Finite element analysis of auxetic plate deformation

The paper deals with computer simulations of mechanical behavior of a thick elastic plate. The plate, made of isotropic material, has been clamped at two lateral surfaces, loaded at the front and back walls and left free at the upper and lower walls. Simulations have been done for Poisson’s ratio from interval � 1< m < 0.5 using the finite element method. An anomalous feature of the plate deformation for negative Poisson’s ratio values compared to classical positive values has been observed: at extremely negative Poisson’s ratios the displacement vector has components which are anti-parallel to the direction of loading.

[1]  Jean-Franccois Semblat.  Rheological Interpretation of Rayleigh Damping , 1997 .

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

[3]  R. Lakes,et al.  Extreme damping in composite materials with negative-stiffness inclusions , 2001, Nature.

[4]  A. Beltzer,et al.  Reexamination of dynamic problems of elasticity for negative Poisson’s ratio , 1988 .

[5]  Zhen-ya Li,et al.  Effective negative refractive index of graded granular composites with metallic magnetic particles , 2005 .

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

[7]  Gaoyuan Wei.  Negative and conventional Poisson’s ratios of polymeric networks with special microstructures , 1992 .

[8]  Tomaso Trombetti,et al.  On the modal damping ratios of shear-type structures equipped with Rayleigh damping systems , 2006 .

[9]  T. Jaglinski,et al.  Composite Materials with Viscoelastic Stiffness Greater Than Diamond , 2007, Science.

[10]  J. Z. Zhu,et al.  The finite element method , 1977 .

[11]  R. Ruppin.  Extinction properties of a sphere with negative permittivity and permeability , 2000 .

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

[13]  K. E. EVANS,et al.  Molecular network design , 1991, Nature.

[14]  Joseph N. Grima,et al.  Negative Poisson's ratios from rotating rectangles , 2004 .

[15]  R. Lakes,et al.  Negative compressibility, negative Poisson's ratio, and stability , 2008 .

[16]  Tungyang Chen,et al.  Poisson's ratio for anisotropic elastic materials can have no bounds , 2005 .

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

[18]  K. Wojciechowski.  Non-chiral, molecular model of negative Poisson ratio in two dimensions , 2003 .

[19]  K. Wojciechowski,et al.  Two-dimensional isotropic system with a negative poisson ratio , 1989 .

[20]  Y. Ishibashi,et al.  A Microscopic Model of a Negative Poisson's Ratio in Some Crystals , 2000 .

[21]  Roderic S. Lakes,et al.  Deformation mechanisms in negative Poisson's ratio materials: structural aspects , 1991 .

[22]  Joseph N. Grima,et al.  Auxetic behavior from rotating squares , 2000 .

[23]  Wojciechowski,et al.  Negative Poisson ratio in a two-dimensional "isotropic" solid. , 1989, Physical review. A, General physics.