Jarosław L. Bojarski (2005)
Applicationes Mathematicae
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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.
Jarosław L. Bojarski (2004)
Applicationes Mathematicae
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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) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. In part II, we will show that the set of solutions of the relaxed problem is equal to the set of solutions of the relaxed problem proposed by Suquet. Moreover, we will prove the existence theorem for the limit analysis...
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) is the lower semicontinuous regularization of the plastic energy. We find the integral representation of a non-locally coercive functional. 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. Moreover, we prove an existence theorem for the limit analysis problem.
M. Chipot, I. Shafrir, G. Vergara Caffarelli (2008)
Bollettino dell'Unione Matematica Italiana
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The energy of magneto-elastic materials is described by a nonconvex functional. Three terms of the total free energy are taken into account: the exchange energy, the elastic energy and the magneto-elastic energy usually adopted for cubic crystals. We focus our attention to a one dimensional penalty problem and study the gradient flow of the associated type Ginzburg-Landau functional. We prove the existence and uniqueness of a classical solution which tends asymptotically for subsequences...
A. Gesualdo, F. Guarracino, V. Mallardo, V. Minutolo, L. Nunziante (1997)
Extracta Mathematicae
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In this work the problem of identificating flaws or voids in elastic solids is addressed both from a theoretical and an experimental point of view. Following a so called inverse procedure, which is based on appropriately devised experiments and a particular bounding of the strain energy, a gap functional for flaw identification is proposed.
Oanh Chau, Dumitru Motreanu, Mircea Sofonea (2002)
Applications of Mathematics
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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution...
Arezki Touzaline (2015)
Applicationes Mathematicae
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We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.
Franco Pastrone (1991)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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It is proved that, as in three-dimensional elasticity, Betti's theorem represents a criterion for the existence of a stored-energy function for a Cosserat elastic shell.
Timothy J. Healey, Stefan Krömer (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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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...