Energy based methods applied in mechanics by using the extended Noether's formalism

Abstract: Physical systems are modeled by field equations; these are coupled, partial differential equations in space and time. Field equations are often given by balance equations and constitutive equations, where the former are axiomatically given and the latter are thermodynamically derived. This approach is useful in thermomechanics and electromagnetism, yet challenges arise once we apply it in damage mechanics for generalized continua. For deriving governing equations, an alternative method is based on a variational framework known as the extended noether's formalism. Its formal introduction relies on mathematical concepts limiting its use in applied mechanics as a field theory. In this work, we demonstrate the power of extended noether's formalism by using tensor algebra and usual continuum mechanics nomenclature. We demonstrate derivation of field equations in damage mechanics for generalized continua, specifically in the case of strain gradient elasticity.

Object Details

• Location: Deutsche Nationalbibliothek Frankfurt am Main
• Extent: Online-Ressource
• Language: Englisch

References and Relationships

• Bibliographic citation: Energy based methods applied in mechanics by using the extended Noether's formalism ; day:29 ; month:07 ; year:2023 ; extent:23 ; ZAMM ; (29.07.2023) (gesamt 23)

Contributors, Places and Time

• Creator: Abali, Bilen Emek

Further information

• DOI: 10.1002/zamm.202300020
• URN: urn:nbn:de:101:1-2023073015011262949697
• Rights: Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
• Last update: 14.08.2025, 10:48 AM CEST