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

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 differ...

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Bibliographic Details
Published in:International journal for numerical and analytical methods in geomechanics Vol. 43; no. 1; pp. 3 - 29
Main Authors: Marinelli, Ferdinando, Buscarnera, Giuseppe
Format: Journal Article
Language:English
Published: Bognor Regis Wiley Subscription Services, Inc 01.01.2019
Subjects:
Algorithms
Boundary value problems
Breakage
Comminution
Computer simulation
Constitutive equations
Constitutive relationships
continuum breakage mechanics
finite element method
Frameworks
integration algorithms
Linearization
Mathematical models
Mechanics
Numerical integration
Perzyna viscoplasticity
rate effects
ISSN:0363-9061, 1096-9853
Online Access:Get full text
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Summary: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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ISSN:0363-9061
1096-9853
DOI:10.1002/nag.2841