22,049 research outputs found
Optimal lower bounds on the local stress inside random thermoelastic composites
A methodology is presented for bounding all higher moments of the local
hydrostatic stress field inside random two phase linear thermoelastic media
undergoing macroscopic thermomechanical loading. The method also provides a
lower bound on the maximum local stress. Explicit formulas for the optimal
lower bounds are found that are expressed in terms of the applied macro- scopic
thermal and mechanical loading, coefficients of thermal expansion, elastic
properties, and volume fractions. These bounds provide a means to measure load
transfer across length scales relating the excursions of the local fields to
the applied loads and the thermal stresses inside each phase. These bounds are
shown to be the best possible in that they are attained by the Hashin-Shtrikman
coated sphere assemblage.Comment: 14 page
Uncertain Loading and Quantifying Maximum Energy Concentration within Composite Structures
We introduce a systematic method for identifying the worst case load among
all boundary loads of fixed energy. Here the worst case load is defined to be
the one that delivers the largest fraction of input energy to a prescribed
subdomain of interest. The worst case load is identified with the first
eigenfunction of a suitably defined eigenvalue problem. The first eigenvalue
for this problem is the maximum fraction of boundary energy that can be
delivered to the subdomain. We compute worst case boundary loads and associated
energy contained inside a prescribed subdomain through the numerical solution
of the eigenvalue problem. We apply this computational method to bound the
worst case load associated with an ensemble of random boundary loads given by a
second order random process. Several examples are carried out on heterogeneous
structures to illustrate the method
Multiscale analysis of heterogeneous media for local and nonlocal continuum theories
The dissertation provides new multiscale methods for the analysis of heterogeneous media. The first part of the dissertation treats heterogeneous media using the theory of linear elasticity. In this context, a methodology is presented for bounding the higher order moments of the local stress and strain fields inside random elastic media. Optimal lower bounds that are given in terms of the applied loading and the volume (area) fractions for random two-phase composites are presented. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. The second part of the dissertation treats heterogeneous media using the peridynamic formulation of nonlocal continuum mechanics. In this context, a multiscale analysis method is presented for capturing the dynamics inside fiber-reinforced composites at both the structural scale and the microscopic scale. The method provides a multiscale numerical method with a cost that is much less than solving the full micro-scale model over the entire macroscopic domain
Rigorous bounds on the effective moduli of composites and inhomogeneous bodies with negative-stiffness phases
We review the theoretical bounds on the effective properties of linear
elastic inhomogeneous solids (including composite materials) in the presence of
constituents having non-positive-definite elastic moduli (so-called
negative-stiffness phases). We show that for statically stable bodies the
classical displacement-based variational principles for Dirichlet and Neumann
boundary problems hold but that the dual variational principle for traction
boundary problems does not apply. We illustrate our findings by the example of
a coated spherical inclusion whose stability conditions are obtained from the
variational principles. We further show that the classical Voigt upper bound on
the linear elastic moduli in multi-phase inhomogeneous bodies and composites
applies and that it imposes a stability condition: overall stability requires
that the effective moduli do not surpass the Voigt upper bound. This
particularly implies that, while the geometric constraints among constituents
in a composite can stabilize negative-stiffness phases, the stabilization is
insufficient to allow for extreme overall static elastic moduli (exceeding
those of the constituents). Stronger bounds on the effective elastic moduli of
isotropic composites can be obtained from the Hashin-Shtrikman variational
inequalities, which are also shown to hold in the presence of negative
stiffness
On the possible effective elasticity tensors of 2-dimensional and 3-dimensional printed materials
The set of possible effective elastic tensors of composites built from
two materials with elasticity tensors \BC_1>0 and \BC_2=0 comprising the
set U=\{\BC_1,\BC_2\} and mixed in proportions and is partly
characterized. The material with tensor \BC_2=0 corresponds to a material
which is void. (For technical reasons \BC_2 is actually taken to be nonzero
and we take the limit \BC_2\to 0). Specifically, recalling that is
completely characterized through minimums of sums of energies, involving a set
of applied strains, and complementary energies, involving a set of applied
stresses, we provide descriptions of microgeometries that in appropriate limits
achieve the minimums in many cases. In these cases the calculation of the
minimum is reduced to a finite dimensional minimization problem that can be
done numerically. Each microgeometry consists of a union of walls in
appropriate directions, where the material in the wall is an appropriate
-mode material, that is easily compliant to independent applied
strains, yet supports any stress in the orthogonal space. Thus the material can
easily slip in certain directions along the walls. The region outside the walls
contains "complementary Avellaneda material" which is a hierarchical laminate
which minimizes the sum of complementary energies.Comment: 39 pages, 11 figure
Homogenization of plain weave composites with imperfect microstructure: Part II--Analysis of real-world materials
A two-layer statistically equivalent periodic unit cell is offered to predict
a macroscopic response of plain weave multilayer carbon-carbon textile
composites. Falling-short in describing the most typical geometrical
imperfections of these material systems the original formulation presented in
(Zeman and \v{S}ejnoha, International Journal of Solids and Structures, 41
(2004), pp. 6549--6571) is substantially modified, now allowing for nesting and
mutual shift of individual layers of textile fabric in all three directions.
Yet, the most valuable asset of the present formulation is seen in the
possibility of reflecting the influence of negligible meso-scale porosity
through a system of oblate spheroidal voids introduced in between the two
layers of the unit cell. Numerical predictions of both the effective thermal
conductivities and elastic stiffnesses and their comparison with available
laboratory data and the results derived using the Mori-Tanaka averaging scheme
support credibility of the present approach, about as much as the reliability
of local mechanical properties found from nanoindentation tests performed
directly on the analyzed composite samples.Comment: 28 pages, 14 figure
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