On Formulating and Assessing Continuum Theories of Electromagnetic Fields in Elastic Materials

My aim is to explore some ideas about the foundations of electromagnetic theory for elastic materials and to suggest some ways of assessing theories of this kind. I will describe some old ideas that seem to have been forgotten, about forces exerted by matter and fields on each other, and a similar idea about energies. Among other things, I will trace Toupin’s thinking about elastic dielectrics, showing how he moved toward using these ideas, although he did not explicitly recognize them. Further, I will explain how his dynamical theory can be interpreted to be consistent with them, although this is not obvious from what he wrote. Dedicated to the memory of Ronald Rivlin.