This article is about hyperelastic deformations of plates (planar domains) which minimize a neohookean-type energy. Particularly, we investigate a stored energy functional introduced by J. M. Ball [Proc. Roy. Soc. Edinb. Sect. A, 88 (1981), pp. 315-328]. The mappings under consideration are Sobolev homeomorphisms and their weak limits. They are monotone in the sense of C. B. Morrey. One major advantage of adopting monotone Sobolev mappings lies in the existence of the energy-minimal deformations. However, injectivity is inevitably lost, so an obvious question to ask is, what are the largest subsets of the reference configuration on which minimal deformations remain injective? The fact that such subsets have full measure should be compared with the notion of global invertibility, which deals with subsets of the deformed configuration instead. In this connection we present a Cantor-type construction to show that both the branch set and its image may have positive area. Another novelty of our approach lies in allowing the elastic deformations to be free along the boundary, known as frictionless problems.

The ground-state rotational band of the neutron-deficient californium (Z = 98) isotope 244Cf was identified for the first time and measured up to a tentative spin and parity of I I-pi = 20(+). The observation of the rotational band indicates that the nucleus is deformed. The kinematic and dynamic moments of inertia were deduced from the measured gamma-ray transition energies. The behavior of the dynamic moment of inertia revealed an up-bend due to a possible alignment of coupled nucleons in high-j orbitals starting at a rotational frequency of about (h) over bar (omega) = 0.20 MeV. The results were compared with the systematic behavior of the even-even N = 146 isotones as well as with available theoretical calculations that have been performed for nuclei in the region.