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

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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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Authors and Affiliations

  1. Department of Mechanical Engineering, Notre Dame University-Louaize, Zouk Mosbeh, PO Box 72, Lebanon

    Chady Ghnatios

  2. University of Delaware, Newark, DE, 19716-3119, USA

    Pavel Simacek & Suresh Advani

  3. PIMM Laboratory & ESI GROUP Chair, ENSAM ParisTech, 151 boulevard de l’Hopital, 75013, Paris, France

    Francisco Chinesta

Authors
  1. Chady Ghnatios
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  2. Pavel Simacek
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  3. Francisco Chinesta
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  4. Suresh Advani
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Correspondence to Chady Ghnatios.

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Ghnatios, C., Simacek, P., Chinesta, F. et al. A non-local void dynamics modeling and simulation using the Proper Generalized Decomposition. Int J Mater Form 13, 533–546 (2020). https://doi.org/10.1007/s12289-019-01490-7

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  • DOI: https://doi.org/10.1007/s12289-019-01490-7

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