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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Bibliographic Details
Published in:Composites. Part B, Engineering Vol. 50; pp. 32 - 43
Main Author: Li, H.X.
Format: Journal Article
Language:English
Published: Kidlington Elsevier Ltd 01.07.2013
Elsevier
Subjects:
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
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
ISSN:1359-8368, 1879-1069
Online Access:Get full text
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Summary: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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ISSN:1359-8368
1879-1069
DOI:10.1016/j.compositesb.2013.01.018