We look at a mechanical dissipation inequality differing from the standard one by what we call a relative power, a notion that is appropriate in the presence of material mutations. We prove that a requirement of structural invariance for such an inequality under the action of diffeomorphism-based changes of observers (covariance) implies (i) the representation of contact actions in terms of the first Piola–Kirchhoff stress, (ii) local balances of standard and configurational actions, (iii) a priori constitutive restrictions in terms of free energy, and (iv) a representation of viscous-type stress components. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

A certain counterpart in dissipative setting of the Noether theorem with no dissipation pseudo-potentials / Paolo Maria Mariano. - In: PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A: MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES. - ISSN 1364-503X. - STAMPA. - 381:(2023), pp. 20220375.1-20220375.24. [10.1098/rsta.2022.0375]

A certain counterpart in dissipative setting of the Noether theorem with no dissipation pseudo-potentials

Paolo Maria Mariano
2023

Abstract

We look at a mechanical dissipation inequality differing from the standard one by what we call a relative power, a notion that is appropriate in the presence of material mutations. We prove that a requirement of structural invariance for such an inequality under the action of diffeomorphism-based changes of observers (covariance) implies (i) the representation of contact actions in terms of the first Piola–Kirchhoff stress, (ii) local balances of standard and configurational actions, (iii) a priori constitutive restrictions in terms of free energy, and (iv) a representation of viscous-type stress components. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.
2023
381
1
24
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Paolo Maria Mariano
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Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1344071
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