Duvan Henao

AN EFFICIENT NUMERICAL METHOD FOR CAVITATION IN NONLINEAR ELASTICITY

This paper is concerned with the numerical computation of cavitation in nonlinear elasticity. The Crouzeix–Raviart nonconforming finite element method is shown to prevent the degeneration of the mesh provoked by the conventional finite element approximation of this problem. Upon the addition of a suitable stabilizing term to the elastic energy, the method is used to solve cavitation problems in both radially symmetric and non-radially symmetric settings. While the radially symmetric examples serve to illustrate the efficiency of the method, and for validation purposes, the experiments with non-centered and multiple cavities (carried out for the first time) yield novel observations of situations potentially leading to void coalescence.

Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals

We extend the recent radial symmetry results by Pisante [J. Funct. Anal., 260 (2011), pp. 892--905] and Millot and Pisante [J. Eur. Math. Soc.

Lusin's condition and the distributional determinant for deformations with finite energy

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Uniaxial versus biaxial character of nematic equilibria in three dimensions

JEMS

ON THE UNIQUENESS OF POSITIVE SOLUTIONS OF A QUASILINEAR EQUATION CONTAINING A WEIGHTED p-LAPLACIAN, THE SUPERLINEAR CASE

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Corrigendum: Symmetry of Uniaxial Global Landau--de Gennes Minimizers in the Theory of Nematic Liquid Crystals

, 12 (2010), pp. 1069--1096] (who show that ...

Invertibility and Weak Continuity of the Determinant for the Modelling of Cavitation and Fracture in Nonlinear Elasticity

Abstract. Based on a previous work by the authors on the modelling of cavitation and fracture in nonlinear elasticity, we give an alternative proof of a recent result by Csörnyei, Hencl and Malý on the regularity of the inverse of homeomorphisms in the Sobolev space . With this aim, we show that the notion of fracture surface introduced by the authors in their model corresponds precisely to the original notion of cavity surface in the cavitation models of Müller and Spector (1995) and Conti and De Lellis (2003). We also find that the surface energy introduced in the model for cavitation and fracture is related to Lusins condition (N) on the non-creation of matter. A fundamental question underlying this paper is whether necessarily implies that the deformation opens no cavities. We show that this is not true unless Müller and Spectors condition INV for the non-interpenetration of matter is satisfied. Having thus provided an additional justification of its importance, we prove the stability of this condition with respect to weak convergence in the critical space . Combining this with the work by Conti and De Lellis, we obtain an existence theory for cavitation in this critical case.

Fracture Surfaces and the Regularity of Inverses for BV Deformations

We study global minimizers of the Landau–de Gennes (LdG) energy functional for nematic liquid crystals, on arbitrary three-dimensional simply connected geometries with topologically non-trivial and physically relevant Dirichlet boundary conditions. Our results are specific to an asymptotic limit coined in terms of a dimensionless temperature and material-dependent parameter, t and some constraints on the material parameters, and we work in the

A numerical study of void coalescence and fracture in nonlinear elasticity

t\rightarrow \infty