A microscopic nonlinear programming approach to shakedown analysis of cohesive–frictional composites
A microscopic approach together with nonlinear programming technique and finite element method is developed for shakedown analysis of a composite which has cohesive–frictional constituents. The macroscopic shakedown limit of a composite subject to cyclic loading is calculated in a direct way and the...
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| Vydané v: | Composites. Part B, Engineering Ročník 50; s. 32 - 43 |
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| Médium: | Journal Article |
| Jazyk: | English |
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Kidlington
Elsevier Ltd
01.07.2013
Elsevier |
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| ISSN: | 1359-8368, 1879-1069 |
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| Abstract | A microscopic approach together with nonlinear programming technique and finite element method is developed for shakedown analysis of a composite which has cohesive–frictional constituents. The macroscopic shakedown limit of a composite subject to cyclic loading is calculated in a direct way and the macro–micro relation is quantitatively evaluated. First, by means of the homogenization theory, the classical kinematic theorem of shakedown analysis is generalized to incorporate the microstructure – Representative Volume Element (RVE) chosen from a periodic heterogeneous material. Pressure-dependence and non-associated plastic flow of cohesive–frictional constituent materials are formulated into shakedown analysis. Based on the mathematical programming technique and the finite element method, the numerical micro-shakedown model is finally formulated as a nonlinear programming problem subject to only a few equality constraints, which is solved by a generalized Lagrangian-penalty iterative algorithm. The proposed approach provides a direct approach for determining the reduced macroscopic strength domain of heterogeneous or composite materials due to cyclic loading. Meanwhile, it can capture different plastic behaviors of materials and therefore the developed method has a wide applicability. |
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| AbstractList | A microscopic approach together with nonlinear programming technique and finite element method is developed for shakedown analysis of a composite which has cohesive–frictional constituents. The macroscopic shakedown limit of a composite subject to cyclic loading is calculated in a direct way and the macro–micro relation is quantitatively evaluated. First, by means of the homogenization theory, the classical kinematic theorem of shakedown analysis is generalized to incorporate the microstructure – Representative Volume Element (RVE) chosen from a periodic heterogeneous material. Pressure-dependence and non-associated plastic flow of cohesive–frictional constituent materials are formulated into shakedown analysis. Based on the mathematical programming technique and the finite element method, the numerical micro-shakedown model is finally formulated as a nonlinear programming problem subject to only a few equality constraints, which is solved by a generalized Lagrangian-penalty iterative algorithm. The proposed approach provides a direct approach for determining the reduced macroscopic strength domain of heterogeneous or composite materials due to cyclic loading. Meanwhile, it can capture different plastic behaviors of materials and therefore the developed method has a wide applicability. |
| Author | Li, H.X. |
| Author_xml | – sequence: 1 givenname: H.X. surname: Li fullname: Li, H.X. email: huaxiang.li@hotmail.com organization: Department of Civil Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK |
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| CitedBy_id | crossref_primary_10_1016_j_compstruct_2018_01_005 crossref_primary_10_1016_j_compstruct_2019_110951 crossref_primary_10_1186_s10033_021_00660_6 crossref_primary_10_1016_j_ijmecsci_2019_06_001 crossref_primary_10_1016_j_apm_2020_09_056 crossref_primary_10_1016_j_compstruct_2023_116938 crossref_primary_10_3390_mi14122191 crossref_primary_10_1007_s11831_015_9158_8 crossref_primary_10_1016_j_cma_2019_04_044 crossref_primary_10_1002_nme_5561 crossref_primary_10_1016_j_euromechsol_2022_104654 crossref_primary_10_1016_j_ijmecsci_2024_109908 |
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| Keywords | C. Numerical analysis C. Finite element analysis (FEA) B. Microstructures Shakedown analysis Representative volume element Theoretical study Mechanical properties Modeling Composite material Finite element method Shakedown Pressure effect Elastoplasticity Non linear model Homogenization methods Numerical simulation |
| Language | English |
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| SubjectTerms | algorithms B. Microstructures C. Finite element analysis (FEA) C. Numerical analysis Cohesion composite materials Constituents Exact sciences and technology Fatigue (materials) finite element analysis Fundamental areas of phenomenology (including applications) homogenization Homogenizing Mathematical analysis Mathematical models microstructure Nonlinear programming Physics Shakedown analysis Solid mechanics Static elasticity (thermoelasticity...) Structural and continuum mechanics |
| Title | A microscopic nonlinear programming approach to shakedown analysis of cohesive–frictional composites |
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