Acta Mechanica

, Volume 229, Issue 9, pp 3727–3765 | Cite as

Homogenization of carbon/polymer composites with anisotropic distribution of particles and stochastic interface defects

  • Damian Sokołowski
  • Marcin Kamiński
Open Access
Original Paper


The main objective is to investigate an effect of anisotropic distribution of the reinforcing particles in a cubic representative volume element (RVE) of the carbon–polymer composite including stochastic interphases on its homogenized elastic characteristics. This is done using a probabilistic homogenization technique implemented using a triple approach based on the stochastic perturbation method, Monte Carlo simulation as well as on the semi-analytical approach. On the other hand, the finite element method solution to the uniform deformations of this RVE is carried out in the system ABAQUS. This composite model consists of two neighboring scales–the micro-contact scale relevant to the imperfect interface and the micro-scale—having 27 particles inside a cubic volume of the polymeric matrix. Stochastic interface defects in the form of semi-spheres with Gaussian radius are replaced with the interphase having probabilistically averaged elastic properties, and then such a three-component composite is subjected to computational homogenization on the microscale. The computational experiments described here include FEM error analysis, sensitivity assessment, deterministic results as well as the basic probabilistic moments and coefficients (expectations, deviations, skewness and kurtosis) of all the components of the effective elasticity tensor. They also include quantification of anisotropy of this stiffness tensor using the Zener, Chung–Buessem and the universal anisotropy indexes. A new tensor anisotropy index is proposed that quantifies anisotropy on the basis of all not null tensor coefficients and remains effective also for tensors other than cubic (orthotropic, triclinic and also monoclinic). Some comparison with previous analyses concerning the isotropic case is also included to demonstrate the anisotropy effect as well as the numerical effort to study randomness in composites with anisotropic distribution of reinforcements and inclusions.


Supplementary material

707_2018_2174_MOESM1_ESM.docx (871 kb)
Supplementary material 1 (docx 871 KB)


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Authors and Affiliations

  1. 1.Faculty of Civil Engineering, Architecture and Environmental EngineeringŁódź University of TechnologyLodzPoland

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