TY - JOUR
T1 - A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model
AU - Marinelli, Ferdinando
AU - Buscarnera, Giuseppe
N1 - Funding Information:
This research was primarily supported by the U.S. Department of Energy through grant DE-SC0017615. Partial support of the U.S. Army Research Office under grant number W911NF-18-1-0035 is also gratefully acknowledged. The authors also wish to thank Yida Zhang for his useful suggestions during the development of the manuscript.
PY - 2019/1
Y1 - 2019/1
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
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U2 - 10.1002/nag.2841
DO - 10.1002/nag.2841
M3 - Article
AN - SCOPUS:85052622083
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 -