Nonlinear Hashin–Shtrikman Bounds For
Hereditary Problems
Author(s)
P. P. Procházka & M. Toman
Abstract
Classical Hashin–Shtrikman variational bounds are based on the assumption that
all phases behave in a purely elastic and locally homogeneous manner.
Hashin–Shtrikman principles, from which the bounds are derived, are extended
in a paper by Procházka and Sejnoha (Applications of Mathematics, 2004). The
extension consists of introducing eigenparameters (either eigenstrain or
eigenstress) into the formulation. Moreover, these eigenparameters were used in
the estimation of bounds with the result that elastic strain is in a certain relation
with plastic strains. This appears to be a very restrictive condition (constraint)
and a new approach will be presented in this paper based on additional estimates.
In the classical approach of Hashin and Shtrikman the overall energies were
compared with local energies (on the micro scale level). From this the
procedure for evaluation of bounds on overall material properties involving
eigenparameters begins. In our case it is possible to consider the eigenparameters
as characterizations of plastic behavior of one or more phases in the composite
structure. Following this idea, the eigenparameters can describe the current
situation in the composite structure and involved in the estimates. In such a way,
the eigenparameters can be considered as plastic strains or relaxation stresses,
and then the properties of eigenparameters can be taken into consideration.
Basically, the former approach of the paper by Hashin–Shtrikman still remains in
the body of the presented derivation of the new principles.
Keywords: extended Hashin–Shtrikman principles, bounds on overall properties,
hereditary problems.
Keywords
extended Hashin–Shtrikman principles, bounds on overall properties,
hereditary problems.
Related Book
Other papers in this volume
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