A statistical descriptor based volume-integral micromechanics model of heterogeneous material with arbitrary inclusion shape.

*(English)*Zbl 1329.74026Summary: A continuing challenge in computational materials design is developing a model to link the microstructure of a material to its material properties in both an accurate and computationally efficient manner. In this paper, such a model is developed which uses image-based data from characterization studies combined with a newly developed self-consistent volume-integral micromechanics model (SVIM) for linear elastic material. It is observed that SVIM is able to capture the effective stress/strain distribution inside the inclusion, as well as effects of volume fraction and nearest inclusion distance on the effective properties of heterogeneous material. More importantly, SVIM can be applied to inclusions with arbitrary shape through discretizing the inclusion domain. For both 2-dimensional and 3-dimensional problems with circular and spherical inhomogeneities, SVIM’s capability of predicting effective elastic properties is validated against experiments and direct numerical simulations using the finite element method. Finally, the effect of inclusion shape is predicted by SVIM.

##### MSC:

74A60 | Micromechanical theories |

74A25 | Molecular, statistical, and kinetic theories in solid mechanics |

##### Keywords:

micro-mechanics; modulus and composites; finite element; materials design; statistical descriptors
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\textit{Z. Liu} et al., Comput. Mech. 55, No. 5, 963--981 (2015; Zbl 1329.74026)

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##### References:

[1] | Olson, GB, Designing a new material world, Science, 288, 993-998, (2000) · Zbl 1107.62383 |

[2] | Panchal, JH; Kalidindi, SR; McDowell, DL, Key computational modeling issues in integrated computational materials engineering, Comput-Aided Des, 45, 4-25, (2013) |

[3] | Monetto, I; Drugan, W, A micromechanics-based nonlocal constitutive equation and minimum RVE size estimates for random elastic composites containing aligned spheroidal heterogeneities, J Mech Phys Solids, 57, 1578-1595, (2009) · Zbl 1371.74236 |

[4] | Liu, C, On the minimum size of representative volume element: an experimental investigation, Exp Mech, 45, 238-243, (2005) |

[5] | Deng, H; Liu, Y; Gai, D; Dikin, DA; Putz, KW; Chen, W; etal., Utilizing real and statistically reconstructed microstructures for the viscoelastic modeling of polymer nanocomposites, Compos Sci Technol, 72, 1725-1732, (2012) |

[6] | Xu H, Deng H, Brinson C, Dikin D, Liu WK, Chen W et al (2012) Stochastic reassembly for managing the information complexity in multilevel analysis of heterogeneous materials. In: ASME. International design engineering technical conferences and computers and information in engineering conference, pp 199-208 |

[7] | Xu, H; Greene, MS; Deng, H; Dikin, D; Brinson, C; Liu, WK; etal., Stochastic reassembly strategy for managing information complexity in heterogeneous materials analysis and design, J Mech Des, 135, 101010, (2013) |

[8] | Moulinec, H; Suquet, P, A numerical method for computing the overall response of nonlinear composites with complex microstructure, Comput Methods Appl Mech Eng, 157, 69-94, (1998) · Zbl 0954.74079 |

[9] | Moore, JA; Ma, R; Domel, AG; Liu, WK, An efficient multiscale model of damping properties for filled elastomers with complex microstructures, Compos Part B, 62, 262-270, (2014) |

[10] | Mori, T; Tanaka, K, Average stress in matrix and average elastic energy of materials with misfitting inclusions, Acta Metall, 21, 571-574, (1973) |

[11] | Halpin JC (1992) Primer on composite materials analysis (revised). CRC Press, Richmond |

[12] | Hashin, Z; Shtrikman, S, A variational approach to the theory of the elastic behaviour of multiphase materials, J Mech Phys Solids, 11, 127-140, (1963) · Zbl 0108.36902 |

[13] | Hashin, Z, The elastic moduli of heterogeneous materials, J Appl Mech, 29, 143-150, (1962) · Zbl 0102.17401 |

[14] | Eshelby, JD, The determination of the elastic field of an ellipsoidal inclusion, and related problems, Proc R Soc Lond Ser A Math Phys Sci, 241, 376-396, (1957) · Zbl 0079.39606 |

[15] | Hill, R, A self-consistent mechanics of composite materials, J Mech Phys Solids, 13, 213-222, (1965) |

[16] | Christensen, R; Lo, K, Solutions for effective shear properties in three phase sphere and cylinder models, J Mech Phys Solids, 27, 315-330, (1979) · Zbl 0419.73007 |

[17] | Bendsoe, MP; Guedes, J; Haber, R; Pedersen, P; Taylor, J, An analytical model to predict optimal material properties in the context of optimal structural design, J Appl Mech, 61, 930-937, (1994) · Zbl 0831.73036 |

[18] | Ju, J; Chen, T, Effective elastic moduli of two-phase composites containing randomly dispersed spherical inhomogeneities, Acta Mech, 103, 123-144, (1994) · Zbl 0811.73044 |

[19] | Ju, J; Chen, TM, Micromechanics and effective moduli of elastic composites containing randomly dispersed ellipsoidal inhomogeneities, Acta Mech, 103, 103-121, (1994) · Zbl 0811.73045 |

[20] | Hassani, B; Hinton, E, A review of homogenization and topology optimization I-homogenization theory for media with periodic structure, Comput Struct, 69, 707-717, (1998) · Zbl 0948.74048 |

[21] | Hill, R, Elastic properties of reinforced solids: some theoretical principles, J Mech Phys Solids, 11, 357-372, (1963) · Zbl 0114.15804 |

[22] | Liu, Y; Steven Greene, M; Chen, W; Dikin, DA; Liu, WK, Computational microstructure characterization and reconstruction for stochastic multiscale material design, Comput-Aided Des, 45, 65-76, (2013) |

[23] | Li S, Wang G (2008) Introduction to micromechanics and nanomechanics, vol 278. World Scientific, Singapore · Zbl 1169.74001 |

[24] | Tanaka, K; Mori, T, Note on volume integrals of the elastic field around an ellipsoidal inclusion, J Elast, 2, 199-200, (1972) |

[25] | Lee J, Mal A (1997) A volume integral equation technique for multiple inclusion and crack interaction problems. J Appl Mech 64:23-31 · Zbl 1002.74597 |

[26] | Li, HB; Han, GM; Mang, HA, A new method for evaluating singular integrals in stress analysis of solids by the direct boundary element method, Int J Numer Methods Eng, 21, 2071-2098, (1985) · Zbl 0576.65129 |

[27] | Hansen J-P, McDonald IR (1990) Theory of simple liquids. Elsevier, Amsterdam |

[28] | Wertheim, M, Exact solution of the percus-yevick integral equation for hard spheres, Phys Rev Lett, 10, 321-323, (1963) · Zbl 0129.44302 |

[29] | Melro, A; Camanho, P; Pinho, S, Generation of random distribution of fibres in long-fibre reinforced composites, Compos Sci Technol, 68, 2092-2102, (2008) |

[30] | Segurado, J; Llorca, J, A numerical approximation to the elastic properties of sphere-reinforced composites, J Mech Phys Solids, 50, 2107-2121, (2002) · Zbl 1151.74335 |

[31] | Smith, JC, Experimental values for the elastic constants of a particulate-filled glassy polymer, J Res NBS A, 80, 45-49, (1976) |

[32] | Richard, TG, The mechanical behavior of a solid microsphere filled composite, J Compos Mater, 9, 108-113, (1975) |

[33] | Percus, JK; Yevick, GJ, Analysis of classical statistical mechanics by means of collective coordinates, Phys Rev, 110, 1, (1958) · Zbl 0096.23105 |

[34] | Love AEH (2013) A treatise on the mathematical theory of elasticity. Cambridge University Press, Cambridge |

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