Three-dimensional stochastic finite element method for elasto-plastic bodies

A new stochastic nite element method (SFEM) is formulated for three-dimensional softening elasto- plastic bodies with random material properties. The method is based on the Karhunen{Loeve and polynomial chaos expansions, and able to e ciently estimate complete probabilistic characteristics of the response, such as moments or PDFs. To reduce the computational complexity in the three-dimensional setting, two alterations are made with respect to the two-dimensional SFEM proposed earlier by the authors. First, a variability preserving modi cation of the Karhunen{Loeve expansion is rigorously derived and applied in the stochastic discretization of random elds representing material properties. Second, an e cient algorithm for parallel processing is developed, with time consumption being the same order as for an ordinary FEM, rendering the proposed SFEM an e ective alternative to Monte- Carlo simulation. The applicability of the proposed method to stochastic analysis of strain localization is examined using Monte-Carlo simulation. Then, it is applied to a fault formation problem which is a recent concern of earthquake engineering. Ground surface layers are modelled by a softening elasto- plastic body, and the evolution of probabilistic characteristics of the rupture process is analysed in detail. Some practical observations are made regarding the nature of the fault formation from the stochastic viewpoint