Covariant Balance Laws in Continua with Microstructure
Arash Yavari, Jerrold E. Marsden
TL;DR
This paper extends the Green-Naghdi-Rivlin energy balance method to microstructured continua by replacing Galilean transformations with diffeomorphisms, deriving comprehensive macro and micro balance laws and Doyle-Erickson formulas.
Contribution
It introduces a covariant approach using diffeomorphisms, providing a unified framework for balance laws in continua with microstructure.
Findings
Derived new balance laws for microstructured continua
Established Doyle-Erickson formulas in the covariant framework
Unified macro and micro level energy balances
Abstract
The purpose of this paper is to extend the Green-Naghdi-Rivlin balance of energy method to continua with microstructure. The key idea is to replace the group of Galilean transformations with the group of diffeomorphisms of the ambient space. A key advantage is that one obtains in a natural way all the needed balance laws on both the macro and micro levels along with two Doyle-Erickson formulas.
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