A multisurface constitutive model for highly cross-linked polymers with yield data obtained from molecular dynamics simu
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A multisurface constitutive model for highly cross-linked polymers with yield data obtained from molecular dynamics simulations P. Areias
. N. Vu-Bac . T. Rabczuk
Received: 29 June 2016 / Accepted: 17 November 2016 Springer Science+Business Media Dordrecht 2016
Abstract Constitutive properties for highly crosslinked glassy polymers are currently determined by molecular dynamics (MD) simulations. This avoids the need for ad-hoc experimentation. Constitutive data in functional form, such as yield surfaces, still require identification and correspondence to an existing function. In addition, loss of information occurs with fitting procedures. The present alternative consists in directly defining piecewise-linear yield functions from a set of points obtained by MD simulations. To prevent the algorithmic issues of multisurface plasticity, we propose an alternative to active-set strategies by simultaneously including all yield functions regardless of being active. We smooth the complementarity conditions using the Chen–Mangasarian function. In addition, extrapolation is proposed for slowly-evolving quantities such as the effective plastic strain while
fully implicit integration is adopted for rapidlyevolving constitutive quantities. Since polymers exhibit finite-strain behavior, we propose a semiimplicit integration algorithm which allows a small number of steps to be used up to very large strains. Experimentally-observed effects herein considered are: thermal effects on strain (i.e. thermal expansion), Young’s modulus dependence on temperature and the effects of strain rate and temperature on the yield stress. A prototype model is first studied to assess the performance of the integration algorithm, followed by a experimental validation and a fully-featured, thermally-coupled 2D example. Keywords Multisurface yield functions Highly cross-linked polymers Constitutive integration Finite strains
1 Introduction P. Areias Department of Physics, University of E´vora, Cole´gio Luı´s Anto´nio Verney, Rua Roma˜ Ramalho, 59, 7002-554 E´vora, Portugal N. Vu-Bac T. Rabczuk Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany P. Areias (&) ICIST/CERIS, Instituto Superior Te´cnico, Lisbon, Portugal e-mail: [email protected]
Substantial studies have been performed with uncross-linked and lightly cross-linked polymer glasses, in particular PMMA and polyethylene, where a complete depiction of the corresponding constitutive behavior now exists, see Vu-Bac et al. (2016). The prediction of macroscopic properties requires the knowledge of molecular features associated with the plastic mechanism (Bouvard et al. 2009). Molecular theories of plastic behavior in amorphous polymers were summarized by Stachurski (1997). Along with
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the development of accurate inter-atomic potentials using quantum mechanics, molecular dynamics (MD) simulations are a powerful tool in visualizing molecular mechanisms of yielding (Sundaraghavan and Kumar 2013). MD simulations offer a
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