Deformation of negative Poisson's ratio materials and
other extreme composites
Roderic Lakes
Department of Engineering Physics
Engineering Mechanics Program
Biomedical Engineering Program
University of Wisconsin-Madison
147 Engineering Research Building
1500 Engineering Drive, Madison, WI 53706-1687
e-mail: lakes@engr.wisc.edu
The question of how much freedom is to be incorporated in an
elasticity theory must ultimately be decided by experiment. However,
during the development of the theory of elasticity, it was by no means
obvious how much freedom was necessary to describe materials. For
example, the early uniconstant theory of Navier is based upon the
assumption that forces act along the lines joining pairs of atoms and
are proportional to changes in distance between them. This theory
entails a Poisson's ratio of 1/4, for all materials. Navier, Cauchy,
Poisson, and Lam� supported this theory. Experimental measurements
(about a century ago) of Poisson's ratio of about 1/3 in common
materials led to the replacement of uniconstant elasticity by the more
general classical elasticity, following the continuum view of Green,
which allows Poisson's ratios between -1 and 1/2.
Recently, cellular solids have been developed which exhibit a
controlled negative Poisson's ratio as small as -0.8. Deformation
mechanisms in these materials include relative rotation of
micro-elements, and non-affine micro-deformation. Cellular solids with
a negative Poisson's ratio exhibit superior resilience and toughness
as a result of the unfolding of the cells. Studies of these materials
conducted via holographic interferometry disclose non-affine
deformation.
Additional freedom is possible in solids: the idea of a couple
stress can be traced to Voigt in the late 1800's during the formative
period of the theory of elasticity, and it was developed further by
the Cosserats in 1909. Many theoretical studies were conducted,
beginning in the 1960's. In Cosserat elasticity there are
characteristic lengths as additional engineering elastic
constants. There are a total of six independent elastic constants in
an isotropic Cosserat solid. Recent experimental work discloses a
variety of cellular and fibrous materials to exhibit such freedom, and
the characteristic lengths have been measured. In selected isotropic
cellular solids all six of the Cosserat elastic constants have been
measured. Several of these constants have been verified by further
experiments in geometries different from those used in the original
measurements. Holographic studies show that strain can spill over into
regions which are classically forbidden, specifically the corners of a
square cross-section prism in torsion. Chiral materials are not
invariant to inversions: there is a distinction between right and left
handed material. Properties such as piezoelectricity, represented by
tensors of odd rank, can only occur in chiral materials. Chiral
elastic effects cannot be expressed within classical elasticity since
the modulus tensor, which is fourth rank, is unchanged under an
inversion. Chiral effects can appear in Cosserat solids.
We consider composite material micro-structures, which give
rise to high stiffness combined with high viscoelastic loss. We
demonstrate that such properties are most easily achieved if the stiff
phase is as stiff as possible. We have characterized several candidate
materials isothermally over 11 decades of time and frequency with a
novel instrument. The rationale is as follows. For some materials,
particularly some amorphous polymers, it is possible to infer material
properties over a wider range from test results taken at different
temperatures. Materials for which such a procedure is possible are
called thermorheologically simple. However many materials,
particularly composites and materials in which multiple viscoelastic
mechanisms are active, are not thermorheologically simple. Direct
measurement of properties over many decades is required for a full
characterization of the material.
Converted from lakes.abs (plain text).