CiteULike: norris Wheeler

On Conditions at an Interface between Two Materials in Three-Dimensional Space

L Wheeler — 2008-05-06T12:45:29-00:00

Mathematics and Mechanics of Solids, Vol. 4, No. 2. (1 June 1999), pp. 183-200.

This article is concerned with expressing the kinematics of a bimaterial-bonded interface in terms of strains in the three-dimensional case. It is shown that the continuity of displacements can be replaced by the requirement that the change in principal curvatures, the mean geodesic torsion, and the interior strains be matched across the interface. The reduction of these conditions for a two-dimensional bonded interface is also discussed. 10.1177/108128659900400203

Extreme Lame Compliance in Anisotropic Crystals

Cliff Guo — 2008-03-11T16:46:52-00:00

Mathematics and Mechanics of Solids (11 March 2008), 1081286507080807.

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

Derivatives of the stretch and rotation tensors

Yi-Chao Chen — 2007-08-29T14:05:40-00:00

Journal of Elasticity, Vol. 32, No. 3. (1993), pp. 175-182.

On the derivatives of the stretch and rotation with respect to the deformation gradient

Lewis Wheeler — 2007-08-29T13:23:27-00:00

Journal of Elasticity, Vol. 24, No. 1. (1 November 1990), pp. 129-133.

In this paper, a result involving the eigenprojections of the right stretch and its derivative with respect to the deformation gradient is derived, and a related result is found for the rotation. As an application, the form of the constitutive law for an isotropic hyperelastic material in the case when the strain energy function is expressed in terms of the right stretch, is shown to follow at once.

Extreme Poisson's ratios and related elastic crystal properties

Cliff Guo — 2007-03-01T20:19:14-00:00

Journal of the Mechanics and Physics of Solids, Vol. 54, No. 4. (April 2006), pp. 690-707.

With the aim of understanding anisotropic crystals that possess a negative Poisson's ratio and to lay a foundation for investigating molecular mechanisms, we discuss the definition of the ratio and establish conditions on the compliance that govern its sign. We derive results on orientation averaging that are useful in the context of anisotropy and helpful in the investigation of isotropic polycrystals. We discuss [alpha]-cristobalite, a polymorph of silicon dioxide that possesses interesting negative ratio properties in single crystals and hypothetical polycrystals. In this connection, we draw attention to the transverse compliance as an alternative and simpler metric for gaging the ratio and for orientation averaging. For [alpha]-cristobalite, we arrive at new results for the directions that yield the most negative Poisson's ratio. This result should be of value in divining the underlying molecular mechanism that explains the negative values of Poisson's ratio in [alpha]-cristobalite, a crystal of tetragonal symmetry that possesses six independent elastic constants.