2003
DOI: 10.1023/b:elas.0000018775.44668.07
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Symmetries and Hamiltonian Formalism for Complex Materials

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Cited by 34 publications
(28 citation statements)
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“…(13) is the Doyle-Ericksen formula for a porous body. It is a particular case of a generalized version of the Doyle-Ericksen formula obtained in Capriz and Mariano (2003) where the microstructural term here presented governs the transfer of energy from substructural level to macroscopic level (Capriz and Mariano, 2003). Moreover we obtain on the boundary that…”
Section: Balance Of Momentum For Phase Onementioning
confidence: 78%
“…(13) is the Doyle-Ericksen formula for a porous body. It is a particular case of a generalized version of the Doyle-Ericksen formula obtained in Capriz and Mariano (2003) where the microstructural term here presented governs the transfer of energy from substructural level to macroscopic level (Capriz and Mariano, 2003). Moreover we obtain on the boundary that…”
Section: Balance Of Momentum For Phase Onementioning
confidence: 78%
“…Eq. (5c) is the hyperelastic constitutive law (4). Particular forms of the strain energy density function W used in models are discussed in Section 2.3.…”
Section: Equations Of Motionmentioning
confidence: 99%
“…In particular, the Lie algebra of generators of point symmetries admitted by a given system of equations is coordinate-independent, i.e., invariant under point transformations acting on the variables of the system (including transformations to curvilinear coordinates, as well as more general transformations). From a more formal point of view, Lie symmetries constitute a guide in the Lagrangian and Hamiltonian formalisms in continuum mechanics, especially for complex materials endowed with a microstructure [4]. For models that admit a variational formulation, there is a oneto-one correspondence between variational Lie symmetries and local conservation laws through Noether's theorem; for non-variational models, this relation generally does not hold [5].…”
Section: Introductionmentioning
confidence: 99%
“…This rate equation is postulated a priori in a manner which guaranties the reversibility of the applied dynamical process and is interpreted as a balance equation between the standard and the substructural interactions, when the microstress tensor [see Capriz and Mariano, 2003;de Fabritiis and Mariano, 2005;Mariano, 2008b;Yavari and Marsden, 2009] is null. The integrability conditions of this rate equation follow naturally by means of Frobenius theorem [e.g., see Bishop and Goldberg, 1980, pp.…”
Section: Introductionmentioning
confidence: 99%