Numerical study of solids with micro-structures - Go, Qing Ming. (2013)
In the current study, the effective elastic modulus of a three-phase continuous heterogeneous material is estimated by using the finite element method. The microstructure of multi-phase heterogeneous materials is generally random with their phases not clearly defined. Without the knowledge of the microstructure, the effective modulus can be estimated by using a finite element mesh of randomly allocated materials to the elements to simulate the continuity of the material phases in the said material. This method has been proven accurate and effective for a bi-continuous material by Xu et al. (2009). The present study expanded upon the finding and found that the accuracy of the estimated effective modulus of a three-phase continuous material is dependent upon the number of domains as well as the element density as observed by the decrement in standard deviation and coefficient of variation with an increment in the above two variables. These results were in agreement with that presented by Xu et al. (2009). The estimated moduli were also in accordance to the Voigt (1910) and Reuss (1929) bounds as well as Budiansky's (1965) model of effective modulus prediction for homogeneous and isotropic materials consisting of continuous irregular grains of constituent materials generally spherical in dimension, thus showing its effectiveness. However, it was observed that the dispersion of the estimated modulus becomes wider as the margin of difference between the constituent material's elastic modulus increases. As such, it was concluded that the method as well as the simulation configuration presented in this current study can provide a estimation of the effective modulus of a three-phase continuous heterogeneous material with acceptable accuracy.