Abstract
Abstract In the paper, a numerical study of the size of representative volume element for the linear elasticity problem is performed. The calculations are carried out for three different types of random microstructures: checkerboard, the Ising model microstructure and Debye microstructure. It is postulated and then verified that there exists a relation between the morphology of microstructure contained in the lineal-path function and the minimum RVE size. It is confirmed, on the basis of numerical examples, that for all the microstructures considered the largest lineal-path can be treated as the size of RVE
Highlights
A sample of random heterogeneous material can be treated as a realization of a certain random or stochastic process
As previously mentioned it is usually proposed in the literature to determine the size of representative volume element (RVE) by investigating the convergence of apparent properties with increasing the size of RVE
It was postulated and verified that there exists some direct relation between RVE size and the “tail” of the lineal-path function
Summary
A sample of random heterogeneous material can be treated as a realization of a certain random or stochastic process. Where ξj is a function corresponding to the j-th random realization of RVE while n is the size of the sample. Such algorithms usually require a very large number of numerical calculations, e.g., FE analysis. In this work, some numerical studies are performed in order to investigate the convergence of apparent elastic properties as well as to search for the relation between the RVE size and the microstructural descriptor, namely the lineal-path function. It would appear that determination of RVE size does not require a large number of numerical simulations, only the morphology of microstructure (contained in the lineal-path) has to be known.
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