On the Theory of Relaxation in Nonlinear Elasticity with Constraints on the Determinant
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| 024 | 7 | 0 | |a 10.1007/s00205-014-0835-9 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0835-9 | ||
| 245 | 0 | 0 | |a On the Theory of Relaxation in Nonlinear Elasticity with Constraints on the Determinant |h [Elektronische Daten] |c [Sergio Conti, Georg Dolzmann] |
| 520 | 3 | |a We consider vectorial variational problems in nonlinear elasticity of the form $${I[u]=\int W(Du)\,{\rm d}x}$$ I [ u ] = ∫ W ( D u ) d x , where W is continuous on matrices with a positive determinant and diverges to infinity along sequences of matrices whose determinant is positive and tends to zero. We show that, under suitable growth assumptions, the functional $${\int W^{\rm qc}(Du)\,{\rm d}x}$$ ∫ W qc ( D u ) d x is an upper bound on the relaxation of I, and coincides with the relaxation if the quasiconvex envelope W qc of W is polyconvex and has p-growth from below with $${p\geqq n}$$ p ≧ n . This includes several physically relevant examples. We also show how a constraint of incompressibility can be incorporated in our results. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Conti |D Sergio |u Institut für Angewandte Mathematik, Universität Bonn, 53115, Bonn, Germany |4 aut | |
| 700 | 1 | |a Dolzmann |D Georg |u Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 413-437 |x 0003-9527 |q 217:2<413 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0835-9 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0835-9 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Conti |D Sergio |u Institut für Angewandte Mathematik, Universität Bonn, 53115, Bonn, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Dolzmann |D Georg |u Fakultät für Mathematik, Universität Regensburg, 93040, Regensburg, Germany |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/2(2015-08-01), 413-437 |x 0003-9527 |q 217:2<413 |1 2015 |2 217 |o 205 | ||