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## Softening materials: an engineering approach

Softening materials: an engineering approach // Fracture and Damage Mechanics / Aliabadi, M.H. (ur.).
London: Queen Mary and Westfield College, 1999. str. 423-431 (predavanje, međunarodna recenzija, cjeloviti rad (in extenso), znanstveni)

Naslov
Softening materials: an engineering approach

Autori

Izvornik
Fracture and Damage Mechanics / Aliabadi, M.H. - London : Queen Mary and Westfield College, 1999, 423-431

Skup
International Congress on Fracture and Damage Mechanics

Mjesto i datum
London, Velika Britanija, 27.-29.7.1999.

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
Softening; bifurcation; post-peak behaviour

Sažetak
A simple example of a bar under tension is examined with softening material behaviour formulated through damage mechanics. For that simple example an energy equation is formed. Graphical presentation of the equation in energy-displacement space demonstrates existence of multiple solutions and bifurcation points. Pre-peak behaviour is well defined and stable and is suitable for both force driven and displacement driven analysis approach. Contrary, the post-peak behaviour can be analysed only with displacement driven analysis. In order to simulate numerical solving Newton procedure is formulated and all mathematically possible solutions are determined. It is clear that the solution obtained depends only on the starting value in the iterative procedure and that it is possible to obtain physically wrong values of displacement that even does not enable localisation of the strain. On the example of a homogenous material it is demonstrated that localisation is possible even without localisation initiator but is hardly to expect because of the iterative character of the solution procedure. Introduction of a localisation initiator eliminates the bifurcation point and forms a solution path that goes from elastic solution to the physically correct localisation in &#39;weaker&#39; material. However, on a finite element example it is demonstrated that other &#39;non-physical&#39; solution path still exists and can be obtained as an (&#39;wrong&#39;) answer.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo