메뉴 건너뛰기




Volumn 200, Issue 17-20, 2011, Pages 1637-1648

A probabilistic model for bounded elasticity tensor random fields with application to polycrystalline microstructures

Author keywords

Apparent elasticity tensor; Heterogeneous materials; Mesoscale modeling; Micromechanics; Non Gaussian; Random field

Indexed keywords

ELASTICITY TENSOR; HETEROGENEOUS MATERIALS; MESOSCALE MODELING; NON-GAUSSIAN; RANDOM FIELDS;

EID: 79951710517     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2011.01.016     Document Type: Article
Times cited : (82)

References (40)
  • 2
    • 77956227456 scopus 로고    scopus 로고
    • A bounded random matrix approach for stochastic upscaling
    • Das S., Ghanem R. A bounded random matrix approach for stochastic upscaling. Multiscale Model. Simul. 2009, 8(1):296-325.
    • (2009) Multiscale Model. Simul. , vol.8 , Issue.1 , pp. 296-325
    • Das, S.1    Ghanem, R.2
  • 4
    • 33750379557 scopus 로고    scopus 로고
    • On the size of representative volume element for Darcy law in random media
    • Du X., Ostoja-Starzewski M. On the size of representative volume element for Darcy law in random media. Proc. Roy. Soc. A 2006, 462:2949-2963.
    • (2006) Proc. Roy. Soc. A , vol.462 , pp. 2949-2963
    • Du, X.1    Ostoja-Starzewski, M.2
  • 6
    • 77956225743 scopus 로고    scopus 로고
    • A stochastic model for elasticity tensors with uncertain material symmetries
    • Guilleminot J., Soize C. A stochastic model for elasticity tensors with uncertain material symmetries. Int. J. Solids Struct. 2010, 47(22-23):3121-3131.
    • (2010) Int. J. Solids Struct. , vol.47 , Issue.22-23 , pp. 3121-3131
    • Guilleminot, J.1    Soize, C.2
  • 8
    • 0000798009 scopus 로고
    • Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume
    • Hazanov S., Huet C. Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. J. Mech. Phys. Solids 1994, 42(12):1995-2011.
    • (1994) J. Mech. Phys. Solids , vol.42 , Issue.12 , pp. 1995-2011
    • Hazanov, S.1    Huet, C.2
  • 9
    • 6544226089 scopus 로고
    • Elastic properties of reinforced solids: some theoretical principles
    • Hill R. Elastic properties of reinforced solids: some theoretical principles. J. Mech. Phys. Solids 1963, 11:357-372.
    • (1963) J. Mech. Phys. Solids , vol.11 , pp. 357-372
    • Hill, R.1
  • 10
    • 0000926336 scopus 로고
    • Application of variational concepts to size effects in elastic heterogeneous bodies
    • Huet C. Application of variational concepts to size effects in elastic heterogeneous bodies. J. Mech. Phys. Solids 1990, 38(6):813-841.
    • (1990) J. Mech. Phys. Solids , vol.38 , Issue.6 , pp. 813-841
    • Huet, C.1
  • 11
    • 84933516758 scopus 로고
    • A distribution-free approach to inducing rank correlation among input variables
    • Iman R.L., Conover W. A distribution-free approach to inducing rank correlation among input variables. Commun. Stat. - Simul. Comput. 1982, 11:311-334.
    • (1982) Commun. Stat. - Simul. Comput. , vol.11 , pp. 311-334
    • Iman, R.L.1    Conover, W.2
  • 12
    • 0442328971 scopus 로고    scopus 로고
    • Spectral stochastic homogenization of divergence-type pdes
    • Jardak M., Ghanem R.G. Spectral stochastic homogenization of divergence-type pdes. Comput. Methods Appl. Mech. Engrg. 2004, 193(6-8):429-447.
    • (2004) Comput. Methods Appl. Mech. Engrg. , vol.193 , Issue.6-8 , pp. 429-447
    • Jardak, M.1    Ghanem, R.G.2
  • 13
    • 11944266539 scopus 로고
    • Information theory and statistical mechanics
    • Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 1957, 106(4):620-630.
    • (1957) Phys. Rev. , vol.106 , Issue.4 , pp. 620-630
    • Jaynes, E.T.1
  • 14
    • 11944275853 scopus 로고
    • Information theory and statistical mechanics
    • Jaynes E.T. Information theory and statistical mechanics. Phys. Rev. 1957, 108(2):171-190.
    • (1957) Phys. Rev. , vol.108 , Issue.2 , pp. 171-190
    • Jaynes, E.T.1
  • 15
    • 20344396845 scopus 로고    scopus 로고
    • Yalmip: a toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE Conference on Computer Aided Control Systems Design (CACSD), Taipei, Taiwan.
    • J. Löfberg, Yalmip: a toolbox for modeling and optimization in MATLAB, in: Proceedings of the IEEE Conference on Computer Aided Control Systems Design (CACSD), Taipei, Taiwan, 2004.
    • (2004)
    • Löfberg, J.1
  • 17
    • 0036687090 scopus 로고    scopus 로고
    • Matrix-variate Kummer-beta distribution
    • Nagar D.K., Gupta A.K. Matrix-variate Kummer-beta distribution. J. Aust. Math. Soc. 2002, 73:11-25.
    • (2002) J. Aust. Math. Soc. , vol.73 , pp. 11-25
    • Nagar, D.K.1    Gupta, A.K.2
  • 18
    • 1642370803 scopus 로고    scopus 로고
    • Slice sampling
    • Neal R.M. Slice sampling. Ann. Stat 2003, 31(3):705-767.
    • (2003) Ann. Stat , vol.31 , Issue.3 , pp. 705-767
    • Neal, R.M.1
  • 20
    • 0003760944 scopus 로고    scopus 로고
    • Spatial Tessellations: Concepts and Applications of Voronoi Diagram
    • Wiley
    • Okabe A. Spatial Tessellations: Concepts and Applications of Voronoi Diagram. Wiley Series in Probability and Statistics 2000, Wiley.
    • (2000) Wiley Series in Probability and Statistics
    • Okabe, A.1
  • 22
    • 44349131648 scopus 로고    scopus 로고
    • Microstructure representation and material characterization for multiscale finite element simulations of local mechanical behavior in damaged metallic structures, in: Proceedings of SPIE, The International Society for Optical Engineering, San Diego, California, USA, 10-12 March.
    • M. Parra Garcia, C. Luo, A. Noshadravan, A. Keck, R. Teale, A. Chattopadhyay, P. Peralta, Microstructure representation and material characterization for multiscale finite element simulations of local mechanical behavior in damaged metallic structures, in: Proceedings of SPIE, The International Society for Optical Engineering, San Diego, California, USA, 10-12 March 2008.
    • (2008)
    • Parra, G.M.1    Luo, C.2    Noshadravan, A.3    Keck, A.4    Teale, R.5    Chattopadhyay, A.6    Peralta, P.7
  • 23
    • 47749116439 scopus 로고    scopus 로고
    • Scaling function, anisotropy and the size of rve in elastic random polycrystals
    • Ranganathan S.I., Ostoja-Starzewski M. Scaling function, anisotropy and the size of rve in elastic random polycrystals. J. Mech. Phys. Solids 2008, 56:2773-2791.
    • (2008) J. Mech. Phys. Solids , vol.56 , pp. 2773-2791
    • Ranganathan, S.I.1    Ostoja-Starzewski, M.2
  • 24
    • 0027100591 scopus 로고
    • On the homogenization and the simulation of random materials
    • Sab K. On the homogenization and the simulation of random materials. Eur. J. Mech. A/Solids 1992, 11(5):585-607.
    • (1992) Eur. J. Mech. A/Solids , vol.11 , Issue.5 , pp. 585-607
    • Sab, K.1
  • 25
    • 33646002343 scopus 로고    scopus 로고
    • A maximum entropy approach for property prediction of random microstructures
    • Sankaran S., Zabaras N. A maximum entropy approach for property prediction of random microstructures. Acta Mater. 2006, 54:2265-2276.
    • (2006) Acta Mater. , vol.54 , pp. 2265-2276
    • Sankaran, S.1    Zabaras, N.2
  • 26
    • 0040356393 scopus 로고
    • Anisotropic growth of Voronoi cells
    • Scheike T.H. Anisotropic growth of Voronoi cells. Adv. Appl. Probab. 1994, 26(1):43-53.
    • (1994) Adv. Appl. Probab. , vol.26 , Issue.1 , pp. 43-53
    • Scheike, T.H.1
  • 29
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • 623-659
    • Shannon C.E. A mathematical theory of communication. Bell System Tech. J. 1948, 27:379-423. 623-659.
    • (1948) Bell System Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 30
    • 84955045119 scopus 로고
    • Simulations of multivariate and multidimensional random processes
    • Shinozuka M. Simulations of multivariate and multidimensional random processes. J. Acoust. Soc. Am. 1971, 39(1):357-367.
    • (1971) J. Acoust. Soc. Am. , vol.39 , Issue.1 , pp. 357-367
    • Shinozuka, M.1
  • 31
    • 0033737120 scopus 로고    scopus 로고
    • A nonparametric model of random uncertainties on reduced matrix model in structural dynamics
    • Soize C. A nonparametric model of random uncertainties on reduced matrix model in structural dynamics. Probabilist. Engrg. Mech. 2000, 15(3):277-294.
    • (2000) Probabilist. Engrg. Mech. , vol.15 , Issue.3 , pp. 277-294
    • Soize, C.1
  • 32
    • 0035041285 scopus 로고    scopus 로고
    • Maximum entropy approach for modeling random uncertainties in transient elastodynamics
    • Soize C. Maximum entropy approach for modeling random uncertainties in transient elastodynamics. J. Acoust. Soc. Am. 2001, 109(5):1979-1996.
    • (2001) J. Acoust. Soc. Am. , vol.109 , Issue.5 , pp. 1979-1996
    • Soize, C.1
  • 33
    • 27244456853 scopus 로고    scopus 로고
    • Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators
    • Soize C. Non-gaussian positive-definite matrix-valued random fields for elliptic stochastic partial differential operators. Comput. Methods Appl. Mech. Engrg. 2006, 195:26-64.
    • (2006) Comput. Methods Appl. Mech. Engrg. , vol.195 , pp. 26-64
    • Soize, C.1
  • 34
    • 41549125432 scopus 로고    scopus 로고
    • Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size
    • Soize C. Tensor-valued random fields for meso-scale stochastic model of anisotropic elastic microstructure and probabilistic analysis of representative volume element size. Probabilist. Engrg. Mech. 2008, 23:307-323.
    • (2008) Probabilist. Engrg. Mech. , vol.23 , pp. 307-323
    • Soize, C.1
  • 35
    • 74949132133 scopus 로고    scopus 로고
    • Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions
    • Soize C. Generalized probabilistic approach of uncertainties in computational dynamics using random matrices and polynomial chaos decompositions. Int. J. Numer. Methods Engrg. 2010, 81(8):939-970.
    • (2010) Int. J. Numer. Methods Engrg. , vol.81 , Issue.8 , pp. 939-970
    • Soize, C.1
  • 36
    • 77956232388 scopus 로고    scopus 로고
    • Modeling of random anisotropic elastic media and impact on wave propagation
    • Ta Q.A., Clouteau D., Cottereau R. Modeling of random anisotropic elastic media and impact on wave propagation. Eur. J. Comput. Mech. 2010, 19(1-2-3):241-253.
    • (2010) Eur. J. Comput. Mech. , vol.19 , Issue.1-2 , pp. 241-253
    • Ta, Q.A.1    Clouteau, D.2    Cottereau, R.3
  • 37
    • 77954271074 scopus 로고    scopus 로고
    • A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties
    • Tootkaboni M., Graham-Brady L. A multi-scale spectral stochastic method for homogenization of multi-phase periodic composites with random material properties. Int. J. Numer. Methods Engrg. 2010, 83:59-90.
    • (2010) Int. J. Numer. Methods Engrg. , vol.83 , pp. 59-90
    • Tootkaboni, M.1    Graham-Brady, L.2
  • 39
    • 0030106462 scopus 로고    scopus 로고
    • Semidefinite programming
    • Vandenberghe L., Boyd S. Semidefinite programming. SIAM Rev. 1996, 38(1):49-95.
    • (1996) SIAM Rev. , vol.38 , Issue.1 , pp. 49-95
    • Vandenberghe, L.1    Boyd, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.