2004 -01 -21
10 :15 at ML J 21

Finite Element Mapping for the Spring Network Models of Elasticity of Solids

Andrei A. Gusev

Polymer Physics, Materials Science, ETH Zurich

Spring network models have frequently been used to simulate deformation and fracture of both homogeneous and heterogeneous solids. In this talk, after a brief review of the existing models, we present a general finite element based procedure for setting spring network models of elasticity of solids. The procedure is equally suitable for setting regular and unstructured spring network models, both in two and three dimensions. As an illustration, we consider a regular three dimensional parent grid of serendipity family linear brick elements and show that there are three distinct mapped springs which are fully sufficient for representing the elastic behavior of an arbitrary homogeneous isotropic elastic medium. We present explicit expressions for the stiffness coefficients of these springs and employ the networks with the so-defined springs for predicting the effective stiffness of periodic heterogeneous media with spherical and cylindrical inclusions. For large grids, the predictions obtained with the parent finite element grids and the mapped spring networks are highly consistent, whereas for small grids the spring network models give significantly more accurate predictions.