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A non-local void dynamics modeling and simulation using the Proper Generalized Decomposition

Type
Articles dans des revues avec comité de lecture
Author
GHNATIOS, Chady
533922 Notre Dame University-Louaize [Lebanon] [NDU]
SIMACEK, Pavel
93432 University of Delaware [Newark]
CHINESTA, Francisco
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
ADVANI, Suresh
93432 University of Delaware [Newark]

URI
http://hdl.handle.net/10985/19415
DOI
10.1007/s12289-019-01490-7
Date
2020
Journal
International Journal of Material Forming

Abstract

In this work we develop a void filling and void motion dynamics model using volatile pressure and squeeze flow during tape placement process. The void motion and filling are simulated using a non-local model where their presence is reflected in the global macroscale behavior. Local pressure gradients during compression do play a critical role in void dynamics, and hence the need for a non-local model. Deriving a non-local model accounting for all the void motion and dynamics entails a prohibitive number of degrees of freedom, leading to unrealistic computation times with classical solution techniques. Hence, Proper Generalized Decomposition – PGD – is used to solve the aforementioned model. In fact, PGD circumvents the curse of dimensionality by using separated representation of the space coordinates. For example, a 2D problem can be solved as a sequence of 1D problems to find the 2D solution. The non-local model solution sheds light on the fundamental of the void dynamics including their pressure variation, motion and closure mechanisms. Finally, a post treatment of the transient compression of the voids is used to derive conclusions regarding the physics of the void dynamics.

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