| Author | M.A. Soare and R.C. Picu |
|---|---|
| Title | Boundary value problems defined on stochastic self-similar multiscale geometries |
| Year | 2007 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 74 |
| Pages | 668-696 |
| Abstract | A method for solving elasticity problems defined on composite bodies with a stochastic multiscale microstructure is presented. It is considered that the composite is made from two types of materials with different elastic moduli. One of these is taken as the matrix, while the other forms the inclusions. The inclusions form a stochastic fractal with a finite, but potentially large, number of scales and are randomly distributed within the matrix. The method presented here leads to the statistics of the solution, i.e. the mean and the variance of the stress and displacement fields. It is based on the stochastic finite element method (spectral approach, second-order technique) and on scaling properties of the spatial distribution of inclusions over the problem domain. This scaling allows for a simple formulation of the multiscale problem and leads to significant computation cost savings, especially when the fractal has a large number of relevant scales. Several examples are presented and used to verify the proposed method against computationally intensive classical finite element models in which the mesh is refined down to the scale of the finest inclusions. |
| DOI Link | 10.1002.nme.2191 |