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A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model
Author(s) -
Marinelli Ferdinando,
Buscarnera Giuseppe
Publication year - 2019
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.2841
Subject(s) - linearization , breakage , constitutive equation , backward euler method , consistency (knowledge bases) , euler method , viscoplasticity , boundary value problem , algorithm , point (geometry) , mathematics , euler's formula , range (aeronautics) , euler equations , computer science , nonlinear system , finite element method , mathematical analysis , structural engineering , engineering , geometry , physics , quantum mechanics , world wide web , aerospace engineering
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.