Abstract
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 language | English (US) |
|---|---|
| Pages (from-to) | 3-29 |
| Number of pages | 27 |
| Journal | International Journal for Numerical and Analytical Methods in Geomechanics |
| Volume | 43 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2019 |
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Keywords
- 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
Cite this
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A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model. / Marinelli, Ferdinando; Buscarnera, Giuseppe.
In: International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 43, No. 1, 01.01.2019, p. 3-29.Research output: Contribution to journal › Article
TY - JOUR
T1 - A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model
AU - Marinelli, Ferdinando
AU - Buscarnera, Giuseppe
PY - 2019/1/1
Y1 - 2019/1/1
N2 - 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.
AB - 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.
KW - Perzyna viscoplasticity
KW - continuum breakage mechanics
KW - finite element method
KW - integration algorithms
KW - rate effects
UR - http://www.scopus.com/inward/record.url?scp=85052622083&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85052622083&partnerID=8YFLogxK
U2 - 10.1002/nag.2841
DO - 10.1002/nag.2841
M3 - Article
VL - 43
SP - 3
EP - 29
JO - International Journal for Numerical and Analytical Methods in Geomechanics
JF - International Journal for Numerical and Analytical Methods in Geomechanics
SN - 0363-9061
IS - 1
ER -