euclidean space which have bounded principal curvatures. We prove Korn's interpolation (or the so called first and a half\footnote{The inequ…
Weighted asymptotic Korn and interpolation Korn inequalities with singular weights
Davit Harutyunyan, Hayk Mikayelyan
In this work we derive asymptotically sharp weighted Korn and Korn-like interpolation (or first and a half) inequalities in thin domains with singular weights. The constants (K…
On the Korn interpolation and second inequalities in thin domains
Davit Harutyunyan
We consider shells of non-constant thickness in three dimensional Euclidean space around surfaces which have bounded principal curvatures. We derive Korn's interpolation (or the so…
On the maximization of the solution of Poisson's equation: Brezis-Gallouet-Wainger type inequalities and applications
Davit Harutyunyan, Hayk Mikayelyan
For the solution of the Poisson problem with an right hand side \begin{equation*} \begin{cases} -Δu(x) = f (x) & \mbox{in } D, u=0 & \mbox{on } \partial D, \end{cases} \…
On ideal dynamic climbing ropes
Davit Harutyunyan, Graeme W. Milton, Trevor J. Dick +1
We consider the rope climber fall problem in two different settings. The simplest formulation of the problem is when the climber falls from a given altitude and is attached to one…
When the Cauchy inequality becomes a formula
Davit Harutyunyan
In this note we revisit the classical geometric-arithmetic mean inequality and find a formula for the difference of the arithmetic and the geometric means of given …
Towards a complete characterization of the effective elasticity tensors of mixtures of an elastic phase and an almost rigid phase
Graeme W. Milton, Davit Harutyunyan, Marc Briane
The set of possible effective elastic tensors of composites built from two materials with positive definite elasticity tensors $\BC_1$ and $\BC_2=\Gd\BC_0$ comprising the se…
Gaussian curvature as an identifier of shell rigidity
Davit Harutyunyan
In the paper we deal with shells with non-zero Gaussian curvature. We derive sharp Korn's first (linear geometric rigidity estimate) and second inequalities on that kind of shells…
On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials
Graeme W. Milton, Marc Briane, Davit Harutyunyan
The set of possible effective elastic tensors of composites built from two materials with elasticity tensors $\BC_1>0$ and $\BC_2=0$ comprising the set $U=\{\BC_1,\BC_2\}$ a…
Quantitative anisotropic isoperimetric and Brunn-Minkowski inequalities for convex sets with improved defect estimates
Davit Harutyunyan
In this paper we revisit the anisotropic isoperimetric and the Brunn-Minkowski inequalities for convex sets. The best known constant depending on the space dimension…
Korn inequalities for shells with zero Gaussian curvature
Yury Grabovsky, Davit Harutyunyan
We consider shells with zero Gaussian curvature, namely shells with one principal curvature zero and the other one having a constant sign. Our particular interests are shells that…
High frequency homogenization for travelling waves in periodic media
Davit Harutyunyan, Richard V. Craster, Graeme W. Milton
We consider high frequency homogenization in periodic media for travelling waves of several different equations: the wave equation for scalar-valued waves such as acoustics; the wa…
Towards characterization of all extremal quasiconvex quadratic forms
Davit Harutyunyan, Graeme W. Milton
Given a quasiconvex quadratic form, we prove that if the determinant of its acoustic tensor is an irreducible extremal polynomial that is not identically zer…
Sharp weighted Korn and Korn-like inequalities and an application to washers
Davit Harutyunyan
In this paper we prove asymptotically sharp weighted "first-and-a-half" Korn and Korn-like inequalities with a singular weight occurring from Cartesian to cylindrical change o…