메뉴 건너뛰기




Volumn 55, Issue 8, 2007, Pages 1677-1701

Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: I-Analysis

Author keywords

Constitutive behavior; Finite strain; Microstructures; Porous material; Soft matter

Indexed keywords

HOMOGENIZATION METHOD; MATHEMATICAL MODELS; MICROSTRUCTURE; POROUS MATERIALS; STIFFNESS;

EID: 34250873314     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.01.007     Document Type: Article
Times cited : (49)

References (31)
  • 1
    • 0021497042 scopus 로고
    • An investigation of localization in a porous elastic material using homogenization theory
    • Abeyaratne R., and Triantafyllidis N. An investigation of localization in a porous elastic material using homogenization theory. J. Appl. Mech. 51 (1984) 481-486
    • (1984) J. Appl. Mech. , vol.51 , pp. 481-486
    • Abeyaratne, R.1    Triantafyllidis, N.2
  • 2
    • 0041097550 scopus 로고
    • A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials
    • Arruda E.M., and Boyce M.C. A three-dimensional constitutive model for the large stretch behavior of rubber elastic materials. J. Mech. Phys. Solids 41 (1993) 389-412
    • (1993) J. Mech. Phys. Solids , vol.41 , pp. 389-412
    • Arruda, E.M.1    Boyce, M.C.2
  • 3
    • 84953648079 scopus 로고
    • Application of finite elasticity theory to the deformation of rubbery materials
    • Blatz P.J., and Ko W.L. Application of finite elasticity theory to the deformation of rubbery materials. Trans. Soc. Rheol. 6 (1962) 223-251
    • (1962) Trans. Soc. Rheol. , vol.6 , pp. 223-251
    • Blatz, P.J.1    Ko, W.L.2
  • 4
    • 4944267168 scopus 로고    scopus 로고
    • Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension
    • Dacorogna B. Necessary and sufficient conditions for strong ellipticity of isotropic functions in any dimension. Discrete Contin. Dyn. Syst. Ser. B 1 (2001) 257-263
    • (2001) Discrete Contin. Dyn. Syst. Ser. B , vol.1 , pp. 257-263
    • Dacorogna, B.1
  • 5
    • 0346094001 scopus 로고    scopus 로고
    • Constitutive modeling of porous hyperelastic materials
    • Danielsson M., Parks D.M., and Boyce M.C. Constitutive modeling of porous hyperelastic materials. Mech. Mater. 36 (2004) 347-358
    • (2004) Mech. Mater. , vol.36 , pp. 347-358
    • Danielsson, M.1    Parks, D.M.2    Boyce, M.C.3
  • 6
    • 0020271545 scopus 로고
    • Nonlinear deformation of elastomeric foams
    • Feng W., and Christensen R.M. Nonlinear deformation of elastomeric foams. Int. J. Non-Linear Mech. 17 (1982) 335-367
    • (1982) Int. J. Non-Linear Mech. , vol.17 , pp. 335-367
    • Feng, W.1    Christensen, R.M.2
  • 7
    • 0002163820 scopus 로고    scopus 로고
    • A new constitutive relation for rubber
    • Gent A.N. A new constitutive relation for rubber. Rubber Chem. Technol. 69 (1996) 59-61
    • (1996) Rubber Chem. Technol. , vol.69 , pp. 59-61
    • Gent, A.N.1
  • 8
    • 85027472678 scopus 로고
    • The deformation of foamed elastic materials
    • Gent A.N., and Thomas A.G. The deformation of foamed elastic materials. J. Appl. Polym. Sci. 1 (1959) 107-113
    • (1959) J. Appl. Polym. Sci. , vol.1 , pp. 107-113
    • Gent, A.N.1    Thomas, A.G.2
  • 9
    • 21144480320 scopus 로고
    • Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity
    • Geymonat G., Müller S., and Triantafyllidis N. Homogenization of nonlinearly elastic materials, microscopic bifurcation and macroscopic loss of rank-one convexity. Arch. Ration. Mech. Anal. 122 (1993) 231-290
    • (1993) Arch. Ration. Mech. Anal. , vol.122 , pp. 231-290
    • Geymonat, G.1    Müller, S.2    Triantafyllidis, N.3
  • 10
  • 11
    • 9944252301 scopus 로고    scopus 로고
    • Compressive response of open-cell foams. Part II: initiation and evolution of crushing
    • Gong L., and Kyriakides S. Compressive response of open-cell foams. Part II: initiation and evolution of crushing. Int. J. Solids Struct. 42 (2005) 1381-1399
    • (2005) Int. J. Solids Struct. , vol.42 , pp. 1381-1399
    • Gong, L.1    Kyriakides, S.2
  • 12
    • 85024598889 scopus 로고
    • The elastic moduli of heterogeneous materials
    • Hashin Z. The elastic moduli of heterogeneous materials. J. Appl. Mech. 29 (1962) 143-150
    • (1962) J. Appl. Mech. , vol.29 , pp. 143-150
    • Hashin, Z.1
  • 13
    • 0021976554 scopus 로고
    • Large isotropic elastic deformation of composites and porous media
    • Hashin Z. Large isotropic elastic deformation of composites and porous media. Int. J. Solids Struct. 21 (1985) 711-720
    • (1985) Int. J. Solids Struct. , vol.21 , pp. 711-720
    • Hashin, Z.1
  • 14
    • 0001155575 scopus 로고
    • On constitutive macro-variables for heterogeneous solids at finite strain
    • Hill R. On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. Lond. A 326 (1972) 131-147
    • (1972) Proc. R. Soc. Lond. A , vol.326 , pp. 131-147
    • Hill, R.1
  • 15
    • 0035816052 scopus 로고    scopus 로고
    • Three-dimensional imaging of large compressive deformations in elastomeric foams
    • Kinney J.H., Marshall G.W., Marshall S.J., and Haupt D.L. Three-dimensional imaging of large compressive deformations in elastomeric foams. J. Appl. Polym. Sci. 80 (2001) 1746-1755
    • (2001) J. Appl. Polym. Sci. , vol.80 , pp. 1746-1755
    • Kinney, J.H.1    Marshall, G.W.2    Marshall, S.J.3    Haupt, D.L.4
  • 16
    • 0016576297 scopus 로고
    • On the ellipticity of the equations of nonlinear elastostatics for a special material
    • Knowles J.K., and Sternberg E. On the ellipticity of the equations of nonlinear elastostatics for a special material. J .Elasticity 5 (1975) 341-361
    • (1975) J .Elasticity , vol.5 , pp. 341-361
    • Knowles, J.K.1    Sternberg, E.2
  • 17
    • 34250877488 scopus 로고    scopus 로고
    • Lopez-Pamies, O., 2006. On the effective behavior, microstructure evolution, and macroscopic stability of elastomeric composites. Ph.D. Dissertation, University of Pennsylvania, USA.
  • 18
    • 17144410025 scopus 로고    scopus 로고
    • Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations
    • Lopez-Pamies O., and Ponte Castañeda P. Second-order estimates for the macroscopic response and loss of ellipticity in porous rubbers at large deformations. J. Elasticity 76 (2004) 247-287
    • (2004) J. Elasticity , vol.76 , pp. 247-287
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 19
    • 31044441045 scopus 로고    scopus 로고
    • On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. I-theory
    • Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. I-theory. J. Mech. Phys. Solids 54 (2006) 807-830
    • (2006) J. Mech. Phys. Solids , vol.54 , pp. 807-830
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 20
    • 31044453405 scopus 로고    scopus 로고
    • On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. II-application to cylindrical fibers
    • Lopez-Pamies O., and Ponte Castañeda P. On the overall behavior, microstructure evolution, and macroscopic stability in reinforced rubbers at large deformations. II-application to cylindrical fibers. J. Mech. Phys. Solids 54 (2006) 831-863
    • (2006) J. Mech. Phys. Solids , vol.54 , pp. 831-863
    • Lopez-Pamies, O.1    Ponte Castañeda, P.2
  • 21
    • 34250899142 scopus 로고    scopus 로고
    • Lopez-Pamies, O., Ponte Castañeda, P., 2007. Homogenization-based constitutive models for porous elastomers and implications for macroscopic instabilities: II-results. J. Mech. Phys. Solids, doi:10.1016/j.jmps.2007.01.008.
  • 22
    • 34047104433 scopus 로고    scopus 로고
    • Michel, J.-C., Lopez-Pamies, O., Ponte Castañeda, P., Triantafyllidis, N., 2007. Microscopic and macroscopic instabilities in finitely strained porous elastomers. J. Mech. Phys. Solids, doi:10.1016/j.jmps.2006.11.006.
  • 23
    • 0017927099 scopus 로고
    • Extremum principles in non-linear elasticity and their application to composites-I. Theory
    • Ogden R. Extremum principles in non-linear elasticity and their application to composites-I. Theory. Int. J. Solids Struct. 14 (1978) 265-282
    • (1978) Int. J. Solids Struct. , vol.14 , pp. 265-282
    • Ogden, R.1
  • 24
    • 0030643661 scopus 로고    scopus 로고
    • The effective elastic constants of solids containing spherical exclusions
    • O'Rourke J.P., Ingber M.S., and Weiser M.W. The effective elastic constants of solids containing spherical exclusions. J. Compos. Mater. 31 (1997) 910-934
    • (1997) J. Compos. Mater. , vol.31 , pp. 910-934
    • O'Rourke, J.P.1    Ingber, M.S.2    Weiser, M.W.3
  • 25
    • 0036533606 scopus 로고    scopus 로고
    • Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory
    • Ponte Castañeda P. Second-order homogenization estimates for nonlinear composites incorporating field fluctuations. I. Theory. J. Mech. Phys. Solids 50 (2002) 737-757
    • (2002) J. Mech. Phys. Solids , vol.50 , pp. 737-757
    • Ponte Castañeda, P.1
  • 26
    • 0020905805 scopus 로고
    • On copositive matrices and strong ellipticity for isotropic materials
    • Simpson H.C., and Spector S.J. On copositive matrices and strong ellipticity for isotropic materials. Arch. Ration. Mech. Anal. 84 (1983) 55-68
    • (1983) Arch. Ration. Mech. Anal. , vol.84 , pp. 55-68
    • Simpson, H.C.1    Spector, S.J.2
  • 27
    • 33745028217 scopus 로고    scopus 로고
    • Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading
    • Triantafyllidis N., Nestorvić M.D., and Schraad M.W. Failure surfaces for finitely strained two-phase periodic solids under general in-plane loading. J. Appl. Mech. 73 (2006) 505-515
    • (2006) J. Appl. Mech. , vol.73 , pp. 505-515
    • Triantafyllidis, N.1    Nestorvić, M.D.2    Schraad, M.W.3
  • 28
    • 49949149864 scopus 로고
    • On bounds for the overall elastic moduli of inhomogeneous systems
    • Walpole L.J. On bounds for the overall elastic moduli of inhomogeneous systems. J. Mech. Phys. Solids 14 (1966) 151-162
    • (1966) J. Mech. Phys. Solids , vol.14 , pp. 151-162
    • Walpole, L.J.1
  • 29
    • 0017502751 scopus 로고
    • Bounds and self-consistent estimates for the overall moduli of anisotropic composites
    • Willis J.R. Bounds and self-consistent estimates for the overall moduli of anisotropic composites. J. Mech. Phys. Solids 25 (1977) 185-202
    • (1977) J. Mech. Phys. Solids , vol.25 , pp. 185-202
    • Willis, J.R.1
  • 30
    • 0027701267 scopus 로고
    • Some forms of the strain energy function for rubber
    • Yeoh O.H. Some forms of the strain energy function for rubber. Rubber Chem. Technol. 66 (1993) 754-771
    • (1993) Rubber Chem. Technol. , vol.66 , pp. 754-771
    • Yeoh, O.H.1
  • 31
    • 0020548419 scopus 로고
    • Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids
    • Zee L., and Sternberg E. Ordinary and strong ellipticity in the equilibrium theory of incompressible hyperelastic solids. Arch. Ration. Mech. Anal. 83 (1983) 53-90
    • (1983) Arch. Ration. Mech. Anal. , vol.83 , pp. 53-90
    • Zee, L.1    Sternberg, E.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.