Negative Poisson coefficient of fractal structures

On the basis of a fractal model the macroscopic elastic properties of an inhomogeneous medium with random structure have been determined. It is shown that if the ratio of the bulk moduli of the phases K2/K1→0, then the percolation threshold pc the Poisson coefficient is equal to 0.2. A study of the behavior of a two-phase medium with negative Poisson coefficient is carried out.

[1]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[2]  Georgios E. Stavroulakis,et al.  Negative Poisson's ratios in composites with star-shaped inclusions: a numerical homogenization approach , 1997 .

[3]  D. Bergman,et al.  Critical Properties of an Elastic Fractal , 1984 .

[4]  Conductivity and Dielectric Breakdown of Heterogeneous Materials. Application of the Renormalization Group Approach , 1995 .

[5]  J. Bernasconi.  Real-space renormalization of bond-disordered conductance lattices , 1978 .

[6]  Seifert,et al.  Negative Poisson ratio in two-dimensional networks under tension. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Peter Reynolds,et al.  Large-cell Monte Carlo renormalization group for percolation , 1980 .

[8]  O. Sigmund,et al.  Design and fabrication of compliant micromechanisms and structures with negative Poisson's ratio , 1996, Proceedings of Ninth International Workshop on Micro Electromechanical Systems.

[9]  Shechao Feng,et al.  Percolation on Elastic Networks: New Exponent and Threshold , 1984 .

[10]  K. Wilson,et al.  The Renormalization group and the epsilon expansion , 1973 .

[11]  H. E. Stanley,et al.  The fractal dimension of the minimum path in two- and three-dimensional percolation , 1988 .

[12]  R. Lakes,et al.  Hysteresis Behaviour and Specific Damping Capacity of Negative Poisson's Ratio Foams , 1996, Cellular Polymers.

[13]  S. Shtrikman,et al.  A variational approach to the theory of the elastic behaviour of multiphase materials , 1963 .

[14]  Robert Almgren,et al.  An isotropic three-dimensional structure with Poisson's ratio =−1 , 1985 .

[15]  Arbabi,et al.  Elastic properties of three-dimensional percolation networks with stretching and bond-bending forces. , 1988, Physical review. B, Condensed matter.

[16]  S. Redner,et al.  Introduction To Percolation Theory , 2018 .

[17]  D. Weitz,et al.  Fractal structures formed by kinetic aggregation of aqueous gold colloids , 1984 .

[18]  I. Webman,et al.  Elastic Properties of Random Percolating Systems , 1984 .

[19]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[20]  Arbabi,et al.  Mechanics of disordered solids. I. Percolation on elastic networks with central forces. , 1993, Physical review. B, Condensed matter.

[21]  Arbabi,et al.  Mechanics of disordered solids. II. Percolation on elastic networks with bond-bending forces. , 1993, Physical review. B, Condensed matter.

[22]  H. Stanley,et al.  Screening of Deeply Invaginated Clusters and the Critical Behavior of the Random Superconducting Network , 1984 .

[23]  S. Timoshenko,et al.  Theory of elasticity , 1975 .

[24]  R. Lakes.  Advances in negative Poisson's ratio materials , 1993 .

[25]  B. D. Caddock,et al.  Microporous materials with negative Poisson's ratios. I. Microstructure and mechanical properties , 1989 .

[26]  R. Lakes,et al.  Properties of a chiral honeycomb with a poisson's ratio of — 1 , 1997 .

[27]  J. Brickmann.  B. Mandelbrot: The Fractal Geometry of Nature, Freeman and Co., San Francisco 1982. 460 Seiten, Preis: £ 22,75. , 1985 .

[28]  V. Privalko,et al.  The Science of Heterogeneous Polymers: Structure and Thermophysical Properties , 1995 .

[29]  Auxeticity windows for composites , 1998 .

[30]  R. Lakes.  Foam Structures with a Negative Poisson's Ratio , 1987, Science.

[31]  Feng,et al.  Position-space renormalization for elastic percolation networks with bond-bending forces. , 1985, Physical Review B (Condensed Matter).

[32]  Luciano Pietronero,et al.  FRACTALS IN PHYSICS , 1990 .

[33]  K. Wojciechowski,et al.  Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers , 1987 .

[34]  Bergman.  Elastic moduli near percolation in a two-dimensional random network of rigid and nonrigid bonds. , 1986, Physical review. B, Condensed matter.