Optimal lower bounds on the hydrostatic stress amplification inside random two-phase elastic composites

Journal of the Mechanics and Physics of Solids

Volumn 53, Issue 11, 2005, Pages 2471-2481

  Lipton, Robert ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

Composite materials; Failure criteria; Stress concentrations

Indexed keywords

ELASTIC MODULI; ELASTICITY; HYDROSTATIC PRESSING; MICROSTRUCTURE; STRESSES;

HYDROSTATIC STRESS AMPLIFICATION; VOLUME FRACTIONS;

COMPOSITE MATERIALS;

EID: 24944467707     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2005.06.007     Document Type: Article

References (12)

1. X. Chen, and W. Mai Three-dimensional elastoplastic finite element modeling of deformation and fracture behaviour of rubber-modified polycarbonates at different triaxiality J. Mater. Sci. 34 1999 2139 2149
2. Y. Grabovsky, and R.V. Kohn Microstructures minimizing the energy of a two phase elastic composite in two space dimensions. II The Vigdergauz microstructure J. Mech. Phys. Solids 43 1995 949 972
3. Z. Hashin The elastic moduli of heterogeneous materials J. Appl. Mech. 29 1962 143 150
4. Z. Hashin, and S. Shtrikman A variational approach to the theory of the effective magnetic permeability of multiphase materials J. Appl. Phys. 33 1962 3125 3131
5. Z. Hashin, and S. Shtrikman A variational approach to the theory of the elastic behavior of multiphase materials J. Mech. Phys. Solids 11 1963 127 140
6. Z. Hashin, and B.W. Rosen The elastic moduli of fiber reinforced materials J. Appl. Mech. 31 1964 223 232
7. Y. Kantor, and D.J. Bergman Improved rigorous bounds on the effective elastic moduli of a composite material J. Mech. Phys. Solids 32 1984 41 62
8. A. Kelly, and N.H. Macmillan Strong solids. Monographs on the Physics and Chemistry of Materials 1986 Clarendon Press Oxford
9. R. Lipton Optimal lower bounds on the electric-field concentration in composite media J. Appl. Phys. 96 2004 2821 2827
10. G.W. Milton The theory of composites. Applied and Computational Mathematics vol. 6 2002 Cambridge University Press Cambridge
11. S.B. Vigdergauz Two-dimensional grained composites of extreme rigidity ASME J. Appl. Mech. 61 1994 390 394
12. Wheeler, L.T. 1993. Inhomogeneities of minimum stress concentration. In: Angel, Y.C. (Ed.), Anisotropy and Inhomogeneity in Elasticity and Plasticity, vol. AMD-158. ASME, pp. 1-6.