Enhanced computational homogenization techniques for modelling size effects in polymer composites

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.

A graded interphase enhanced phase-field approach for modeling fracture in polymer composites

“…It is evident that the standard two-phase continuum model is not capable of capturing the aforementioned size effect since it does not posses an inherent length scale necessary for this purpose. In light of these facts, we consider the physically motivated graded interphase concept introduced in [27] and revisit it with specific focus on its extension to application in phase-field fracture models. The underlying concept, here, is the explicit modeling of the interphase region around the filler particle, and continuous grading (or variation) in the material properties across the interphase, cf.…”

“…Thus, keeping the interphase thickness t = r m − r f constant, the interphase volume fraction, and, hence, the graded interphase effect increases with decreasing particle size, thereby enabling the modeling of the desired size effect. In contrast to the interpolation ansatz presented in [27], the ansatz in (23) ensures that the interpolation function is always continuous at the matrix end, regardless of the value of the exponent n.…”

“…An intuitive choice is the inclusion of the above-mentioned sharp cohesive crack model for material interface as done in [25,26]. As discussed in [27], cohesive interfaces cannot account for additional stiffening and toughening observed in case of silica polymer nano-composites. Contrarily, [28] considered diffuse interfaces, wherein the elastic and fracture properties within a finite thickness around the original sharp interface were varied spatially and their values were determined by interpolating those of the constituent materials (and the sharp interface, if applicable).…”

“…Consequently, appropriate enhancements are inevitable. See [27] and the references therein for a review on these enhanced approaches within the context of finite deformation hyperelasticity. Although both the aforementioned crack modeling techniques do posses an inherent length scale via the consideration of a lower dimensional crack manifold in case of sharp crack modeling approaches, or the crack length scale parameter in case of PFF, the size effect in terms of increased stiffness and strength at lower scales is not considered therein.…”

“…Although both the aforementioned crack modeling techniques do posses an inherent length scale via the consideration of a lower dimensional crack manifold in case of sharp crack modeling approaches, or the crack length scale parameter in case of PFF, the size effect in terms of increased stiffness and strength at lower scales is not considered therein. In this work, we consider a combination of the graded interphase concept, which has been successfully employed for capturing the desired size effect within the context of finite strain hyperelasticity in our previous work [27], and the standard PFF approach described above, resulting in the graded interphase enhanced phase-field fracture (PFF-GI) model. Motivated by experimental observations [31], we consider an interphase region of prescribed thickness around the filler particle, and allow for continuous grading or variation of the elastic and fracture properties within the interphase region.…”