Abstract
Several experimental investigations corroborate nanosized inclusions as being much more efficient reinforcements for strengthening polymers as compared to their microsized counterparts. The inadequacy of the standard first-order computational homogenization scheme, by virtue of lack of the requisite length scale to model such size effects, necessitates enhancements to the standard scheme. In this work, a thorough assessment of one such extension based on the idea of interface energetics is conducted. Systematic numerical experimentation and analysis demonstrate the limitation of the aforementioned approach in modeling mechanical behavior of composite materials where the filler material is much stiffer than the matrix. An alternative approach based on the idea of continuously graded interphases is introduced. Comprehensive evaluation of this technique by means of representative numerical examples reveals it to be the appropriate one for modeling nano-composite materials with different filler-matrix stiffness combinations.
Highlights
Incorporation of a secondary phase in the form of fibers or particles for the purpose of improving structural properties of polymers has been in practice for almost a century
Written in python and employing the open source framework GMSH [18] as a back end for mesh generation, this code currently allows for generation for finite element meshes for 2D representative volume element (RVE) consisting of randomly placed circular inclusions of arbitrary sizes
An alternative approach considering a continuous variation in the material properties within the interphase region has been introduced in this paper and has been named the Gradient-Interphase-Enhanced Computational Homogenization (GICH)
Summary
Incorporation of a secondary phase in the form of fibers or particles for the purpose of improving structural properties of polymers has been in practice for almost a century now. A microscopic representative volume element (RVE) is attached to each point on the micro-scale and the macroscopic constitutive response is determined by means of averaging the response over the RVE, which in turn results from the solution of the micro-scale boundary value problem (BVP) (cf Fig. 1) For applications of this technique to the modeling of nanocomposites involving size effects, see [23,40,49]. The numerics-based approach, i.e. computational homogenization [45,46], on the other hand, allows for consideration of micro-structure details such as inclusion shape and dispersion of the filler particles In this technique, the constitutive response at each point on the macro-scale is determined by subjecting a cut-out or the so-called RVE [3] of the material to a predefined macroscopic deformation gradient. The following sub-sections attempt to outline the underlying concepts of the standard first-order computational homogenization technique
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