Numerical Analysis Of Effective Macro-mechanical Properties Of Random Heterogeneous Elastic Materials

Most of materials used in engineering fields are heterogeneous. Moreover, materials, even homogeneous in macro scale, present stochastic heterogeneity when the scale is small enough. It is always a significant and important investigation to found the quantitative correlation between the effective macro-mechanical properties of heterogeneous materials and their microstructures. Based on the 2-D random lattice model, tessellation technique and finite element method, the 3-D random lattice model will be founded in this paper. According to the model, the statistical theory is employed to research the distribution characteristic of macro-mechanical properties and effects of randomicity and heterogeneity on the macro-mechanical properties of four materials, namely one-parameter and two-parameter heterogeneous elastic isotropic materials with normal distribution, heterogeneous two-phase elastic isotropic materials and heterogeneous elastic transversely isotropic materials with random orientation angle.The results can be shown as following: (1) Random lattice model can be employed to research the effective macro-mechanical properties of heterogeneous materials. (2) The effective properties of heterogeneous materials, researched in this paper, meet with normal distribution. (3) The effective Poisson ratio of the materials, whose microstructures satisfy with normal distribution, indicates material directivity, which is so weak that the directivity can be ignored. (4) For heterogeneous elastic transversely isotropic materials with random orientation angle, the effective macro-mechanical properties are approximately equal to the previous set values when the standard deviation of random orientation angles is less than 2°.The results obtained by this study have prospective guiding significances to the engineering problem, such as structural integrity, design of materials and so on.