Currents and curvature varifolds in continuum mechanics. (English) Zbl 1235.49080
Arkhipova, Aina A. (ed.) et al., Nonlinear partial differential equations and related topics. Dedicated to Nina U. Uraltseva on the occasion of her 75th birthday. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4997-2/hbk). Translations. Series 2. American Mathematical Society 229; Advances in the Mathematical Sciences 64, 97-117 (2010).
Summary: The use in continuum mechanics of weak diffeomorphisms, Cartesian currents and curvature \(k\)-varifolds with boundary is discussed. The attention is focused on the analysis of the existence of minimizers for the energies of elastic complex bodies and bodies admitting cracks. The interplay between the analytical features and the physical needs is stressed.
For the entire collection see [Zbl 1193.35001].
For the entire collection see [Zbl 1193.35001].
MSC:
| 49Q15 | Geometric measure and integration theory, integral and normal currents in optimization |
| 49J45 | Methods involving semicontinuity and convergence; relaxation |
| 74A30 | Nonsimple materials |
| 74A45 | Theories of fracture and damage |
| 74A60 | Micromechanical theories |
