To the memory of Clifford Ambrose Truesdell. Kinetic energy is frequently disregarded in continua with structure, as applications or macroscopic evidences are essentially concerned with static or quasi-static phenomena. Whenever dynamics happens to be relevant, people customarily appeal to a quadratic form of the kinematic variables of the microstructure, by analogy with the classical form of the kinetic energy. However, such a quadratic form may be inappropriate or even incorrect in some cases. Examples of the inadequacy of this quadratic form are illustrated in reference [1], where a systematic treatment for the dynamics of continua with microstructure is also expounded. In that context, the notion of kinetic co-energy is introduced, along with that of kinetic energy. Although the proposed treatment is irrespective of thorough variational procedures, the notion of kinetic co-energy naturally addresses to a variational formulation, if this novel notion is understood as a primitive quantity. In this view, a procedure for deriving the kinetic energy can be proposed. Other approaches are proposed in the literature. A specific Lagrangian can be introduced, for instance, whenever some of the equations that govern the microstructure are a priori known and, in addition, admit a variational formulation. Possibly, such a Lagrangian formulation may not unambiguously allow for the classical distinction between forces (in the sense of material constitutive response) and inertial forces. In this respect, the question may arise whether the notion of kinetic co-energy can be consistently introduced in such a context. Hopefully, such a consistency can be assessed for a broad class of structured materials and the novel notion can provide a qualified tool for selecting momentum and stress. Eventually, a deformable electromagnetic material is discussed hereby.

On the kinetic energy in Non-classical Continua. The Electromagnetic Body

TRIMARCO, CARMINE
2002-01-01

Abstract

To the memory of Clifford Ambrose Truesdell. Kinetic energy is frequently disregarded in continua with structure, as applications or macroscopic evidences are essentially concerned with static or quasi-static phenomena. Whenever dynamics happens to be relevant, people customarily appeal to a quadratic form of the kinematic variables of the microstructure, by analogy with the classical form of the kinetic energy. However, such a quadratic form may be inappropriate or even incorrect in some cases. Examples of the inadequacy of this quadratic form are illustrated in reference [1], where a systematic treatment for the dynamics of continua with microstructure is also expounded. In that context, the notion of kinetic co-energy is introduced, along with that of kinetic energy. Although the proposed treatment is irrespective of thorough variational procedures, the notion of kinetic co-energy naturally addresses to a variational formulation, if this novel notion is understood as a primitive quantity. In this view, a procedure for deriving the kinetic energy can be proposed. Other approaches are proposed in the literature. A specific Lagrangian can be introduced, for instance, whenever some of the equations that govern the microstructure are a priori known and, in addition, admit a variational formulation. Possibly, such a Lagrangian formulation may not unambiguously allow for the classical distinction between forces (in the sense of material constitutive response) and inertial forces. In this respect, the question may arise whether the notion of kinetic co-energy can be consistently introduced in such a context. Hopefully, such a consistency can be assessed for a broad class of structured materials and the novel notion can provide a qualified tool for selecting momentum and stress. Eventually, a deformable electromagnetic material is discussed hereby.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/72914
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