Random fields and processes in mechanics of granular materials

This paper gives a review of some newly developed stochastic methods for analysis of the effects of granular materials' randomness at the microscale on their response at the macroscale. Two problem areas are discussed: i) determination of constituitve laws for a wide class of materials with random microstructures, ii) wavefront propagation in random continuous and heterogenous media. Techniques in both areas take advantage of results in mechanics of microstructures and methods of random processes and fields.

[1]  M. Ostoja-Starzewski,et al.  Linear elasticity of planar delaunay networks. Part II: Voigt and Reuss bounds, and modification for centroids , 1990 .

[2]  Gilles A. Francfort,et al.  Homogenization and optimal bounds in linear elasticity , 1986 .

[3]  I. Jasiuk,et al.  SUCCESSIVE ITERATION METHOD APPLIED TO COMPOSITES CONTAINING SLIDING INCLUSIONS: EFFECTIVE MODULUS AND ANELASTICITY , 1990 .

[4]  R. Hill.  A self-consistent mechanics of composite materials , 1965 .

[5]  Feng,et al.  Effective-medium theory of percolation on central-force elastic networks. , 1985, Physical review. B, Condensed matter.

[6]  M. Ostoja-Starzewski.  Wavefront propagation in a class of random microstructures—1. bilinear elastic grains☆ , 1991 .

[7]  Z. Hashin.  Analysis of Composite Materials—A Survey , 1983 .

[8]  B. Budiansky.  On the elastic moduli of some heterogeneous materials , 1965 .

[9]  Martin Ostoja-Starzewski,et al.  Damage in a random microstructure: Size effects, fractals, and entropy maximization , 1989 .

[10]  J. Nunziato,et al.  On the influence of void compaction and material non-uniformity on the propagation of one-dimensional acceleration waves in granular materials , 1977 .

[11]  K. Sobczyk.  Stochastic waves: The existing results and new problems , 1986 .

[12]  M. Ostoja-Starzewski.  On Wavefront Propagation in Random Nonlinear Media , 1991 .

[13]  M. Ostoja-Starzewski,et al.  Linear elasticity of planar delaunay networks: Random field characterization of effective moduli , 1989 .

[14]  J. Nunziato,et al.  The behavior of one-dimensional acceleration waves in an inhomogeneous granular solid , 1978 .

[15]  Bounds on constitutive response for a class of random material microstructures , 1990 .