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 is axiomatically given and the latter is thermodynamically derived. This method has difficulties in damage mechanics in generalized continua. An alternative method to derive governing equations is based on a variational framework known as the extended N 's formalism. Albeit being very prominent, its use is less known in applied mechanics as a field theory. In this work, we demonstrate the power of extended N 's formalism by using tensor algebra and usual continuum mechanics nomenclature.