An efficient approach to the numerical solution of rate-independent problems with nonconvex energies

0364707 - ÚTIA 2012 RIV US eng J - Journal Article
Bartels, S. - Kružík, Martin
An efficient approach to the numerical solution of rate-independent problems with nonconvex energies.
Multiscale Modeling and Simulation. Roč. 9, č. 3 (2011), s. 1275-1300. ISSN 1540-3459. E-ISSN 1540-3467
R&D Projects: GA AV ČR IAA100750802
Grant - others:GA ČR(CZ) GAP201/10/0357
Institutional research plan: CEZ:AV0Z10750506
Keywords : numerical solution * nonconvexity
Subject RIV: BA - General Mathematics
Impact factor: 2.009, year: 2011
http://library.utia.cas.cz/separaty/2011/MTR/kruzik-0364707.pdf

We propose a new approach to the numerical treatment of non(quasi)convex rate-independent evolutionary problems. The main idea is to replace the original microscopic energy density by its polyconvexification. For this problem, first-order optimality conditions are derived and used in finding a discrete solution. The effectiveness of the method is illustrated with some numerical experiments.
Permanent Link: http://hdl.handle.net/11104/0200115