Three-dimensional stochastic analysis using a perturbation-based homogenization method for elastic properties of composite material considering microscopic uncertainty

Abstract

This paper discusses evaluation of influence of microscopic uncertainty on a homogenized macroscopic elastic property of an inhomogeneous material. In order to analyze the influence, the perturbation-based homogenization method is used. A higher order perturbation-based analysis method for investigating stochastic characteristics of a homogenized elastic tensor and an equivalent elastic property of a composite material is formulated.As a numerical example, macroscopic stochastic characteristics such as an expected value or variance, which is caused by microscopic uncertainty in material properties, of a homogenized elastic tensor and homogenized equivalent elastic property of unidirectional fiber reinforced plastic are investigated. The macroscopic stochastic variation caused by microscopic uncertainty in component materials such as Young's modulus or Poisson's ratio variation is evaluated using the perturbation-based homogenization method. The numerical results are compared with the results of the Monte-Carlo simulation, validity, effectiveness and a limitation of the perturbation-based homogenization method is investigated. With comparing the results using the first-order perturbation-based method, effectiveness of a higher order perturbation is also investigated.

Stochastic multi-scale analysis of homogenised properties considering uncertainties in cellular solid microstructures using a first-order perturbation

“…Moreover, in the first-order perturbation, the approximation of the variance is largely influenced by the value of the stochastic variable. Considering the fluctuations of the microscopic properties, approximation using a first-order perturbation can result in accurate results for the Young's modulus variation, but estimations using the Poisson's ratio variation require higher order expansions (Sakata et al 2008). Furthermore, higher order approximation does not always improve the accuracy of the stochastic estimation especially for Young's moduli that exhibit variations (Sakata et al 2008).…”

“…Our approach is based on the concept of the first-order perturbation proposed by Koishi et al(1996), which was later developed by Sakata et al(2008). Koishi et al(1996) and Sakata et al(2008) demonstrated the validity of the theoretical formulation by comparing this formulation with a stochastic finite element method and using a Monte Carlo simulation, respectively. However, both researchers tested the numerical algorithm using a fibre-reinforced composite.…”

Stochastic Modeling of Chaotic Masonry via Mesostructural Characterization

“…Complementary, systems with random material properties quantified by random variables and deterministic (or slightly perturbed) geometry of the representative volume can be treated employing numerical techniques of stochastic mechanics such as MonteCarlo simulations [20], perturbation-based methods [22,35] or approaches based on an empirical probability distribution function [36]; see also [21] for a systematic overview. Most generally, uncertainties in spatial distribution and material properties of individual phases can be jointly characterized when resorting to random field description [42].…”

Influence of random shrinkage porosity on equivalent elastic modulus of casting: A statistical and numerical approach

“…Sakata et al [10] formulated stochastic characteristics of an equivalent elastic property model by a higher order perturbation-based method. Wu et al [11] obtained the differential expression of effective modulus variation…”

“…Moreover, the crack growth behaviors were correlated with the probability distributions, such as the number (defect density), size, and location of defects [21,22] . It was complicated to obtain this kind of random-defected material's mechanical function by traditional determinable methods [10,23] . To consider this random inhomogeneous defected material, some numerical simulations methods were developed, such as the cell method [24] and lattice model [25,26] .…”