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

Abstract

Randomness in the microstructure due to variations in microscopic properties and geometrical information is used to predict the stochastically homogenised properties of cellular media. Two stochastic problems at the micro-scale level that commonly occur due to fabrication inaccuracies, degradation mechanisms or natural heterogeneity were analysed using a stochastic homogenisation method based on a first-order perturbation. First, the influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminium-adhesive honeycomb structure was investigated. The fluctuations in the microscopic properties were then combined by varying the microstructure periodicity in a corrugated-core sandwich plate to obtain the variation of the homogenised property. The numerical results show that the uncertainties in the microstructure affect the dispersion of the homogenised property. These results indicate the importance of the presented stochastic multi-scale analysis for the design and fabrication of cellular solids when considering microscopic random variation.

Finite element analysis on femur subjected to knee joint forces during incline-decline walking

“…Although there are numerous studies [8−12] on the effect of slope surface activities either walking and running on joint reaction forces have been conducted, however investigation up to joint stresses and strains relatively very few. Finite element analysis (FEA) is a common computational tools to investigate the stress and strain response including for porous materials [13] and bone mechanics [14]. Hence, this study was undertaken to investigate the effect of knee joint reaction forces due to incline-decline walking on stresses and strains of femur bone.…”

Failure Behavior of Aircraft Sandwich Panels under Bending Load

“…Sandwich panels with honeycomb cores have been studied by many researchers. The influence of Young's modulus variation in an adhesive on the macroscopic properties of an aluminum-adhesive honeycomb structure also has been investigated so far [3]. According to the statistics by Aircraft Crashes Record Office (ACRO), there were amount of totaling up to 1115 fatalities due to aviation accidents in 2012 [4].…”

Stochastic Homogenized Properties for Honeycomb Microstructure Based on First Order Perturbation

“…Those methods were introduced to solve the problems related to fiber reinforced composites. Recently, the analysis of stochastic modeling was also been used in application of porous media [7] and trabecular bone [8]. However, to the best of our knowledge, no one has tested the stochastic multi-scale analysis on the honeycomb microstructure especially when the randomness in the geometrical microstructure is put into consideration.…”