1,233 research outputs found
A Bayesian approach for uncertainty quantification in elliptic Cauchy problem
International audienceWe study the Cauchy problem in the framework of static linear elasticity and its resolution via the Steklov-Poincaré approach. In the linear Gaussian framework, the straightforward application of Bayes theory leads to formulas allowing to deduce the uncertainty on the identified field from the noise level. We use a truncated Ritz decomposition of the Steklov-Poincaré operator, which reduces the number of degrees of freedom and significantly lowers the computational cost
Likely oscillatory motions of stochastic hyperelastic solids
Stochastic homogeneous hyperelastic solids are characterised by strain-energy
densities where the parameters are random variables defined by probability
density functions. These models allow for the propagation of uncertainties from
input data to output quantities of interest. To investigate the effect of
probabilistic parameters on predicted mechanical responses, we study radial
oscillations of cylindrical and spherical shells of stochastic incompressible
isotropic hyperelastic material, formulated as quasi-equilibrated motions where
the system is in equilibrium at every time instant. Additionally, we study
finite shear oscillations of a cuboid, which are not quasi-equilibrated. We
find that, for hyperelastic bodies of stochastic neo-Hookean or Mooney-Rivlin
material, the amplitude and period of the oscillations follow probability
distributions that can be characterised. Further, for cylindrical tubes and
spherical shells, when an impulse surface traction is applied, there is a
parameter interval where the oscillatory and non-oscillatory motions compete,
in the sense that both have a chance to occur with a given probability. We
refer to the dynamic evolution of these elastic systems, which exhibit inherent
uncertainties due to the material properties, as `likely oscillatory motions'
Robust Multiscale Identification of Apparent Elastic Properties at Mesoscale for Random Heterogeneous Materials with Multiscale Field Measurements
The aim of this work is to efficiently and robustly solve the statistical
inverse problem related to the identification of the elastic properties at both
macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a
complex microstructure that usually cannot be properly described in terms of
their mechanical constituents at microscale. Within the context of linear
elasticity theory, the apparent elasticity tensor field at a given mesoscale is
modeled by a prior non-Gaussian tensor-valued random field. A general
methodology using multiscale displacement field measurements simultaneously
made at both macroscale and mesoscale has been recently proposed for the
identification the hyperparameters of such a prior stochastic model by solving
a multiscale statistical inverse problem using a stochastic computational model
and some information from displacement fields at both macroscale and mesoscale.
This paper contributes to the improvement of the computational efficiency,
accuracy and robustness of such a method by introducing (i) a mesoscopic
numerical indicator related to the spatial correlation length(s) of kinematic
fields, allowing the time-consuming global optimization algorithm (genetic
algorithm) used in a previous work to be replaced with a more efficient
algorithm and (ii) an ad hoc stochastic representation of the hyperparameters
involved in the prior stochastic model in order to enhance both the robustness
and the precision of the statistical inverse identification method. Finally,
the proposed improved method is first validated on in silico materials within
the framework of 2D plane stress and 3D linear elasticity (using multiscale
simulated data obtained through numerical computations) and then exemplified on
a real heterogeneous biological material (beef cortical bone) within the
framework of 2D plane stress linear elasticity (using multiscale experimental
data obtained through mechanical testing monitored by digital image
correlation)
Traction force microscopy on soft elastic substrates: a guide to recent computational advances
The measurement of cellular traction forces on soft elastic substrates has
become a standard tool for many labs working on mechanobiology. Here we review
the basic principles and different variants of this approach. In general, the
extraction of the substrate displacement field from image data and the
reconstruction procedure for the forces are closely linked to each other and
limited by the presence of experimental noise. We discuss different strategies
to reconstruct cellular forces as they follow from the foundations of
elasticity theory, including two- versus three-dimensional, inverse versus
direct and linear versus non-linear approaches. We also discuss how biophysical
models can improve force reconstruction and comment on practical issues like
substrate preparation, image processing and the availability of software for
traction force microscopy.Comment: Revtex, 29 pages, 3 PDF figures, 2 tables. BBA - Molecular Cell
Research, online since 27 May 2015, special issue on mechanobiolog
Inferring Displacement Fields from Sparse Measurements Using the Statistical Finite Element Method
A well-established approach for inferring full displacement and stress fields
from possibly sparse data is to calibrate the parameter of a given constitutive
model using a Bayesian update. After calibration, a (stochastic) forward
simulation is conducted with the identified model parameters to resolve
physical fields in regions that were not accessible to the measurement device.
A shortcoming of model calibration is that the model is deemed to best
represent reality, which is only sometimes the case, especially in the context
of the aging of structures and materials. While this issue is often addressed
with repeated model calibration, a different approach is followed in the
recently proposed statistical Finite Element Method (statFEM). Instead of using
Bayes' theorem to update model parameters, the displacement is chosen as the
stochastic prior and updated to fit the measurement data more closely. For this
purpose, the statFEM framework introduces a so-called model-reality mismatch,
parametrized by only three hyperparameters. This makes the inference of
full-field data computationally efficient in an online stage: If the stochastic
prior can be computed offline, solving the underlying partial differential
equation (PDE) online is unnecessary. Compared to solving a PDE, identifying
only three hyperparameters and conditioning the state on the sensor data
requires much fewer computational resources.
This paper presents two contributions to the existing statFEM approach:
First, we use a non-intrusive polynomial chaos method to compute the prior,
enabling the use of complex mechanical models in deterministic formulations.
Second, we examine the influence of prior material models (linear elastic and
St.Venant Kirchhoff material with uncertain Young's modulus) on the updated
solution. We present statFEM results for 1D and 2D examples, while an extension
to 3D is straightforward.Comment: 29 pages, 15 figures, Preprint submitted to Elsevie
Identification of weakly coupled multiphysics problems. Application to the inverse problem of electrocardiography
This work addresses the inverse problem of electrocardiography from a new
perspective, by combining electrical and mechanical measurements. Our strategy
relies on the defini-tion of a model of the electromechanical contraction which
is registered on ECG data but also on measured mechanical displacements of the
heart tissue typically extracted from medical images. In this respect, we
establish in this work the convergence of a sequential estimator which combines
for such coupled problems various state of the art sequential data assimilation
methods in a unified consistent and efficient framework. Indeed we ag-gregate a
Luenberger observer for the mechanical state and a Reduced Order Unscented
Kalman Filter applied on the parameters to be identified and a POD projection
of the electrical state. Then using synthetic data we show the benefits of our
approach for the estimation of the electrical state of the ventricles along the
heart beat compared with more classical strategies which only consider an
electrophysiological model with ECG measurements. Our numerical results
actually show that the mechanical measurements improve the identifiability of
the electrical problem allowing to reconstruct the electrical state of the
coupled system more precisely. Therefore, this work is intended to be a first
proof of concept, with theoretical justifications and numerical investigations,
of the ad-vantage of using available multi-modal observations for the
estimation and identification of an electromechanical model of the heart
Evolutionary topology optimization of continuum structures under uncertainty using sensitivity analysis and smooth boundary representation
This paper presents an evolutionary approach for the Robust Topology Optimization (RTO) of continuum structures under loading and material uncertainties. The method is based on an optimality criterion obtained from the stochastic linear elasticity problem in its weak form. The smooth structural topology is determined implicitly by an iso-value of the optimality criterion field. This iso-value is updated using an iterative approach to reach the solution of the RTO problem. The proposal permits to model the uncertainty using random variables with different probability distributions as well as random fields. The computational burden, due to the high dimension of the random field approximation, is efficiently addressed using anisotropic sparse grid stochastic collocation methods. The numerical results show the ability of the proposal to provide smooth and clearly defined structural boundaries. Such results also show that the method provides structural designs satisfying a trade-off between conflicting objectives in the RTO problem.The authors would like to thank Dr. Francisco Periago for constructive suggestions and discussions. This work has been partially supported by the AEI/FEDER and UE under the contract DPI2016-77538-R and by the “Fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia” under the contract 19274/PI/14
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