I recent read the book of Prof. J. Tinsley Oden "A short course on nonlinear continuum mechanics"
http://users.ices.utexas.edu/~arbogast/cam397/oden0908.pdf
which declares that reference configuration is an open, bounded, connected subset of R3 with a smooth boundary (in Page 1).
It is strange to me beacause that means we cannot consider the boundary of the deformable bodies in its following discussion.
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