Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains

0482050 - ÚT 2018 RIV GB eng J - Journal Article
Adam, Lukáš - Outrata, Jiří - Roubíček, Tomáš
Identification of some nonsmooth evolution systems with illustration on adhesive contacts at small strains.
Optimization. Roč. 66, č. 12 (2017), s. 2025-2049. ISSN 0233-1934. E-ISSN 1029-4945
R&D Projects: GA ČR GAP201/10/0357; GA ČR GA14-15264S
Institutional support: RVO:61388998 ; RVO:67985556
Keywords : rate-independent systems * optimal control * identification
OECD category: Pure mathematics; Pure mathematics (UTIA-B)
Impact factor: 1.170, year: 2017
http://www.tandfonline.com/doi/abs/10.1080/02331934.2015.1111364

A class of evolution quasi-static systems which leads, after a suitable time discretization, to recursive non-linear programs, is considered and optimal control or identification problems governed by such systems are investigated. The resulting problem is an evolutionary Mathematical Programs with Equilibrium Constraints. A subgradient information of the (in general nonsmooth) composite objective function is evaluated and the problem is solved by the implicit programming approach. The abstract theory is illustrated on an identification problem governed by delamination of a unilateral adhesive contact of elastic
bodies discretized by finite-element method in space and a semiimplicit formula in time. Being motivated by practical tasks, an identification
problem of the fracture toughness and of the elasticity moduli of the adhesive is computationally implemented and tested numerically on a two-dimensional example. Other applications including frictional contacts or bulk damage, plasticity or phase transformations are outlined.
Permanent Link: http://hdl.handle.net/11104/0278090