By means of balanced virtual powers, it is developed an axiomatic approach, in the spirit of Noll, to second-gradient continua. The measure-theoretical formulation allows a considerable simplification, since the existence of an edge stress density is regarded as a special case of a surface stress which is a singular measure with respect to the area. In order to prove our results, we introduce a particular class of subbodies, namely the sets with curvature measure.
Degiovanni, M., Marzocchi, A., Musesti, A., Edge-force densities and second-order powers, <<ANNALI DI MATEMATICA PURA ED APPLICATA>>, 2006; 185 (1): 81-103. [doi:10.1007/s10231-004-0129-1] [http://hdl.handle.net/10807/19588]
Edge-force densities and second-order powers
Degiovanni, Marco;Marzocchi, Alfredo;Musesti, Alessandro
2006
Abstract
By means of balanced virtual powers, it is developed an axiomatic approach, in the spirit of Noll, to second-gradient continua. The measure-theoretical formulation allows a considerable simplification, since the existence of an edge stress density is regarded as a special case of a surface stress which is a singular measure with respect to the area. In order to prove our results, we introduce a particular class of subbodies, namely the sets with curvature measure.
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