Finite element modeling of effective properties of elastic materials with random nanosized porosity
DOI:
https://doi.org/10.7242/1999-6691/2017.10.4.29Keywords:
porous elastic composite, nanosized pores, Gurtin-Murdoch model, surface stress, effective moduli, modeling of representative volumes, finite element methodAbstract
An integrated approach for determination of the effective properties of anisotropic porous elastic materials with a nanoscale stochastic porosity structure is presented. This approach includes an effective moduli method of composite mechanics, modeling of representative volumes and finite element method. The Gurtin-Murdoch model of surface stresses on the boundaries between material and pores is used for taking into account the nanodimension of pores. The general methodology for determination of the effective properties of porous composites is demonstrated for a two-phase composite with special conditions of stresses discontinuity on the phase interfaces. The mathematical statements of boundary value problems and the resulting formulae to determine the complete set of effective constants of the two-phase composites with arbitrary anisotropy and surface properties are described; the generalized statements is formulated and the finite element approximations are given. It is noted that the homogenization problem for the composites under study can be solved using the known finite element software and choosing the shell finite elements with the options of membrane stiffness only for taking into consideration the surface interphase stresses. It is also shown that the homogenization procedures for porous composites with surface stresses can be considered as special cases of the corresponding procedures for two-phase composites with interphase stresses if the stiffness moduli of nanoinclusions are negligibly small. The specific realization of these approaches is made in the finite element package ANSYS. An algorithm for automatic determination of interphase boundaries and location of shell elements on them, which works for different sizes of representative volumes, built in the form of a cubic lattice of hexahedral finite elements, is described. The efficiency of the algorithm has been tested using the models of porous material of hexagonal system at different values of surface moduli, porosity and number of pores. Simulations have revealed the influence of the area of the value of interphase boundaries on the effective moduli of the porous material with nanosized structure.
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Eremeyev V.A. On effective properties of materials at the nano- and microscales considering surface effects // Acta Mech. - 2016. - Vol. 227, no. 1. - P. 29-42.
2. Hamilton J.C., Wolfer W.G. Theories of surface elasticity for nanoscale objects // Surf. Sci. - 2009. - Vol. 603, no. 9. - P. 1284-1291.
3. Wang J., Huang Z., Duan H., Yu S., Feng X., Wang G., Zhang W., Wang T. Surface stress effect in mechanics of nanostructured materials // Acta Mech. Solida Sin. - 2011. - Vol. 24, no. 1. - P. 52-82.
4. Wang K.F., Wang B.L., Kitamura T. A review on the application of modified continuum models in modeling and simulation of nanostructures // Acta Mech. Sinica. - 2016. - Vol. 32, no. 1. - P. 83-100.
5. Gurtin M.E., Murdoch A.I. A continuum theory of elastic material surfaces // Arch. Ration Mech. An. - 1975. - Vol. 57, no. 4. - P. 291-323.
6. Chatzigeorgiou G., Javili A., Steinmann P. Multiscale modelling for composites with energetic interfaces at the micro- or nanoscale // Math. Mech. Solids. - 2015. - Vol. 20, no. 9. - P. 1130-1145.
7. Duan H.L., Wang J., Huang Z.P., Karihaloo B.L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress // J. Mech. Phys. Solids. - 2005. - Vol. 53, no. 7. - P. 1574-1596.
8. Javili A., Steinmann P., Mosler J. Micro-to-macro transition accounting for general imperfect interfaces // Comput. Method. Appl. M. - 2017. - Vol. 317. - P. 274-317.
9. Le Quang H., He Q.-C. Variational principles and bounds for elastic inhomogeneous materials with coherent imperfect interfaces // Mech. Mater. - 2008. - Vol. 40, no. 10. - P. 865-884.
10. Brisard S., Dormieux L., Kondo D. Hashin-Shtrikman bounds on the bulk modulus of a nanocomposite with spherical inclusions and interface effects // Comp. Mater. Sci. - 2010. - Vol. 48, no. 3. - P. 589-596.
11. Brisard S., Dormieux L., Kondo D. Hashin-Shtrikman bounds on the shear modulus of a nanocomposite with spherical inclusions and interface effects // Comp. Mater. Sci. - 2010. - Vol. 50, no. 2. - P. 403-410.
12. Chen T., Dvorak G.J., Yu C.C. Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal-mechanical connections // Int. J. Solids Struct. - 2007. - Vol. 44, no. 3-4. - P. 941-955.
13. Duan H.L., Wang J., Huang Z.P., Karihaloo B.L. Eshelby formalism for nano-inhomogeneities // P. Roy. Soc. Lond. A. - 2005. - Vol. 461. - P. 3335-3353.
14. Duan H.L., Wang J., Karihaloo B.L., Huang Z.P. Nanoporous materials can be made stiffer than non-porous counterparts by surface modification // Acta Mater. - 2006. - Vol. 54, no. 11. - P. 2983-2990.
15. Eremeev V.A., Morozov N.F. Ob effektivnoj zestkosti nanoporistogo sterzna // DAN. - 2010. - T. 432, No 4. - S. 473-476.
16. Jeong J., Cho M., Choi J. Effective mechanical properties of micro/nano-scale porous materials considering surface effects // Interaction and Multiscale Mechanics. - 2011. - Vol. 4, no. 2. - P. 107-122.
17. Kushch V.I., Mogilevskaya S.G., Stolarski H.K., Crouch S.L. Elastic interaction of spherical nanoinhomogeneities with Gurtin-Murdoch type interfaces // J. Mech. Phys. Solids. - 2011. - Vol. 59, no. 9. - P. 1702-1716.
18. Nazarenko L., Bargmann S., Stolarski H. Energy-equivalent inhomogeneity approach to analysis of effective properties of nanomaterials with stochastic structure // Int. J. Solids Struct. - 2015. - Vol. 59. - P. 183-197.
19. Nasedkin A.V., Kornievsky A.S. Finite element modeling and computer design of anisotropic elastic porous composites with surface stresses / Wave dynamics and mechanics of composites for analysis of microstructured materials and metamaterials. Ser. Advanced Structured Materials. - 2017. - Vol. 59. - P. 107-122.
20. Nasedkin A.V., Nasedkina A.A., Kornievsky A.S. Modeling of nanostructured porous thermoelastic composites with surface effects // AIP Conf. Proc. - 2017. - Vol. 1798. - 020110.
21. Nasedkin A.V., Nasedkina A.A., Kornievsky A.S. Finite element modeling of effective properties of nanoporous thermoelastic composites with surface effects // Coupled Problems 2017 - Proceedings of the VII International Conference on Coupled Problems in Science and Engineering, 12-14 June 2017, Rhodes Island, Greece. - P. 1140-1151.
22. Tian L., Rajapakse R.K.N.D. Finite element modelling of nanoscale inhomogeneities in an elastic matrix // Comp. Mater. Sci. - 2007. - Vol. 41, no. 1. - P. 44-53.
23. Riaz U., Ashraf S.M. Application of finite element method for the design of nanocomposites // Computational finite element methods in nanotechnology / Ed. by S.M. Musa. - CRC Press, 2012. - Ch. 7. - P. 241-290.
24. Smith J.F., Arbogast C.L. Elastic constants of single crystal beryllium // J. Appl. Phys. - 1960. - Vol. 31. - P. 99-101.
25. Nasedkin A.V., Nasedkina A.A., Remizov V.V. Konecno-elementnoe modelirovanie poristyh termouprugih kompozitov s ucetom mikrostruktury // Vycisl. meh. splos. sred. - 2014. - T. 7, No 1. - S. 100-109.
26. Kurbatova N.V., Nadolin D.K., Nasedkin A.V., Nasedkina A.A., Oganesyan P.A., Skaliukh A.S., Soloviev A.N. Models of active bulk composites and new opportunities of ACELAN finite element package / Wave dynamics and mechanics of composites for analysis of microstructured materials and metamaterials. Ser. Advanced Structured Materials. - 2017. - Vol. 59. - P. 133-158.
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