A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model

Ferdinando Marinelli, Giuseppe Buscarnera*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate-dependent model defined within a breakage mechanics framework. For this purpose, a Generalized Backward Euler (GBE) algorithm has been implemented according to two different linearization strategies: The former is derived by a direct linearization of the constitutive equations, while the latter introduces rate effects through a consistency parameter. The accuracy and efficiency of the GBE algorithm have been investigated by (1) performing material point analyses and (2) solving initial boundary value problems. In both cases, the overall performance of the underlying algorithm is inspected for a range of loading rates, thus simulating comminution from slow to fast dynamic problems. As the viscous response of the breakage model can be recast through a viscous nucleus function, the presented algorithm can be considered as a general framework to integrate constitutive equations relying on the overstress approach typical of Perzyna-like viscoplastic models.

Original languageEnglish (US)
Pages (from-to)3-29
Number of pages27
JournalInternational Journal for Numerical and Analytical Methods in Geomechanics
Issue number1
StatePublished - Jan 2019


  • Perzyna viscoplasticity
  • continuum breakage mechanics
  • finite element method
  • integration algorithms
  • rate effects

ASJC Scopus subject areas

  • Computational Mechanics
  • Materials Science(all)
  • Geotechnical Engineering and Engineering Geology
  • Mechanics of Materials

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