Displaying similar documents to “Injective weak solutions in second-gradient nonlinear elasticity”

Injective weak solutions in second-gradient nonlinear elasticity

Timothy J. Healey, Stefan Krömer (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on...

General method of regularization. III: The unilateral contact problem

Jarosław L. Bojarski (2004)

Applicationes Mathematicae

Similarity:

The aim of this paper is to prove that the relaxation of the elastic-perfectly plastic energy (of a solid made of a Hencky material with the Signorini constraints on the boundary) is the weak* lower semicontinuous regularization of the plastic energy. We consider an elastic-plastic solid endowed with the von Mises (or Tresca) yield condition. Moreover, we show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet....

Regularization of noncoercive constraints in Hencky plasticity

Jarosław L. Bojarski (2005)

Applicationes Mathematicae

Similarity:

The aim of this paper is to find the largest lower semicontinuous minorant of the elastic-plastic energy of a body with fissures. The functional of energy considered is not coercive.

Ground states in complex bodies

Paolo Maria Mariano, Giuseppe Modica (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

A unified framework for analyzing the existence of ground states in wide classes of elastic complex bodies is presented here. The approach makes use of classical semicontinuity results, Sobolev mappings and cartesian currents. Weak diffeomorphisms are used to represent macroscopic deformations. Sobolev maps and cartesian currents describe the inner substructure of the material elements. Balance equations for irregular minimizers are derived. A contribution to the debate about the role...

Line-energy Ginzburg-Landau models : zero-energy states

Pierre-Emmanuel Jabin, Felix Otto, BenoÎt Perthame (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Similarity:

We consider a class of two-dimensional Ginzburg-Landau problems which are characterized by energy density concentrations on a one-dimensional set. In this paper, we investigate the states of vanishing energy. We classify these zero-energy states in the whole space: They are either constant or a vortex. A bounded domain can sustain a zero-energy state only if the domain is a disk and the state a vortex. Our proof is based on specific entropies which lead to a kinetic formulation, and...