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

Marinelli, Ferdinando; Buscarnera, Giuseppe

doi:10.1002/nag.2841

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

Journal Article · Wed Aug 22 00:00:00 EDT 2018 · International Journal for Numerical and Analytical Methods in Geomechanics

DOI:https://doi.org/10.1002/nag.2841· OSTI ID:1612717

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Northwestern Univ., Evanston, IL (United States)

Summary 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.

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Research Organization:: Northwestern Univ., Evanston, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC); US Army Research Office (ARO)

Grant/Contract Number:: SC0017615; W911NF-18-1-003

OSTI ID:: 1612717

Alternate ID(s):: OSTI ID: 1465899

Journal Information:: International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, Issue 1; ISSN 0363-9061

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 4 works

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42 ENGINEERING
36 MATERIALS SCIENCE
Engineering
materials science
continuum breakage mechanics
finite element method
integration algorithms
Perzyna viscoplasticity
rate effects

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

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