Estimation Of Material Parameters Research Articles

A Bayesian Inference Framework for Procedural Material Parameter Estimation

AbstractProcedural material models have been gaining traction in many applications thanks to their flexibility, compactness, and easy editability. We explore the inverse rendering problem of procedural material parameter estimation from photographs, presenting a unified view of the problem in a Bayesian framework. In addition to computing point estimates of the parameters by optimization, our framework uses a Markov Chain Monte Carlo approach to sample the space of plausible material parameters, providing a collection of plausible matches that a user can choose from, and efficiently handling both discrete and continuous model parameters. To demonstrate the effectiveness of our framework, we fit procedural models of a range of materials—wall plaster, leather, wood, anisotropic brushed metals and layered metallic paints—to both synthetic and real target images.

Photothermal Porosity Estimation in CFRP by the Time-of-Flight of Virtual Waves

Porosity is an unavoidable defect in carbon fiber reinforced polymers and has noticeable effects on mechanical properties since gas filled voids weaken the epoxy matrix. Pulsed thermography is advantageous because it is a non-contacting, non-destructive and fast photothermal testing method that allows the estimation of material parameters. Using the Virtual Wave Concept for thermography data, ultrasonic evaluation methods are applicable. In this work, the pulse-echo method for Time-of-Flight measurements is used, whereby the determined Time-of-Flight is directly related to the thermal diffusion time of the examined material. We introduce a signal-to-noise dependent approach, the optimum evaluation time, for evaluating only relevant time ranges which contain information of heat diffusion. After the validation of the method for heterogeneous materials, effective medium theories can be used for quantitative porosity estimation from the estimated diffusion time. This model-based approach for porosity estimation delivers more accurate results for transmission and reflection configuration measurements compared to thermographic state-of-the-art methods. The results are validated by X-ray computed tomography reference measurements on a wide range of different porous carbon fiber reinforced plastic specimens with different number of plies and varying porosity contents.

Cost-effective search for lower-error region in material parameter space using multifidelity Gaussian process modeling

Information regarding precipitate shapes is critical for estimating material parameters. Hence, we considered estimating a region of material parameter space in which a computational model produces precipitates having shapes similar to those observed in the experimental images. This region, called the lower-error region (LER), reflects intrinsic information of the material contained in the precipitate shapes. However, the computational cost of LER estimation can be high because the accurate computation of the model is required many times to better explore parameters. To overcome this difficulty, we used a Gaussian-process-based multifidelity modeling, in which training data can be sampled from multiple computations with different accuracy levels (fidelity). Lower-fidelity samples may have lower accuracy, but the computational cost is lower than that for higher-fidelity samples. Our proposed sampling procedure iteratively determines the most cost-effective pair of a point and a fidelity level for enhancing the accuracy of LER estimation. We demonstrated the efficiency of our method through estimation of the interface energy and lattice mismatch between MgZn2 and {\alpha}-Mg phases in an Mg-based alloy. The results showed that the sampling cost required to obtain accurate LER estimation could be drastically reduced.

Stress−strain curves and derived mechanical parameters of P91 steel from spherical nanoindentation at a range of temperatures

This work compares different measurement and analysis protocols of spherical nanoindentation tests performed at different temperatures on a ferritic/martensitic P91 grade steel, in order to derive meaningful indentation stress−strain curves (ISSC) and estimate material parameters such as indentation modulus, yield strength, work hardening exponent and ultimate tensile strength. Quasi-static multi-cycle and dynamic continuous stiffness measurement indentation using a spherical indenter with a tip radius of 20 μm has been carried out from room temperature to 600 °C in vacuum in a set-up where thermal drift has been minimised by an active surface referencing system and accurate temperature stabilization in the contact area. The methodology used to determine the contact radius is critical to achieve consistent results. The application of different combinations of definitions of contact radius and indentation-induced strain to nanoindentation data obtained by the quasi-static and dynamic measurements reveals that Tabor's approach combined with a geometrically determined contact radius best represents the ISSC relationship for the P91 characterized. This method is then extended to predict the high temperature tensile properties of the steel from nanoindentation results.

Out-of-plane motion and non-perpendicular alignment compensation for 2D-DIC based on cross-shaped structured light

Although the 3D-DIC method has matured both theoretically and technically, the 2D-DIC method still plays an important role in in-plane deformation measurements. However, the accuracy of 2D-DIC is affected by out-of-plane motion (including out-of-plane translation and out-of-plane rotation) and non-perpendicular alignment. To tackle this problem, we propose to directly measure these unfavorable error sources by cross-shaped structured light (CSSL) and the optical triangulation method. Subsequently, pseudo-strains are calculated and compensated using an integrated mathematical model developed in this paper. To avoid mutual interference between the structured light strips and the speckle image, color coding is also proposed to use different color information for 2D-DIC processing and error compensation. Experiments with controlled out-of-the-plane motions show that the mean error after compensation can be as small as 50με. Uniaxial tension tests were also conducted to verify the feasibility of the proposed method in the real material parameter estimation experiment.

Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material.

This paper describes the propagation of shear waves in a Holzapfel-Gasser-Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (μ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

Reference-Free Material Characterisation of Objects Based on Terahertz Ellipsometry

Material characterization in the 0.1 - 10 THz range has been a major topic of research since its first demonstration 30 years ago. Advances in terahertz generation, detection, and data acquisition have contributed to improved bandwidth, signal power and signal-to-noise ratio. However, material characterization is still performed using conventional spectroscopic measurement schemes which require detailed information about the test object's shape, location, orientation relative to the measurement system, and a reference measurement. Here, we present a method for reference-free material characterization of dielectric objects using a terahertz time-domain spectroscopy system without a priori knowledge about the object and its position. The proposed method is based on ellipsometry combined with lensless imaging for the estimation of the refractive index. The method is a multistage procedure designed for small test objects in reflection mode. The diffracted terahertz radiation is separated from the specular reflected radiation in a post-processing step to enable a valid material parameter estimation. In this way, small dielectric objects can be located, imaged with a sub-mm resolution, and their material parameters extracted.

A simple correlation for predicting the material parameter in micropolar modeling of EHD-enhanced forced convection through a flat channel

Numerical modeling of Electrohydrodynamic (EHD) induced flow in hydraulically laminar regimes has always been a discussible subject. Recently, the micropolar approach has been examined as an alternative for the aforementioned cases. The model was found to be reliable, but time-consuming, since it needed difficult attempts to make guesses at the material parameter (κω/μ). This study aims to complement and facilitate the use of this model by providing a fast tool to guess the material parameter. In this regard, the studies show that the EHD number is a sufficient criterion to predict an adequate parameter. To satisfy this purpose, a series of well-designed studies have been carried out to calculate the EHD number for different flow characteristics; Reynolds number, applied voltage, type of the collector electrode, size of the collector plate, and the arrangement of emitter electrodes. In each case, the desired material parameter has been numerically determined by trial and error. A two-dimensional flat channel was chosen as the computational model and the results of the computational attempts, which were made using the k-ε turbulence model, were selected as the basis of the appropriate material parameter estimation.

Estimation of material parameters based on precipitate shape: efficient identification of low-error region with Gaussian process modeling

In this study, an efficient method for estimating material parameters based on the experimental data of precipitate shape is proposed. First, a computational model that predicts the energetically favorable shape of precipitate when a d-dimensional material parameter (x) is given is developed. Second, the discrepancy (y) between the precipitate shape obtained through the experiment and that predicted using the computational model is calculated. Third, the Gaussian process (GP) is used to model the relation between x and y. Finally, for identifying the “low-error region (LER)” in the material parameter space where y is less than a threshold, we introduce an adaptive sampling strategy, wherein the estimated GP model suggests the subsequent candidate x to be sampled/calculated. To evaluate the effectiveness of the proposed method, we apply it to the estimation of interface energy and lattice mismatch between MgZn2 ({{rm{beta }}}_{1}^{text{'}}) and α-Mg phases in an Mg-based alloy. The result shows that the number of computational calculations of the precipitate shape required for the LER estimation is significantly decreased by using the proposed method.

Estimating the material parameters of an inhomogeneous poroelastic plate from ultrasonic measurements in water.

The estimation of poroelastic material parameters based on ultrasound measurements is considered. The acoustical characterisation of poroelastic materials based on various measurements is typically carried out by minimising a cost functional of model residuals, such as the least squares functional. With a limited number of unknown parameters, least squares type approaches can provide both reliable parameter and error estimates. With an increasing number of parameters, both the least squares parameter estimates and, in particular, the error estimates often become unreliable. In this paper, the estimation of the material parameters of an inhomogeneous poroelastic (Biot) plate in the Bayesian framework for inverse problems is considered. Reflection and transmission measurements are performed and 11 poroelastic parameters, as well as 4 measurement setup-related nuisance parameters, are estimated. A Markov chain Monte Carlo algorithm is employed for the computational inference to assess the actual uncertainty of the estimated parameters. The results suggest that the proposed approach for poroelastic material characterisation can reveal the heterogeneities in the object, and yield reliable parameter and uncertainty estimates.

Inverse finite element characterization of the human thigh soft tissue in the seated position.

Pressure ulcers are localized damage to the skin and underlying tissues caused by sitting or lying in one position for a long time. Stresses within the soft tissue of the thigh and buttocks area play a crucial role in the initiating mechanism of these wounds. Therefore, it is crucial to develop reliable finite element models to evaluate the stresses caused by physiological loadings. In this study, we compared how the choice of material model and modeling area dimension affect prediction accuracy of a model of the thigh. We showed that the first-order Ogden and Fung orthotropic material models could approximate the mechanical behavior of soft tissue significantly better than neo-Hookean and Mooney-Rivlin. We also showed that, significant error results from using a semi-3D model versus a 3D model. We then developed full 3D models for 20 participants employing Ogden and Fung material models and compared the estimated material parameters between different sexes and locations along the thigh. We showed that males tissues are less deformable overall when compared to females and the material parameters are highly dependent on location, with tissues getting softer moving distally for both men and women.

Investigating the Grain Boundary Transport and Resulting Effective Bulk Properties for Polycrystalline Solid Electrolytes

All-solid-state batteries (ASSB) are candidates for the next-generation of safe and high energy density storage systems. In order to reach the full potential in terms of energy and power density the current limiting processes on the microscopic interface level as well as the macroscopic cell level need to be overcome. In this contribution, we explore the working principle of ASSBs and their interfaces in a multi-scale approach. We combine our 3D microstructure-resolved simulation tool BEST [1,2] with a supplementary thermodynamically consistent modelling framework [3] to capture the electrochemical performance and gain insight on - homogeneous solid-solid interface processes. Through this combined approach we are able to provide additional microscopic interface and bulk properties which are transferred as theory-based input parameters to our 3D microstructure-resolved simulations. Our focus lies on the transport limiting phenomena occurring at the homogeneous solid-solid interface e.g. grain boundary resistance in the polycrystalline electrolyte. On the microscopic level we resolve the formation of space charge layers in the solid electrolyte under the influence of grains and grain boundaries. This local electrostatic perturbation of the system through the additional polarization of the crystal grain boundaries is approximated by a mean-field approach to derive an effective dielectric constant for the polycrystalline bulk solid electrolyte. The new effective material parameter depends on the magnitude of the induced polarization and therefore relies on the material specific parameters e.g. grain size, grain width, grain volume fraction. This approach provides a link between microscopic material parameters and macroscopic electrochemical transport phenomena on cell level. Besides the effective material parameter estimation of the system, the three dimensional resolved transport through the granular solid electrolyte e.g., the grain and grain boundary transport is of special interest. In order to account for the lithium ion hopping probability between two neighbouring particles we introduce a modified interface flux at the grain interfaces. By explicit modelling of the polycrystalline electrolyte, the experimentally observed impedance characteristics are reproduced and identified. In an extended study for oxidic garnet type systems the correlation between grain size and grain impedance as well as the varying transport properties between boundary and core phase are presented. The comparison between simulations and experiments demonstrates the importance of interfacial processes and gives directions for the development of future ASSBs.

Measurement of Axially Inhomogeneous Permittivity Distributions in Resonant Microwave Cavities

The cavity perturbation method is a standard technique for material parameter estimation. It typically assumes that the sample consisting of the material under test (MUT) is small. This and other assumptions are violated in in-process measurement scenarios that involve big and inhomogeneous samples. We analyze the limitations of the classical perturbation method and present a new approach toward the measurement of spatially varying material parameters associated with a large sample in a rectangular or a circular cylindrical microwave cavity. The method is based on the measurement of multiple resonance frequencies and quality factors and is validated by numerical and laboratory experiments. It is demonstrated that relative permittivities and conductivities may be measured with typical accuracies on the order of 1%.

Modeling and experimental verification of nonlinear behavior of cellulose nanocrystals reinforced poly(lactic acid) composites

In this paper, a constitutive modeling framework was introduced to characterize the time-dependent behavior in poly(lactic acid) reinforced by cellulose nanocrystals (CNCs). The mechanical properties of PLA and its corresponding nanocomposites were analyzed at three different extension rates (1, 5, 10 mm/min) using a stress relaxation test. Six hyperelastic strain energy functions were employed to describe the instantaneous mechanical behavior. The deviatoric and volumetric material constants were verified using Drucker stability criterion, and the instability limits of each model were reported. Furthermore, a hyper-viscoelastic model consisting of Neo-Hookean strain energy function and time-dependent Prony series was used to study the viscoelastic behavior of PLA and the corresponding nanocomposites. The model constants were determined using finite element (FE) simulations through an iterative process for the whole loading history of the relaxation test. Nelder–Mead Simplex method was applied to optimize the results of the FE simulations using the experimental data. The mechanical response observed for PLA and nanocomposites from model exhibited a good agreement with both short and long-term experimental data, suggesting the applicability of the estimated material parameters by this technique.

Dimensionality reduction in thermal tomography

Estimation of material parameters plays an important role in many scientific fields ranging from geophysics, medical imaging, archaeology, material science to the preservation of historical structures. This paper focuses on the civil engineering problem of heat transfer in cases where an intervention into a structure might not be allowed and where estimation of the material parameter can be conducted using only boundary measurements. For two decades, thermal tomography has addressed such scenarios. This study introduces a novel approach for recovering spatially distributed thermal properties based on the random field theory, which efficiently parametrizes the unknown parameter fields. The proposed approach is verified computationally and the results achieved correspond well to those provided by standard thermal tomography procedures.

Application of Sequential Data Assimilation for Estimating Material Parameters using Digital Image Correlation Method

Numerical simulations and CAE technologies have become essential tool to reduce costs in product development stage since they can be substituted with the tests that involve actual manufacturing process and products. However, in order to obtain the simulation results which accurately reproduce the actual phenomena, model parameters and simulation conditions have to be determined accurately. In many cases, such parameters and simulation conditions are determined by trial and error, which is a time consuming process. When comparing the result of finite element analysis of deformation or fracture, one of the experimental measurement used is the data obtained using digital image correlation (DIC) method. DIC method enables us to measure deformation and strain on the surface of test specimen in three dimension. Meanwhile, data assimilation have attracted much attention as the methodology to utilize experimental measurements to improve the simulation results. In this study, we demonstrate application of data assimilation methodology to finite element analysis for utilizing DIC measurements to improve analysis result by estimating material parameters.

Application of Sequential Data Assimilation for Estimating Material Parameters and Boundary Conditions using Digital Image Correlation Method

Numerical simulations and CAE technologies have become essential tool to reduce costs in development and designing of products. However, in order to obtain the simulation results which accurately reproduce the actual phenomena, model parameters and simulation conditions need to be determined accurately. In many cases, such parameters and simulation conditions are determined by trial and error, which is a time-consuming process, or done by the well experienced engineer. Recently, measurement data obtained using digital image correlation (DIC) method is often used to be compared with the result of numerical analysis. DIC method is the optical method that provides full-field displacement and strain on the surface of the target object. Meanwhile, data assimilation (DA) has attracted much attention as the methodology to utilize experimental measurements to improve the simulation results. In this study, we demonstrate application of data assimilation methodology to finite element analysis for utilizing DIC measurements to improve analysis result by estimating material parameters and boundary conditions.

Analysis of measured pore pressure response to atmospheric pressure changes to evaluate small-strain moduli: methodology and case studies

The use of pore pressure responses to fluctuations in total stress (resulting from barometric pressure changes) to calculate moduli and other material properties is a recently developed technique being applied to deep aquitard formations. Initially, the method has relied on visual interpretation of the data from grouted-in piezometers, resulting in a qualitative result with little opportunity to define the quality of measured data; more recently, linear and multiple regression analyses were used to assess the same properties with limited success. Here, a methodology is developed to determine loading efficiency from pore pressure measurements using filtering and numerical regression. The results indicate a near linear relationship between the change in pore pressure and change in stress (barometric pressure), resulting in an estimation of loading efficiency and quantification of the quality of fit. Four to 6 days of data appear to best isolate the barometric fluctuation with the developed filters. The technique is successfully applied to a “simple” site, where groundwater conditions are relatively stable, as well as a complex site, where groundwater conditions are changing due to fluctuating river levels. The successful application to the latter site shows that robust analysis is possible, even for dynamic and complex environments, and that the method represents a viable alternative for estimating material parameters of formations that are historically difficult to characterize.

Validation of Orthotropic Parameters of Timber by Means of Elastic Layer Theory

The known solution of isotropic elastic layer was modified for orthotropic elastic material behavior in this contribution. The solution was original derived for calculation of footing settlement. However it should be useful for estimation of orthotropic material parameters. Timber is classical orthotropic material. Timber board which is placed on the rigid basement it could be considered as the elastic layer. From the known load displacement curve we can, vice versa, estimate the material parameters. The present solution should be able to control loading by rigid strip footing acting perpendicular to the plane of orthotropy. The contribution summarize the first steps of the proposed back analysis.

Spatial Estimation of Material Parameters and Refined Finite-Element Analysis of Rockfill Dam Based on Construction Digitization

Spatial Estimation of Material Parameters and Refined Finite-Element Analysis of Rockfill Dam Based on Construction Digitization