In compressible Neohookean elasticity one minimizes functionals which are composed by the sum of the norm of the deformation gradient and a nonlinear function of the determinant of the gradient. Non-interpenetrability of matter is then represented by additional invertibility conditions. An existence theory which includes a precise notion of invertibility and allows for cavitation was formulated by Müller and Spector in 1995. It applies, however, only if some -norm of the gradient with is controlled (in three dimensions). We first characterize their class of functions in terms of properties of the associated rectifiable current. Then we address the physically relevant case, and show how their notion of invertibility can be extended to . The class of functions so obtained is, however, not closed. We prove this by giving an explicit construction.
@article{ASNSP_2003_5_2_3_521_0, author = {Conti, Sergio and de Lellis, Camillo}, title = {Remarks on the theory of elasticity}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {521--549}, publisher = {Scuola normale superiore}, volume = {Ser. 5, 2}, number = {3}, year = {2003}, mrnumber = {2020859}, zbl = {1114.74004}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2003_5_2_3_521_0/} }
TY - JOUR AU - Conti, Sergio AU - de Lellis, Camillo TI - Remarks on the theory of elasticity JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2003 SP - 521 EP - 549 VL - 2 IS - 3 PB - Scuola normale superiore UR - http://www.numdam.org/item/ASNSP_2003_5_2_3_521_0/ LA - en ID - ASNSP_2003_5_2_3_521_0 ER -
%0 Journal Article %A Conti, Sergio %A de Lellis, Camillo %T Remarks on the theory of elasticity %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2003 %P 521-549 %V 2 %N 3 %I Scuola normale superiore %U http://www.numdam.org/item/ASNSP_2003_5_2_3_521_0/ %G en %F ASNSP_2003_5_2_3_521_0
Conti, Sergio; de Lellis, Camillo. Remarks on the theory of elasticity. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 2 (2003) no. 3, pp. 521-549. http://www.numdam.org/item/ASNSP_2003_5_2_3_521_0/
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