Numerical comparison of a deformable discrete element model and an equivalent continuum analysis for the compaction of ductile porous material D.T. Gethin a , R.S. Ransing a , R.W. Lewis a, * , M. Dutko b , A.J.L. Crook c a Department of Mechanical Engineering, University of Wales ± Swansea, Singleton Park, Swansea SA2 8PP, UK b Department of Civil Engineering , University of Wales ± Swansea, Swansea SA2 8PP, UK c Rock®eld Software Ltd., University of Wales ± Swansea, Swansea SA2 8PP, UK Received 3 November 1999; accepted 15 January 2001 Abstract The combined ®nite and discrete element technique has been considered for the compaction of an assembly of particles. Each particle is mapped with ®nite elements and the interaction between particles is solved using a discrete element technique. Compaction of a few particles in two dimensions using the combined discrete/®nite element method is shown to be equivalent to the Gurson model in the continuum analysis. Results generated from both analyses are compared and found to be in good agreement up to 95% densi®cation. The work demonstrates the potential appli- cabilityofthedeformablediscreteelementmethodforparticulateanalysisorpowdercompactioninparticular. Ó 2001 Elsevier Science Ltd. All rights reserved. 1. Introduction In this paper, a comparison has been made between two distinct and novel approaches to represent com- paction of granular media ± the deformable discrete el- ement analysis and an equivalent continuum analysis. The objective of this comparison is to generate con®- dence in the use of the discrete element method as a reliable simulation method for the compaction of gran- ular materials. Compactionofgranularmaterialsisanareaofactive research in both soil mechanics as well as powder compaction. The continuum approach employs numer- ical schemes such as the ®nite element method to model the deformation process, which has been successfully established and is becoming more widely used. The de- formable discrete element approach focuses on model- ling the deformation of individual particles that are themselves modelled using the ®nite element method employing a continuum approach. As a result, simple plasticity models can be used to represent the deforma- tion characteristics of individual particles and discrete element algorithms can be used to take into account inter-particle behaviour including geometry changes. Once developed, the distinct advantage of this over an equivalent continuum analysis is that a mixture of par- ticles with dierent materials, sizes and shapes can be analysed easily. An equivalent continuum analysis will require experimental characterisation of each powder mix as well as new constitutive relationships to associate stress and strain variation. Thenextsectionbrie¯ydescribesthediscreteelement method and explains the principles of the deformable discreteelementmethod.Section3describesthephysical model used for the comparison and the assumptions made. An equivalent continuum analysis model is out- lined in the Section 4 followed by the comparison of results in Section 5. The paper is concluded in Sec- tion 6. Computers and Structures 79 2001) 1287±1294 www.elsevier.com/locate/compstruc * Corresponding author. E-mail address: r.w.lewis@swansea.ac.uk R.W. Lewis). 0045-7949/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII:S0045-794901)00015-3