Extreme Lame Compliance in Anisotropic Crystals

@article{citeulike:2515667, abstract = {For a crystalline material, Poisson�s ratio depends upon two orthogonal directions, one corresponding to the applied uniaxial stress and another for the resulting transverse strain. Interest in directions that yield a negative value leads to a consideration of extreme values and associated directions. Another indicator of a negative Poisson�s ratio is the Lame compliance, defined as the transverse strain response to a unit uniaxial stress. Where this quantity is positive, Poisson�s ratio is negative and it is natural to associate a near mnimum value of the ratio with a maximum of the Lame compliance. Moreover, the stationary directions associated with the compliance bear a clearer relationship to the crystallographic directions than those of the ratio. Indeed, many of these directions are not dependent upon the elastic constants within a given crystal symmetry class. In the case of {alpha}-cristobalite, the maximum value of the Lame compliance is associated with such invariant stationary points. In the present work, we describe the invariant stationary directions and touch on a few of the simplest material-dependent stationary points. 10.1177/1081286507080807}, author = {Guo, Cliff Y. and Wheeler, Lewis }, citeulike-article-id = {2515667}, doi = {10.1177/1081286507080807}, journal = {Mathematics and Mechanics of Solids}, keywords = {anisotropy, poisson}, month = {March}, pages = {1081286507080807+}, posted-at = {2008-03-11 16:47:34}, priority = {1}, title = {Extreme Lame Compliance in Anisotropic Crystals}, url = {http://dx.doi.org/10.1177/1081286507080807}, year = {2008} }

TY - JOUR ID - citeulike:2515667 L3 - citeulike-article-id:2515667 TI - Extreme Lame Compliance in Anisotropic Crystals JF - Mathematics and Mechanics of Solids SP - 1081286507080807 N2 - For a crystalline material, Poisson�s ratio depends upon two orthogonal directions, one corresponding to the applied uniaxial stress and another for the resulting transverse strain. Interest in directions that yield a negative value leads to a consideration of extreme values and associated directions. Another indicator of a negative Poisson�s ratio is the Lame compliance, defined as the transverse strain response to a unit uniaxial stress. Where this quantity is positive, Poisson�s ratio is negative and it is natural to associate a near mnimum value of the ratio with a maximum of the Lame compliance. Moreover, the stationary directions associated with the compliance bear a clearer relationship to the crystallographic directions than those of the ratio. Indeed, many of these directions are not dependent upon the elastic constants within a given crystal symmetry class. In the case of {alpha}-cristobalite, the maximum value of the Lame compliance is associated with such invariant stationary points. In the present work, we describe the invariant stationary directions and touch on a few of the simplest material-dependent stationary points. 10.1177/1081286507080807 KW - anisotropy KW - poisson AU - Guo, Cliff AU - Wheeler, Lewis PY - 2008/03/11/ UR - http://dx.doi.org/10.1177/1081286507080807 ER -