REMARKABLE IDENTITIES IN MECHANICS AND ELECTROMAGNETISM Carmine Trimarco University of Pisa, Italy Dipartimento di Matematica Applicata ‘U.Dini’ Via Bonanno 25/B I-56126 Pisa e-mail: trimarco@dma.unipi.it Abstract. In homogeneous hyperelastic solids some identities, which are based on the classical balance laws of continua, can be arranged in the form of conservations laws. In the presence of inhomogeneities, singularities or defects, these identities still hold true, though in a slightly modified form, and can be interpreted as balance laws of nonclassical forces that act on the inhomogeneity or on the defect. In this view, novel physical quantities are envisaged through these laws, which in turn address configurational mechanics. These quantities are known as material quantities and can be readily extended to the more general context of nonclassical continua and to continua with microstructure. In electromagnetic materials similar identities can be established. They hold true along the solutions of the mechanical equations, which are now coupled with the Maxwell equations of electromagnetism. A different standpoint may be adopted however and, by reversing the reasoning, the aforementioned conservation laws can be viewed as primary equations rather than identities. This view is supported by a nonclassical variational approach, which addresses interesting remarks in the case of electromagnetic materials.
Remarkable Identities in Mechanics and Thermodynamics
TRIMARCO, CARMINE
2006-01-01
Abstract
REMARKABLE IDENTITIES IN MECHANICS AND ELECTROMAGNETISM Carmine Trimarco University of Pisa, Italy Dipartimento di Matematica Applicata ‘U.Dini’ Via Bonanno 25/B I-56126 Pisa e-mail: trimarco@dma.unipi.it Abstract. In homogeneous hyperelastic solids some identities, which are based on the classical balance laws of continua, can be arranged in the form of conservations laws. In the presence of inhomogeneities, singularities or defects, these identities still hold true, though in a slightly modified form, and can be interpreted as balance laws of nonclassical forces that act on the inhomogeneity or on the defect. In this view, novel physical quantities are envisaged through these laws, which in turn address configurational mechanics. These quantities are known as material quantities and can be readily extended to the more general context of nonclassical continua and to continua with microstructure. In electromagnetic materials similar identities can be established. They hold true along the solutions of the mechanical equations, which are now coupled with the Maxwell equations of electromagnetism. A different standpoint may be adopted however and, by reversing the reasoning, the aforementioned conservation laws can be viewed as primary equations rather than identities. This view is supported by a nonclassical variational approach, which addresses interesting remarks in the case of electromagnetic materials.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
