Explicit coupled thermo-mechanical finite element model of steel solidification

Seid Koric, Lance C. Hibbeler, Brian G. Thomas

Research output: Contribution to journalArticlepeer-review


The explicit finite element method is applied in this work to simulate the coupled and highly non-linear thermo-mechanical phenomena that occur during steel solidification in continuous casting processes. Variable mass scaling is used to efficiently model these processes in their natural time scale using a Lagrangian formulation. An efficient and robust local-global viscoplastic integration scheme (Int. J. Numer. Meth. Engng 2006; 66:1955-1989) to solve the highly temperature- and rate-dependent elastic-viscoplastic constitutive equations of solidifying steel has been implemented into the commercial software ABAQUS/Explicit (ABAQUS User Manuals v6.7. Simulia Inc., 2007) using a VUMAT subroutine. The model is first verified with a known semi-analytical solution from Weiner and Boley (J. Mech. Phys. Solids 1963; 11:145-154). It is then applied to simulate temperature and stress development in solidifying shell sections in continuous casting molds using realistic temperature-dependent properties and including the effects of ferrostatic pressure, narrow face taper, and mechanical contact. Example simulations include a fully coupled thermo-mechanical analysis of a billet-casting and thin-slab casting in a funnel mold. Explicit temperature and stress results are compared with the results of an implicit formulation and computing times are benchmarked for different problem sizes and different numbers of processor cores. The explicit formulation exhibits significant advantages for this class of contact-solidification problems, especially with large domains on the latest parallel computing platforms.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalInternational Journal for Numerical Methods in Engineering
Issue number1
StatePublished - 2009


  • Continuous casting
  • Explicit
  • Finite element
  • Parallel computational benchmarks
  • Solidification
  • Thermal stress

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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