Modeling thin films applying an extended continuum theory based on a scalar-valued order parameter. Part I: isothermal case

In the current work we develop a thermo-mechanically consistent model describing the behavior of thin polymeric films. In industrial applications of such thin films, e.g. in bonding metal sheets in automotive industry, boundary layers and, as a further result, scale effects depending on the thickness of the film are observed (see e.g. [Toney et a]., 1995; Frank et al., 1996; J. Polym. Sci., Part B: Polym. Phys. 40 (2001) 2343-2353]). In contrast to the well-analyzed size effects in many other micro-structured materials, e.g. granular materials, porous materials or foams (see e.g. [Int. J. Mech. Sci. 43 (2001) 701-713] or [Proc. R. Soc. London A 458 (2002) 2869-2883]), the macroscopic behavior of the former material differs completely from an experimental point of view. In the analyzed polymeric films a weaker zone at the boundary of the film is observed in comparison with the stiffer material behavior of the bulk material. To capture these and more general types of boundary layer effects, we develop an extended continuum model based on a scalarvalued order parameter following the line of [Continua with Microstructures. Vol. 35 of Springer Tracts in Natural Philosophy. Springer, New York, 1980; Meccanica 17 (1982) 80-84; Ann. Mater. Pura Appl. 135 (1983) 1-25; Continuum Mech. Thermodyn. 4 (1999) 247-262]. (C) 2004 Elsevier Ltd. All rights reserved.