Force and Energy
Charles Grant Blairfindie Allen
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Charles Grant Blairfindie Allen
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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...
Amandine Aftalion, Xavier Blanc (2008)
Annales de l'I.H.P. Analyse non linéaire
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Boyarsky, A. (2006)
Discrete Dynamics in Nature and Society
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István Ecsedi, Ákos József Lengyel (2015)
Curved and Layered Structures
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This paper presents a derivation of the Rayleigh- Betti reciprocity relation for layered curved composite beams with interlayer slip. The principle of minimum of potential energy is also formulated for two-layer curved composite beams and its applications are illustrated by numerical examples. The solution of the presented problems are obtained by the Ritz method. The applications of the Rayleigh-Betti reciprocity relation proven are illustrated by some examples.
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.
Giulio Maier, Giorgio Novati (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
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For the finite-step, backward-difference analysis of elastic-plastic solids in small strains, a kinematic (potential energy) and a static (complementary energy) extremum property of the step solution are given under the following hypotheses: each yield function is the sum of an equivalent stress and a yield limit; the former is a positively homogeneous function of order one of stresses, the latter a nonlinear function of nondecreasing internal variables; suitable conditions of "material...
N. S. Wilkes (1979)
Stochastica
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In 1964, Green and Rivlin [1, 2] proposed two non-standard theories of continua. Both papers concerned non-simple materials: the first considered deformation gradients of higher order than the first as dependent variables; and the second, which generalised the first, treated materials whose kinematic state was not completely detemined by the deformation function, but was also dependent upon some multipolar deformation functions. In both theories the existence of higher order stresses...
Burgess, Cliff P. (2004)
Living Reviews in Relativity [electronic only]
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M. Trlifaj (1973)
Acta Universitatis Carolinae. Mathematica et Physica
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