Bounds on the distribution of extreme values for the stress in composite materials

Journal of the Mechanics and Physics of Solids

Volumn 52, Issue 5, 2004, Pages 1053-1069

  Lipton, Robert ^a  

^a LOUISIANA STATE UNIVERSITY   (United States)

Author keywords

A. Composite materials; B. Failure criteria; C. Stress concentrations

Indexed keywords

ANISOTROPY; ELASTICITY; MATHEMATICAL MODELS; POLYNOMIALS; STRESS ANALYSIS; TENSORS; THEOREM PROVING;

STRESS CONCENTRATIONS; STRESS MODULATIONS;

COMPOSITE MATERIALS;

EID: 1642326693     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2003.09.033     Document Type: Article

References (10)

1. Bensoussan A., Lions J.L., Papanicolaou G. Asymptotic Analysis for Periodic Structures. Studies in Mathematics and its Applications. Vol. 5:1978;North-Holland, Amsterdam.
2. Evans, L.C., 1990. Weak Convergence Methods for Nonlinear Partial Differential Equations. CBMS Regional Conference Series in Mathematics, No. 74. American Mathematical Society, Providence, RI.
3. Hashin Z., Shtrikman S. A variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys. 33:1962;3125-3131.
4. Jeulin D. Random structure models for composite media and fracture statistics. Markov K.Z. Advances in Mathematical Modeling of Composite Materials. Advances in Mathematics for Applied Sciences. Vol. 15:1994;239-289 World Scientific Company, Singapore.
5. John F., Nirenberg L. On functions of bounded mean oscillation. Comm. Pure Appl. Math. 14:1961;415-426.
6. Kelly A., Macmillan N.H. Strong solids. Monographs on the Physics and Chemistry of Materials. 1986;Clarendon Press, Oxford.
7. Lipton R. Assessment of the local stress state through macroscopic variables. Philos. Trans. Roy. Soc. Math. Phy. Eng. Sc. 361:2003;921-946.
8. Luciano R., Willis J.R. Boundary-layer corrections for stress and strain fields in randomly heterogeneous materials. J. Mech. Phys. Solids. 51:2003;1075-1088.
9. Milton G.W. The theory of composites. Applied and Computational Mathematics. Vol. 6:2002;Cambridge University Press, Cambridge.
10. Tsai S.W., Hahn H.T. Introduction to Composite Materials. 1980;Technomic Press, Lancaster, PA.