8,191 research outputs found
Microstructure-based modeling of elastic functionally graded materials: One dimensional case
Functionally graded materials (FGMs) are two-phase composites with
continuously changing microstructure adapted to performance requirements.
Traditionally, the overall behavior of FGMs has been determined using local
averaging techniques or a given smooth variation of material properties.
Although these models are computationally efficient, their validity and
accuracy remain questionable, since a link with the underlying microstructure
(including its randomness) is not clear. In this paper, we propose a modeling
strategy for the linear elastic analysis of FGMs systematically based on a
realistic microstructural model. The overall response of FGMs is addressed in
the framework of stochastic Hashin-Shtrikman variational principles. To allow
for the analysis of finite bodies, recently introduced discretization schemes
based on the Finite Element Method and the Boundary Element Method are employed
to obtain statistics of local fields. Representative numerical examples are
presented to compare the performance and accuracy of both schemes. To gain
insight into similarities and differences between these methods and to minimize
technicalities, the analysis is performed in the one-dimensional setting.Comment: 33 pages, 14 figure
A multi-resolution, non-parametric, Bayesian framework for identification of spatially-varying model parameters
This paper proposes a hierarchical, multi-resolution framework for the
identification of model parameters and their spatially variability from noisy
measurements of the response or output. Such parameters are frequently
encountered in PDE-based models and correspond to quantities such as density or
pressure fields, elasto-plastic moduli and internal variables in solid
mechanics, conductivity fields in heat diffusion problems, permeability fields
in fluid flow through porous media etc. The proposed model has all the
advantages of traditional Bayesian formulations such as the ability to produce
measures of confidence for the inferences made and providing not only
predictive estimates but also quantitative measures of the predictive
uncertainty. In contrast to existing approaches it utilizes a parsimonious,
non-parametric formulation that favors sparse representations and whose
complexity can be determined from the data. The proposed framework in
non-intrusive and makes use of a sequence of forward solvers operating at
various resolutions. As a result, inexpensive, coarse solvers are used to
identify the most salient features of the unknown field(s) which are
subsequently enriched by invoking solvers operating at finer resolutions. This
leads to significant computational savings particularly in problems involving
computationally demanding forward models but also improvements in accuracy. It
is based on a novel, adaptive scheme based on Sequential Monte Carlo sampling
which is embarrassingly parallelizable and circumvents issues with slow mixing
encountered in Markov Chain Monte Carlo schemes
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