Size Effects in Computational Homogenization of Polymer Nano‐Composites

Abstract

Nano-particles, as compared to micro-sized inclusions, result in a much better improvement to the mechanical properties of otherwise brittle polymers. Standard first-order computational homogenization lacks the length scale necessary to capture this size effect. In this work, a computational homogenization scheme enhanced with interface energetics is considered and its applicability to polymer nano-composites with different types of filler particles is assessed through systematic numerical experimentation. The study reveals that the method performs quantitatively much better in the case of softer inclusions as compared to the case where the inclusions are much stiffer than the matrix material, which happens in the case of silica nano-particles.

Computational modeling of fracture in polymer nano‐composites undergoing large deformations via the graded‐interphase‐enhanced phase‐field fracture approach

“…This section provides a succinct overview of the two ingredients underlying the PFF‐GI approach, namely the standard finite‐deformation PFF approach and the graded interphase concept. Further details regarding the various modeling and algorithmic aspects can be found in [6] and [8, Ch. 4].…”

“…We adopt a rate‐type variational formulation along with appropriate modifications of the resulting Euler‐Lagrange equations to deal with the irreversibility of crack propagation, as described in Kumar et al. [6] (see also Kumar [8, Ch. 4]), in order to determine the governing equations for the two unknown fields, namely the deformation field φ and the crack phase‐field z .…”

“…Refs. [8, Chapater 4] and [5]), that is, $$\mathcal {H} \approx \mathcal {H}_{n} \coloneqq \max \lbrace \Psi _{+}(\bm{C}_{n}), \mathcal {H}_{n-1} \rbrace$$ with $$\mathcal {H}_{0}=0$$, which culminates in $$Y_{n+1} = g^{\prime }(z_{n+1};k) \thinspace \mathcal {H}_{n}$$. Consequently, we end up with a one‐way coupled system of PDEs since the evolution of the crack phase‐field now depends on the deformation field from the previous time‐step.…”

“…This contribution applies the generic PFF‐GI formulation to the case of polymer nano‐composites undergoing large strains prior to fracture. As discussed in detail in Kumar [8], large deformation phase‐field fracture (PFF) problems pose further modeling and numerics‐related difficulties when compared to the small‐strain problems.…”