14,034 research outputs found
Multiscale approach including microfibril scale to assess elastic constants of cortical bone based on neural network computation and homogenization method
The complexity and heterogeneity of bone tissue require a multiscale
modelling to understand its mechanical behaviour and its remodelling
mechanisms. In this paper, a novel multiscale hierarchical approach including
microfibril scale based on hybrid neural network computation and homogenisation
equations was developed to link nanoscopic and macroscopic scales to estimate
the elastic properties of human cortical bone. The multiscale model is divided
into three main phases: (i) in step 0, the elastic constants of collagen-water
and mineral-water composites are calculated by averaging the upper and lower
Hill bounds; (ii) in step 1, the elastic properties of the collagen microfibril
are computed using a trained neural network simulation. Finite element (FE)
calculation is performed at nanoscopic levels to provide a database to train an
in-house neural network program; (iii) in steps 2 to 10 from fibril to
continuum cortical bone tissue, homogenisation equations are used to perform
the computation at the higher scales. The neural network outputs (elastic
properties of the microfibril) are used as inputs for the homogenisation
computation to determine the properties of mineralised collagen fibril. The
mechanical and geometrical properties of bone constituents (mineral, collagen
and cross-links) as well as the porosity were taken in consideration. This
paper aims to predict analytically the effective elastic constants of cortical
bone by modelling its elastic response at these different scales, ranging from
the nanostructural to mesostructural levels. Our findings of the lowest scale's
output were well integrated with the other higher levels and serve as inputs
for the next higher scale modelling. Good agreement was obtained between our
predicted results and literature data.Comment: 2
Three scales asymptotic homogenization and its application to layered hierarchical hard tissues
In the present work a novel multiple scales asymptotic homogenization approach is proposed to study the effective properties of hierarchical composites with periodic structure at different length scales. The method is exemplified by solving a linear elastic problem for a composite material with layered hierarchical structure. We recover classical results of two-scale and reiterated homogenization as particular cases of our formulation. The analytical effective coefficients for two phase layered composites with two structural levels of hierarchy are also derived. The method is finally applied to investigate the effective mechanical properties of a single osteon, revealing its practical applicability in the context of biomechanical and engineering applications
Tensor Computation: A New Framework for High-Dimensional Problems in EDA
Many critical EDA problems suffer from the curse of dimensionality, i.e. the
very fast-scaling computational burden produced by large number of parameters
and/or unknown variables. This phenomenon may be caused by multiple spatial or
temporal factors (e.g. 3-D field solvers discretizations and multi-rate circuit
simulation), nonlinearity of devices and circuits, large number of design or
optimization parameters (e.g. full-chip routing/placement and circuit sizing),
or extensive process variations (e.g. variability/reliability analysis and
design for manufacturability). The computational challenges generated by such
high dimensional problems are generally hard to handle efficiently with
traditional EDA core algorithms that are based on matrix and vector
computation. This paper presents "tensor computation" as an alternative general
framework for the development of efficient EDA algorithms and tools. A tensor
is a high-dimensional generalization of a matrix and a vector, and is a natural
choice for both storing and solving efficiently high-dimensional EDA problems.
This paper gives a basic tutorial on tensors, demonstrates some recent examples
of EDA applications (e.g., nonlinear circuit modeling and high-dimensional
uncertainty quantification), and suggests further open EDA problems where the
use of tensor computation could be of advantage.Comment: 14 figures. Accepted by IEEE Trans. CAD of Integrated Circuits and
System
Enabling High-Dimensional Hierarchical Uncertainty Quantification by ANOVA and Tensor-Train Decomposition
Hierarchical uncertainty quantification can reduce the computational cost of
stochastic circuit simulation by employing spectral methods at different
levels. This paper presents an efficient framework to simulate hierarchically
some challenging stochastic circuits/systems that include high-dimensional
subsystems. Due to the high parameter dimensionality, it is challenging to both
extract surrogate models at the low level of the design hierarchy and to handle
them in the high-level simulation. In this paper, we develop an efficient
ANOVA-based stochastic circuit/MEMS simulator to extract efficiently the
surrogate models at the low level. In order to avoid the curse of
dimensionality, we employ tensor-train decomposition at the high level to
construct the basis functions and Gauss quadrature points. As a demonstration,
we verify our algorithm on a stochastic oscillator with four MEMS capacitors
and 184 random parameters. This challenging example is simulated efficiently by
our simulator at the cost of only 10 minutes in MATLAB on a regular personal
computer.Comment: 14 pages (IEEE double column), 11 figure, accepted by IEEE Trans CAD
of Integrated Circuits and System
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