• partition of unity;
  • XFEM;
  • multiscale;
  • enrichment;
  • thermo-elastic


This paper details a novel new multiscale technique for modeling heterogeneous materials undergoing substantial thermal stresses. The technique is based on an enriched partition of unity approach that incorporates the thermal effects occurring on the microstructure into the global model. We demonstrate the effectiveness of this technique by implementing it into both the standard finite element method and the octree partition of unity method (OctPUM). The results demonstrate that the technique has uniquely improved accuracy over the homogenization method conditional to the method into which it is implemented in. The multiscale technique, when implemented into either the standard finite element method or OctPUM, increases the accuracy of the strain energy calculation. When the multiscale technique is implemented into OctPUM, it also is able to capture the unique stress fields on the microstructure of the model. Published 2012. This article is a US Government work and is in the public domain in the USA.