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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| Vydáno v: | International journal for numerical and analytical methods in geomechanics Ročník 43; číslo 1; s. 3 - 29 |
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| Jazyk: | angličtina |
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Bognor Regis
Wiley Subscription Services, Inc
01.01.2019
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| ISSN: | 0363-9061, 1096-9853 |
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| Abstract | 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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| AbstractList | 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. 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. |
| Author | Buscarnera, Giuseppe Marinelli, Ferdinando |
| Author_xml | – sequence: 1 givenname: Ferdinando orcidid: 0000-0002-1069-8655 surname: Marinelli fullname: Marinelli, Ferdinando organization: Northwestern University – sequence: 2 givenname: Giuseppe orcidid: 0000-0003-1664-9616 surname: Buscarnera fullname: Buscarnera, Giuseppe email: g‐buscarnera@northwestern.edu organization: Northwestern University |
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| CitedBy_id | crossref_primary_10_1016_j_gsf_2019_11_006 crossref_primary_10_3390_app11083513 crossref_primary_10_1016_j_mechmat_2023_104722 crossref_primary_10_1016_j_jmps_2020_103975 crossref_primary_10_1007_s11043_021_09485_1 crossref_primary_10_1016_j_compgeo_2025_107425 |
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This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate‐dependent model defined... This paper discusses the formulation and the numerical performance of a fully implicit algorithm used to integrate a rate‐dependent model defined within a... |
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| SubjectTerms | 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 |
| Title | A Generalized Backward Euler algorithm for the numerical integration of a viscous breakage model |
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