Novel strategy to model deformation-induced strand contraction/dilatation during mechanical reduction

Research output: Contribution to journalArticleResearchpeer-review


  • Rui Guan
  • Christian M.G. Rodrigues
  • Cheng Ji
  • Miaoyong Zhu
  • Shengli Li

External Organisational units

  • CD-Laboratory for Fatigue Analysis
  • School of Metallurgy
  • University of Science and Technology Liaoning
  • Christian-Doppler Lab for Metallurgical Applications of Magnetohydrodynamics


When a strand is subjected to rolling and pressing during mechanical reduction (MR), deformation-induced strand contraction or dilatation can occur. A novel modeling strategy has been designed to account for this mechanism in a two-phase Eulerian–Eulerian volume-average model with a fixed geometry. The strategy is based on the following ideas: (1) during MR, the pressing force from the rolls to the solidifying strand leads to the compression of the viscoplastic network that causes melt to be squeezed out of that region; (2) if the pressing is strong enough to cause the melt to penetrate the surrounding solid shell, the strand deflects outwards (the dilatation state); (3) as the melt flow weakens and the following pair of rolls approaches, the “expanded” strand structure is forced to go back to its original form (the contraction state). Numerically, special Robin type boundary conditions have been imposed on the strand surface to comply with the above description while maintaining a fixed domain. Strand deflection has been estimated and correlates well with the mush deformation intensity and solidification evolution during the casting process. Macrosegregation is also discussed based on the strand deflection and deformation parameters.


Original languageEnglish
Pages (from-to)770-784
Number of pages15
JournalApplied Mathematical Modelling
Issue numberFebruary
Early online date19 Oct 2022
Publication statusPublished - Feb 2023