Estimation Of Material Parameters Research Articles

Volcano deformation and eruption forecasting

Abstract Recent advances in Global Positioning System (GPS), tilt and Interferometric Synthetic Aperture Radar (InSAR) have greatly increased the availability of volcano deformation data. These measurements, combined with appropriate source models, can be used to estimate magma chamber depth, and to provide information on chamber shape and volume change. However, kinematic models cannot constrain magma chamber volume, and provide no predictive capability. Volcanic eruptions are commonly preceded by periods of inflation. Under appropriate conditions, eruptions are ‘inflation predictable’; that is, subsequent eruptions occur when inflation recovers the deflation during the preceding event. Notable successes in forecasting eruptions have come largely through the ability to discern repeatable patterns in seismic activity, ground deformation and gas emission, combined with historical and geological evidence of past eruptive behaviour. To move beyond empirical pattern recognition to forecasting based on deterministic physical–chemical models of the underlying dynamics, will require integration of different data types and models. I suggest two areas poised for progress: quantitative integration of deformation and seismicity; and model-based forecasts conditioned on estimates of material parameters and initial conditions from inversion of available datasets. Deformation and seismicity are the principal geophysical methods for volcano monitoring, and in some cases have signalled dyke propagation minutes to hours prior to eruptions. Quantitative models relating these processes, however, have been lacking. Modern theories of seismicity rate variations under changing stress conditions can be used to integrate deformation and (volcano–tectonic) seismicity into self-consistent inversions for the spatio-temporal evolution of dyke geometry and excess magma pressure. This approach should lead to improved resolution over existing methods and, perhaps, to improved real-time forecasts. The past few decades have also witnessed a marked increase in the sophistication of physical–chemical models of volcanic eruptions. I review conduit models that can be combined with GPS and extrusion rate data through Markov Chain Monte Carlo (MCMC) inversion to estimate the absolute volume of the crustal magma chamber, initial chamber overpressure, initial volatile concentrations and other parameters of interest. The MCMC estimation procedure can be extended to deterministic forecasting by using the distribution of initial conditions and material parameters consistent with available data to initiate predictive forward models. Such physics-based MCMC forecasts would be based on all knowledge of the system, including data up to the current date. The underlying model is completely deterministic; however, because the method samples initial conditions and physical parameters consistent with the given data, it yields probabilistic forecasts including uncertainties in the underlying parameters. Because there are almost certain to be effects not factored into the forward models, there is likely to be a substantial learning curve as models evolve to become more realistic.

Example-guided physically based modal sound synthesis

Linear modal synthesis methods have often been used to generate sounds for rigid bodies. One of the key challenges in widely adopting such techniques is the lack of automatic determination of satisfactory material parameters that recreate realistic audio quality of sounding materials. We introduce a novel method using prerecorded audio clips to estimate material parameters that capture the inherent quality of recorded sounding materials. Our method extracts perceptually salient features from audio examples. Based on psychoacoustic principles, we design a parameter estimation algorithm using an optimization framework and these salient features to guide the search of the best material parameters for modal synthesis. We also present a method that compensates for the differences between the real-world recording and sound synthesized using solely linear modal synthesis models to create the final synthesized audio. The resulting audio generated from this sound synthesis pipeline well preserves the same sense of material as a recorded audio example. Moreover, both the estimated material parameters and the residual compensation naturally transfer to virtual objects of different sizes and shapes, while the synthesized sounds vary accordingly. A perceptual study shows the results of this system compare well with real-world recordings in terms of material perception.

Terahertz time-domain spectroscopy of absorbing materials

In this paper, we study the noise-limited precision on the complex refractive index value of materials in the terahertz frequency range as determined by terahertz time-domain spectroscopy. As absorbing samples are almost opaque, transmission measurements are not suitable to determine the refractive index and reflection indices have to be employed instead, but at the expense of precision. We give rules to select the most adapted technique, i.e. in transmission or in reflection, for any given sample of arbitrary transparence Full Text: PDF References M. van Exter and D. Grischkowsky, "Optical and electronic properties of doped silicon from 0.1 to 2 THz", Appl. Phys. Lett. 56, 1694 (1990); CrossRef Sensing with Terahertz Radiation, ed. D. Mittleman, Springer Series in Optical Sciences Vol. 85, Berlin (2003). DirectLink For example: http://www.menlosystems.com; , http://www.rainbowphotonics.com; , http://www.teraview.com; , http://www.ekspla.com; , http://www.picometrix.com; , http://www.zomega-terahertz.com; . T. Dorney, R. Baraniuk, and D. Mittleman, "Material parameter estimation with terahertz time-domain spectroscopy", J. Opt. Soc. Am. A 18, 1562 (2001); CrossRef I. Pupeza, R. Wilk, and M. Koch, "Highly accurate optical material parameter determination with THz time-domain spectroscopy", Opt. Exp. 15, Issue 7, 4335 (2007). CrossRef L. Thrane, R. H. Jacobsen, P. U. Jepsen, and S. R. Keiding, "THz reflection spectroscopy of liquid water", Chem. Phys. Lett. 240, 330 (1995); CrossRef S. C. Howells and L. A. Schlie, "Transient terahertz reflection spectroscopy of undoped InSb from 0.1 to 1.1 THz", Appl. Phys. Lett. 69, 550 (1996). CrossRef P. Uhd Jepsen and B. M. Fischer, "Dynamic range in terahertz time-domain transmission and reflection spectroscopy", Optics Letters 30, 29 (2005). CrossRef L. Duvillaret, F. Garet, J.-L. Coutaz, "Influence of noise on the characterization of materials by terahertz time-domain spectroscopy", J. Opt. Soc. Amer. B17, 452 (2000). CrossRef

Sigmoidal crack growth rate curve: statistical modelling and applications

ABSTRACTThe present paper proposes a statistical model for describing sigmoidal crack growth rate curves. Major novelties are: a) exploitation of the maximum likelihood principle for obtaining material estimates by pooling together experimental data belonging to the different crack propagation regions; b) a general formulation which allows to adopt different sigmoidal models and any kind of statistical distribution for the model variables; c) fatigue life predictions through numerical integration of analytical functions with no need of Monte Carlo simulations. Experimental data taken from NASGRO database are used to check the validity of the statistical model in estimating material parameters included in the crack growth NASGRO algorithm. Illustrative plots of number of cycles to failure and crack length after a given number of cycles are presented, showing good agreement between the proposed statistical model and NASGRO results.

True Hardness Evaluation of Bulk Metallic Materials in the Presence of Pile Up: Analytical and Enhanced Lobes Method Approaches

In the last few decades, a great deal of attention has been paid to understanding the factors controlling the detailed shape of loading-unloading curves obtained by the Oliver and Pharr's nanoindentation analysis, to enable us estimate material parameters such as true contact area, Young’s modulus, and hardness. In fact, it is well known that the Oliver and Pharr's analysis can overestimate hardness, especially in such cases where the material plastically deforms by piling up around the indentation. In recent years, different direct and analytic methods have been proposed. Direct visual methods are based on measurements of the produced indentation by scanning probe microscopy (SPM) or by atomic force microscopy (AFM). Some other analytic methods are based on the work of indentation analysis, that is to say, the analysis of the area of the load-displacement curve. In the case of the current study, DHP-copper hardness measurements using nanoindentation, in both H58 and annealed metallurgical conditions, were investigated by both direct and analytic methods. Three different SPM-based methods and work of indentation analysis methods were used to determine the true hardness. Among the three SPM-based methods, one showed quite a good agreement with the literature data and microhardness tests. This method was therefore developed and improved to make it dependent on curve parameters and no longer dependent on SPM or AFM, the measurements of the real contact area. The correlation between the pile-up phenomenon and the m exponent of the P = B(h − h f)m relationship is also discussed.

Model-Based Material Parameter Estimation for Terahertz Reflection Spectroscopy

One important yet commonly overlooked phenomenon in terahertz (THz) reflection spectroscopy is the etalon effect-interference caused by multiple reflections from dielectric layers. Material layers are present in many THz applications from the monitoring of pharmaceutical tablet coating thickness to the detection of drugs, explosives, or other contraband concealed beneath layers of packaging and/or clothing. This paper focuses on the development and implementation of a model-based material parameter estimation technique, primarily for use in reflection mode THz spectroscopy that takes the etalon effect into account. The technique is adapted from techniques developed for transmission spectroscopy of thin samples and includes a priori information; namely, the assumption that a material's complex refractive index behaves consistently with the Lorentz dispersion model. The inclusion of the multiple returns provides additional information about the material and its structure, alleviating the need for short time windows in the fast Fourier transform (FFT) processing, which can limit spectral resolution. In addition, the parametrization of the material's dielectric function offers the potential for material classification based on these estimated dispersion model parameters. The parametric model-based method is validated by comparison with results from a conventional, non-parametric method applied to transmission mode data before being applied to reflection mode data for further validation with transmission mode results. Tests are also conducted to evaluate the parametric technique's robustness against measurement noise and ambiguity in sample thickness.

Uncertainty analysis of solder alloy material parameters estimation based on model calibration method

Quantification of the uncertainties in the material characterization of solder joint has been one of the major concerns in the microelectronics packaging industry to predict fatigue failure accurately. Therefore, in this study, a model calibration method based on Bayesian approach is proposed to quantify these uncertainties arising in the material parameter estimation of the solder alloy. A specimen is fabricated to this end, which closely simulates solder joint behavior of the actual package under a thermal cycle. Experiment is conducted to examine the deformation by using Moiré interferometry. Viscoplastic finite element analysis procedure is constructed for the specimen based on the Anand model. The uncertainties which include inherent experimental error and insufficient data of experiments are addressed by using the likelihood estimation. Two materials, one being conventional solder of Sn36Pb2Ag and the other the lead-free solder of Sn3.0Ag0.5Cu, are considered to illustrate the approach. As a result, material parameters are identified in the form of credible interval (CI), and the displacements and strains using these parameters are given by the predictive interval (PI). The results suggest that the proposed approach can be a useful tool in the probabilistic estimation of the unknown material parameters of solder joint by accounting for the uncertainties due to the experimental data.

Quantitative observations of cavitation activity in a viscoelastic medium

Quantitative experimental observations of single-bubble cavitation in viscoelastic media that would enable validation of existing models are presently lacking. In the present work, single bubble cavitation is induced in an agar gel using a 1.15 MHz high intensity focused ultrasound transducer, and observed using a focused single-element passive cavitation detection (PCD) transducer. To enable quantitative observations, a full receive calibration is carried out of a spherically focused PCD system by a bistatic scattering substitution technique that uses an embedded spherical scatterer and a hydrophone. Adjusting the simulated pressure received by the PCD by the transfer function on receive and the frequency-dependent attenuation of agar gel enables direct comparison of the measured acoustic emissions with those predicted by numerical modeling of single-bubble cavitation using a modified Keller-Miksis approach that accounts for viscoelasticity of the surrounding medium. At an incident peak rarefactional pressure near the cavitation threshold, period multiplying is observed in both experiment and numerical model. By comparing the two sets of results, an estimate of the equilibrium bubble radius in the experimental observations can be made, with potential for extension to material parameter estimation. Use of these estimates yields good agreement between model and experiment.

A rod model for three dimensional deformations of single-walled carbon nanotubes

A continuum model for single-walled carbon nanotubes (SWCNT) is presented which is based on an extension to the special Cosserat theory of rods ( Kumar and Mukherjee, 2011). The model allows deformation of a nanotube’s lateral surface in a one dimensional framework and hence is an efficient substitute to the commonly used two dimensional shell models for nanotubes. The model predicts a new coupling mode in chiral nanotubes – coupling between twist and cross-sectional shrinkage implying that the three deformation modes (extension, twist and cross-sectional shrinkage) are all coupled to each other. Atomistic simulations based on the density functional based tight binding method (DFTB) are performed on a (9, 6) SWCNT and the simulation data is used to estimate material parameters of this rod model. A peculiar behavior of the nanotube is observed when it is axially stretched – induced rotation of each cross-section is equal in magnitude but opposite to that of its two neighboring cross-sections. This is shown to be an effect of relative shift/inner-displacement between the two SWCNT sub-lattices.

Computer simulation of the high temperature creep behaviour of Cr–Mo steels

Continuum damage mechanics (CDM) based model developed by Dyson and McLean has been used to simulate creep behaviour of 2.25Cr–1Mo steel having a large creep database. Material parameters evaluated for this steel were used as the initial set to estimate material parameters for 9CrMoVNb steel where only a limited creep database was available. A simple iteration scheme and optimisation procedure has been developed. The simulated plots were found to describe experimental data fairly well. Using an additional data on elastic modulus stress relaxation test was also simulated. The nature of such plots was quite similar to that of the experimental plots.

Novel optical system for in vitro quantification of full surface strain fields in small arteries: II. Correction for refraction and illustrative results

In a companion paper, we described a theoretical foundation for and initial experimental implementation of a novel stereo-digital image correlation (DIC) method for quantifying the size, shape and deformation of small cylindrical specimens along their full length and around their entire circumference. In this paper, we further show that this panoramic-DIC method can be used to study mouse carotid arteries without affecting their native mechanical properties and show the advantage of the approach in studying more complex mouse aorta. In particular, we first resolve the ubiquitous issue of refraction in non-contacting optical measurements of strain while tissues are immersed in physiologic saline and we show that surface preparation for DIC does not affect the inferred mechanical properties either qualitatively or quantitatively, the latter via the use of a four-fibre family hyperelastic constitutive relation and associated estimation of material parameters using nonlinear regression. We thus submit that panoramic-DIC-based strain measurement has significant potential to increase our understanding of arterial mechanics in genetic models of arterial health and disease by allowing investigators to exploit advances in transgenic mice.

On thermoelastostatics of composites with nonlocal properties of constituents II. Estimation of effective material and field parameters

One considers a linear thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous random set of ellipsoidal uncoated or coated heterogeneities. It is assumed that the stress–strain constitutive relations of constituents are described by the nonlocal integral operators, whereas the equilibrium and compatibility equations remain unaltered as in classical local elasticity. The general integral equations connecting the stress and strain fields in the point being considered and the surrounding points are obtained. The method is based on a centering procedure of subtraction from both sides of a known initial integral equation their statistical averages obtained without any auxiliary assumptions such as, e.g., effective field hypothesis implicitly exploited in the known centering methods. In a simplified case of using of the effective field hypothesis for analyzing composites with one sort of heterogeneities, one proves that the effective moduli explicitly depend on both the strain and stress concentrator factor for one heterogeneity inside the infinite matrix and does not directly depend on the elastic properties (local or nonlocal) of heterogeneities. In such a case, the Levin’s (1967) formula in micromechanics of composites with locally elastic constituents is generalized to their nonlocal counterpart. A solution of a volume integral equation for one heterogeneity subjected to inhomogeneous remote loading inside an infinite matrix is proposed by the iteration method. The operator representation of this solution is incorporated into the new general integral equation of micromechanics without exploiting of basic hypotheses of classical micromechanics such as both the effective field hypothesis and “ ellipsoidal symmetry” assumption. Quantitative estimations of results obtained by the abandonment of the effective field hypothesis are presented.

Poroviscoelastic characterization of particle-reinforced gelatin gels using indentation and homogenization

Hydrogels are promising materials for bioengineering applications, and are good model materials for the study of hydrated biological tissues. As these materials often have a structural function, the measurement of their mechanical properties is of fundamental importance. In the present study gelatin gels reinforced with ceramic microspheres are produced and their poroviscoelastic response in spherical indentation is studied. The constitutive responses of unreinforced gels are determined using inverse finite element modeling in combination with analytical estimates of material parameters. The behavior of composite gels is assessed by both analytical and numerical homogenization. The results of the identification of the constitutive parameters of unreinforced gels show that it is possible to obtain representative poroviscoelastic parameters by spherical indentation without the need for additional mechanical tests. The agreement between experimental results on composite gelatin and the predictions from homogenization modeling show that the adopted modeling tools are capable of providing estimates of the poroviscoelastic response of particle-reinforced hydrogels.

Implementation of strain-life fatigue parameters estimation methods in a web-based system

In order to address problems connected with the choice of a proper material during early stages of product development when limited or no experimental data on candidate materials are available, a web-based information system consisting of material properties database and expert system for the estimation of cyclic and fatigue material parameters has been established. Material properties database is user-expandable and draws mainly on existing, published literature sources and results of relevant research. Besides the well-established estimation methods and the methodology for their evaluation, the results of own research in the form of a newly proposed approach and method for the estimation of strain-life fatigue parameters as well as the methodology for the evaluation of estimation methods are incorporated in the system as well.

Estimating material parameters of a structurally based constitutive relation for skin mechanics

This paper presents a structurally based modeling framework to characterize the structure-function relation in skin tissues, based upon biaxial tensile experiments performed in vitro on porcine skin. Equi-axial deformations were imposed by stretching circular skin specimens uniformly along twelve directions, and the resultant loads at the membrane attachment points were measured. Displacement fields at each deformation step were tracked using an image 2D cross-correlation technique. A modeling framework was developed to simulate the experiments, whereby measured forces were applied to finite element models that were created to represent the geometry and structure of the tissue samples. Parameters of a structurally based constitutive relation were then identified using nonlinear optimization. Results showed that the ground matrix stiffness ranged from 5 to 32kPa, fiber orientation mean from 2 to 13(◦) from the torso midline, fiber undulation mean from 1.04 to 1.34 and collagen fiber stiffness from 48 to 366MPa. It was concluded that the objective function was highly sensitive to the mean orientation and that a priori information about fiber orientation mean was important for the reliable identification of constitutive parameters.

Estimation of inelastic seismic material properties of a surficial sea‐bed from multi‐component marine seismic data

ABSTRACTTo date, state‐of‐the‐art seismic material parameter estimates from multi‐component sea‐bed seismic data are based on the assumption that the sea‐bed consists of a fully elastic half‐space. In reality, however, the shallow sea‐bed generally consists of soft, unconsolidated sediments that are characterized by strong to very strong seismic attenuation. To explore the potential implications, we apply a state‐of‐the‐art elastic decomposition algorithm to synthetic data for a range of canonical sea‐bed models consisting of a viscoelastic half‐space of varying attenuation. We find that in the presence of strong seismic attenuation, as quantified by ‐values of 10 or less, significant errors arise in the conventional elastic estimation of seismic properties. Tests on synthetic data indicate that these errors can be largely avoided by accounting for the inherent attenuation of the seafloor when estimating the seismic parameters. This can be achieved by replacing the real‐valued expressions for the elastic moduli in the governing equations in the parameter estimation by their complex‐valued viscoelastic equivalents. The practical application of our parameter procedure yields realistic estimates of the elastic seismic material properties of the shallow sea‐bed, while the corresponding ‐estimates seem to be biased towards too low values, particularly for S‐waves. Given that the estimation of inelastic material parameters is notoriously difficult, particularly in the immediate vicinity of the sea‐bed, this is expected to be of interest and importance for civil and ocean engineering purposes.

New Layer-Moduli Back-Calculation Method Based on the Constrained Extended Kalman Filter

In pavement engineering, good estimation of layer moduli from nondestructive methods is an important tool for scheduling and designing rehabilitation projects. The falling weight deflectometer test is perhaps the most commonly used nondestructive method for the evaluation of the structural performance of pavement systems. These measurements are then used to back-calculate the properties of the layered pavement materials. A new method based on constrained extended Kalman filter (EKF) is proposed for back-calculating layer moduli. The method uses a transformation to constrain the searchable domain for determining the optimal estimates of material parameters and a weighted iteration algorithm that enhances the speed and convergence of the iterative procedure. In numerical examples, the proposed method converges to the actual layer moduli with high accuracy for three-, four-, and five-layer pavement systems even though very different initial values are used. The paper also compares the performance of EKF with other methods published in the literatures. The proposed method shows excellent performance in terms of speed and stability while providing highly accurate estimates of material properties including cases in which nonlinear layers were considered. It is concluded that the constrained EKF is a fast, stable, and consistent algorithm used in back-calculation of layer moduli.

A finite element study of invariant-based orthotropic constitutive equations in the context of myocardial material parameter estimation

A previous study investigated a number of invariant-based orthotropic and transversely isotropic constitutive equations for their suitability to fit three-dimensional simple shear mechanics data of passive myocardial tissue. The study was based on the assumption of a homogeneous deformation. Here, we extend the previous study by performing an inverse finite element material parameter estimation. This ensures a more realistic deformation state and material parameter estimates. The constitutive relations were compared on the basis of (i) ‘goodness of fit’: how well they fit a set of six shear deformation tests and (ii) ‘variability’: how well determined the material parameters are over the range of experiments. These criteria were utilised to discuss the advantages and disadvantages of the constitutive relations. It was found that a specific form of the polyconvex type as well as the exponential Fung-type equations were most suitable for modelling the orthotropic behaviour of myocardium under simple shear.

Comparison of analytical and inverse finite element approaches to estimate cell viscoelastic properties by micropipette aspiration

The viscoelastic properties of cells are important in predicting cell deformation under mechanical loading and may reflect cell phenotype or pathological transition. Previous studies have demonstrated that viscoelastic parameters estimated by finite element (FE) analyses of micropipette aspiration (MA) data differ from those estimated by the analytical half-space model. However, it is unclear whether these differences are statistically significant, as previous studies have been based on average cell properties or parametric analyses that do not reflect the inherent experimental and biological variability of real experimental data. To determine whether cell material parameters estimated by the half-space model are significantly different from those predicted by the FE method, we implemented an inverse FE method to estimate the viscoelastic parameters of a population of primary porcine aortic valve interstitial cells tested by MA. We found that inherent differences between the analytical and inverse FE estimation methods resulted in statistically significant differences in individual cell properties. However, in cases with small pipette to cell radius ratios and short loading periods, model-dependent differences were masked by experimental and cell-to-cell variability. Analytical models that account for finite cell-size and loading rate further relaxed the experimental conditions for which accurate cell material parameter estimates could be obtained. These data provide practical guidelines for analysis of MA data that account for the wide range of conditions encountered in typical experiments.

Simultaneous Determination of Complex Permittivity and Permeability of Columnar Materials With Arbitrarily Shaped Cross Section

An effective simultaneous evaluation method for the complex permittivity and permeability of lossy materials is proposed by applying it to an arbitrarily shaped cross-sectional post placed in a rectangular waveguide. We use one sample and only measure S 21 parameters for two different locations of the sample. The measurement of complex reflection parameter S 11 is not required in this evaluation method. The scheme of electromagnetic field analysis for the evaluation is based on the extended spectral-domain approach combined with the mode-matching method, which is accurate and efficient, and can be flexibly used for the iterative fitting operation for the estimation of material parameters. Sample preparation and setting is significantly easier in this method compared to conventional methods. The error caused by deviations in the setting of a sample is investigated. The estimated values for the sample material by this procedure show good agreement with the results obtained using the conventional method over the X-band.