Abstract
A new class of fit regions is proposed as an alternative to those available in the literature, and specifically to the class defined by Noll and Virga in their paper [12]. An advantage of the proposed class is that of being based mostly on topological concepts rather than on less familiar concepts from geometric measure theory. A distinction is introduced between fit regions and shapes of continuous bodies. The latter are defined as equivalence classes of fit regions, made of regions all with the same interior and with the same closure. In the final part of the paper the axioms for a universe of bodies, formulated by Noll and incorporated in Truesdell's book [15], are re-discussed and partially re-formulated.
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Del Piero, G. A Class of Fit Regions and a Universe of Shapes for Continuum Mechanics. Journal of Elasticity 70, 175–195 (2003). https://doi.org/10.1023/B:ELAS.0000005551.92536.c6
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DOI: https://doi.org/10.1023/B:ELAS.0000005551.92536.c6