2,979 research outputs found
Neo-Hookean fiber composites undergoing finite out-of-plane shear deformations
The response of a neo-Hookean fiber composite undergoing finite out-of-plane
shear deformation is examined. To this end an explicit close form solution for
the out-of-plane shear response of a cylindrical composite element is
introduced. We find that the overall response of the cylindrical composite
element can be characterized by a fictitious homogeneous neo-Hookean material.
Accordingly, this macroscopic response is identical to the response of a
composite cylinder assemblage. The expression for the effective shear modulus
of the composite cylinder assemblage is identical to the corresponding
expression in the limit of small deformation elasticity, and hence also to the
expression for the Hashin-Shtrikman bounds on the out-of-plane shear modulus
Non-linear behavior of fiber composite laminates
The non-linear behavior of fiber composite laminates which results from lamina non-linear characteristics was examined. The analysis uses a Ramberg-Osgood representation of the lamina transverse and shear stress strain curves in conjunction with deformation theory to describe the resultant laminate non-linear behavior. A laminate having an arbitrary number of oriented layers and subjected to a general state of membrane stress was treated. Parametric results and comparison with experimental data and prior theoretical results are presented
Nonlinear effects on composite laminate thermal expansion
Analyses of Graphite/Polyimide laminates shown that the thermomechanical strains cannot be separated into mechanical strain and free thermal expansion strain. Elastic properties and thermal expansion coefficients of unidirectional Graphite/Polyimide specimens were measured as a function of temperature to provide inputs for the analysis. The + or - 45 degrees symmetric Graphite/Polyimide laminates were tested to obtain free thermal expansion coefficients and thermal expansion coefficients under various uniaxial loads. The experimental results demonstrated the effects predicted by the analysis, namely dependence of thermal expansion coefficients on load, and anisotropy of thermal expansion under load. The significance of time dependence on thermal expansion was demonstrated by comparison of measured laminate free expansion coefficients with and without 15 day delay at intermediate temperature
Studies of mechanics of filamentary composites Annual report, Sep. 27, 1964 - Sep. 26, 1965
Mechanics of binder and filament reinforced composite material
Theory of fiber reinforced materials
A unified and rational treatment of the theory of fiber reinforced composite materials is presented. Fundamental geometric and elasticity considerations are throughly covered, and detailed derivations of the effective elastic moduli for these materials are presented. Biaxially reinforced materials which take the form of laminates are then discussed. Based on the fundamentals presented in the first portion of this volume, the theory of fiber-reinforced composite materials is extended to include viscoelastic and thermoelastic properties. Thermal and electrical conduction, electrostatics and magnetostatics behavior of these materials are discussed. Finally, a brief statement of the very difficult subject of physical strength is included
Overall Dynamic Properties of 3-D periodic elastic composites
A method for the homogenization of 3-D periodic elastic composites is
presented. It allows for the evaluation of the averaged overall frequency
dependent dynamic material constitutive tensors relating the averaged dynamic
field variable tensors of velocity, strain, stress, and linear momentum. The
formulation is based on micromechanical modeling of a representative unit cell
of a composite proposed by Nemat-Nasser & Hori (1993), Nemat-Nasser et. al.
(1982) and Mura (1987) and is the 3-D generalization of the 1-D elastodynamic
homogenization scheme presented by Nemat-Nasser & Srivastava (2011). We show
that for 3-D periodic composites the overall compliance (stiffness) tensor is
hermitian, irrespective of whether the corresponding unit cell is geometrically
or materially symmetric.Overall mass density is shown to be a tensor and, like
the overall compliance tensor, always hermitian. The average strain and linear
momentum tensors are, however, coupled and the coupling tensors are shown to be
each others' hermitian transpose. Finally we present a numerical example of a
3-D periodic composite composed of elastic cubes periodically distributed in an
elastic matrix. The presented results corroborate the predictions of the
theoretical treatment.Comment: 26 pages, 2 figures, submitted to Proceedings of the Royal Society
Bounds on Effective Dynamic Properties of Elastic Composites
We present general, computable, improvable, and rigorous bounds for the total
energy of a finite heterogeneous volume element or a periodically distributed
unit cell of an elastic composite of any known distribution of inhomogeneities
of any geometry and elasticity, undergoing a harmonic motion at a fixed
frequency or supporting a single-frequency Bloch-form elastic wave of a given
wave-vector. These bounds are rigorously valid for \emph{any consistent
boundary conditions} that produce in the finite sample or in the unit cell,
either a common average strain or a common average momentum. No other
restrictions are imposed. We do not assume statistical homogeneity or isotropy.
Our approach is based on the Hashin-Shtrikman (1962) bounds in elastostatics,
which have been shown to provide strict bounds for the overall elastic moduli
commonly defined (or actually measured) using uniform boundary tractions and/or
linear boundary displacements; i.e., boundary data corresponding to the overall
uniform stress and/or uniform strain conditions. Here we present strict bounds
for the dynamic frequency-dependent constitutive parameters of the composite
and give explicit expressions for a direct calculation of these bounds
Overall Dynamic Constitutive Relations of Micro-structured Elastic Composites
A method for homogenization of a heterogeneous (finite or periodic) elastic
composite is presented. It allows direct, consistent, and accurate evaluation
of the averaged overall frequency-dependent dynamic material constitutive
relations. It is shown that when the spatial variation of the field variables
is restricted by a Bloch-form (Floquet-form) periodicity, then these relations
together with the overall conservation and kinematical equations accurately
yield the displacement or stress modeshapes and, necessarily, the dispersion
relations. It also gives as a matter of course point-wise solution of the
elasto-dynamic field equations, to any desired degree of accuracy. The
resulting overall dynamic constitutive relations however, are general and need
not be restricted by the Bloch-form periodicity. The formulation is based on
micro-mechanical modeling of a representative unit cell of the composite
proposed by Nemat-Nasser and coworkers; see, e.g., [1] and [2].Comment: 23 pages, 6 figures, submitted to JMP
Elastic moduli of model random three-dimensional closed-cell cellular solids
Most cellular solids are random materials, while practically all theoretical
results are for periodic models. To be able to generate theoretical results for
random models, the finite element method (FEM) was used to study the elastic
properties of solids with a closed-cell cellular structure. We have computed
the density () and microstructure dependence of the Young's modulus ()
and Poisson's ratio (PR) for several different isotropic random models based on
Voronoi tessellations and level-cut Gaussian random fields. The effect of
partially open cells is also considered. The results, which are best described
by a power law (), show the influence of randomness
and isotropy on the properties of closed-cell cellular materials, and are found
to be in good agreement with experimental data.Comment: 13 pages, 13 figure
Universal bounds on the electrical and elastic response of two-phase bodies and their application to bounding the volume fraction from boundary measurements
Universal bounds on the electrical and elastic response of two-phase (and
multiphase) ellipsoidal or parallelopipedic bodies have been obtained by
Nemat-Nasser and Hori. Here we show how their bounds can be improved and
extended to bodies of arbitrary shape. Although our analysis is for two-phase
bodies with isotropic phases it can easily be extended to multiphase bodies
with anisotropic constituents. Our two-phase bounds can be used in an inverse
fashion to bound the volume fractions occupied by the phases, and for
electrical conductivity reduce to those of Capdeboscq and Vogelius when the
volume fraction is asymptotically small. Other volume fraction bounds derived
here utilize information obtained from thermal, magnetic, dielectric or elastic
responses. One bound on the volume fraction can be obtained by simply immersing
the body in a water filled cylinder with a piston at one end and measuring the
change in water pressure when the piston is displaced by a known small amount.
This bound may be particularly effective for estimating the volume of cavities
in a body. We also obtain new bounds utilizing just one pair of (voltage, flux)
electrical measurements at the boundary of the body.Comment: 5 figures, 27 page
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