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Random homogenization analysis for heterogeneous materials with full randomness and correlation in microstructure based on finite element method and Monte-Carlo method. (English) Zbl 1309.74063

Summary: The computationally random homogenization analysis of a two-phase heterogeneous materials is addressed in the context of linear elasticity where the randomness of constituents’ moduli and microstructural morphology together with the correlation among random moduli are fully considered, and random effective quantities such as effective elastic tensor and effective stress as well as effective strain energy together with their numerical characteristics are then sought for different boundary conditions. Based on the finite element method and Monte-carlo method, the RVE with randomly distributing particles determined by a numerical convergence scheme is firstly generated and meshed, and two types of boundary conditions controlled by average strain are then applied to the RVE where the uncertainty existing in the microstructure is accounted for simultaneously. The numerical characteristics of random effective quantities such as coefficients of variation and correlation coefficients are then evaluated, and impacts of different factors on random effective quantities are finally investigated and revealed as well.

MSC:

74Q05 Homogenization in equilibrium problems of solid mechanics
65C05 Monte Carlo methods
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74A40 Random materials and composite materials
74B05 Classical linear elasticity
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