IGFEM: Interface-enriched Generalized Finite Element Method

PROJECT TITLE:
DEVELOPMENT AND IMPLEMENTATION OF A NOVEL INTERFACE-ENRICHED GENERALIZED FINITE ELEMENT METHOD FOR THE SIMULATION OF HETEROGENEOUS AND MICROVASCULAR MATERIALS USING NON-CONFORMING MESHES

PARTICIPANTS: SOHEIL SOGHRATI (PhD), DR. MASOUD SAFDARI (Postdoctoral Research Associate), AHMAD NAJAFI (PhD), ALEJANDRO ARAGON (PhD), MARCUS TAN (PhD), DAVID BRANDYBERRY (PhD), QI DANG (MS), DR. MARYAM SHAKIBA (Postdoctoral Research Associate), AND PROF. PHILIPPE GEUBELLE

SUPPORT: AFOSR MURI, NSF CMMI, AFOSR/AFRL CEIMM


PROJECT DESCRIPTION: In this project, we develop a new enriched finite element method for the efficient and accurate simulation of heterogeneous materials, using meshes that do not conform to the microstructure. The enrichment functions are introduced to capture discontinuity of the solution in the elements traversed by the material interfaces: if the interface is ‘intact’, we use a weak (C0) discontinuity; if the interface is failing, we use an enrichment with a strong (i.e., C-1) discontinuity. The method is applied to thermal and structural problems involving microvascular composites (for which the temperature field has a weak discontinuity across the embedded microchannels), particulate composites, fiber-reinforced composites, and other heterogeneous materials.

Illustration of the IGFEM concept.

Examples of 3D microstructures modeled with NURBS-based IGFEM hexahedral elements.

RELATED PUBLICATIONS:

  1. Soghrati, S., Aragón, A. M., Duarte, C. A. and Geubelle, P. H. (2012) “An interface-enriched generalized finite element method for problems with discontinuous gradient fields.” International Journal for Numerical Methods in Engineering, 89(8), 991-1008. DOI: 10.1002/nme.3273.
  2. Soghrati, S. and Geubelle, P. H. (2012) “A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries.” Computational Methods for Applied Mechanics and Engineering, 217-220, 46-57. http://dx.doi.org/10.1016/j.cma.2011.12.010.
  3. Aragón, A. M., Soghrati, S., and Geubelle, P. H. (2013) “Effect of in-plane deformation on the cohesive failure of heterogeneous adhesives.” Journal of the Mechanics and Physics of Solids, 61:7, 1600-1611.  http://dx.doi.org/10.1016/j.jmps.2013.03.003.
  4. Soghrati, S., Najafi, A. R., Hughes, K. M., Lin, J. H., White, S. R., Sottos, N. R. and Geubelle, P. H. (2013) “Computational analysis of actively-cooled 3D woven microvascular composites using a stabilized interface-enriched generalized finite element method.” International Journal of Heat and Mass Transfer, 65, 153-164. DOI: 10.1016/j.ijheatmasstransfer.2013.05.054.
  5. Soghrati, S., Duarte, C. A. and Geubelle, P. H. (2015) “An adaptive interface-enriched generalized finite element method for the treatment of problems with curved interfaces.” International Journal of Numerical Methods in Engineering, 102, 1352-1370. DOI: 10.1002/nme.4860.
  6. Cuba-Ramos, A., Aragón, A. M., Soghrati, S., Geubelle, P. H., and Molinari, J.-F. (2015) “A new formulation for imposing Dirichlet boundary conditions on non-matching meshes.” International Journal for Numerical Methods in Engineering, 103, 430-444. DOI: 10.1002/nme.4898.
  7. Tan, M., Safdari, M., Najafi, A. R., and Geubelle, P. H. (2015) “A NURBS-based interface-enriched generalized finite element scheme for the thermal analysis and design of microvascular composites.” Computational Methods for Applied Mechanics and Engineering, 283, 1382-1400. http://dx.doi.org/10.1016/j.cma.2014.09.008.
  8. Safdari, M., Najafi, A., Sottos, N. R., and Geubelle, P. H. (2015) “A NURBS-based interface-enriched generalized finite element method for problems with complex discontinuous gradient field.” International Journal of Numerical Methods in Engineering, 101, 950-964. DOI: 10.1002/nme.4852.
  9. Safdari, M., Sottos, N. R., and Geubelle, P. H. (2016) “A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials.” Journal of Computational Physics, 318, 373-390.
  10. Tan, M., and Geubelle, P. H. (2017) “3D dimensionally reduced modeling and gradient-based optimization of microchannel cooling networks.” Computational Methods in Applied Mechanics and Engineering, 323, 230–249. http://dx.doi.org/10.1016/j.cma.2017.05.024.