Properties Of Heterogeneous Materials Research Articles

An open-source FEniCS-based framework for hyperelastic parameter estimation from noisy full-field data: Application to heterogeneous soft tissues

We introduce a finite-element-model-updating-based open-source framework to identify mechanical parameters of heterogeneous hyperelastic materials from in silico generated full-field data which can be downloaded here https://github.com/aflahelouneg/inverse_identification_soft_tissue. The numerical process consists in simulating an extensometer performing in vivo uniaxial tensile experiment on a soft tissue. The reaction forces and displacement fields are respectively captured by force sensor and Digital Image Correlation techniques. By means of a forward nonlinear FEM model and an inverse solver, the model parameters are estimated through a constrained optimization function with no quadratic penalty term. As a case study, our Finite Element Model Updating (FEMU) tool has been applied on a model composed of a keloid scar surrounded by healthy skin. The results show that at least 4 parameters can be accurately identified from an uniaxial test only. The originality of this work lies in two major elements. Firstly, we develop a low-cost technique able to characterize the mechanical properties of heterogeneous nonlinear hyperelastic materials. Secondly, we explore the model accuracy via a detailed study of the interplay between discretization error and the error due to measurement uncertainty. Next steps consist in identifying the real parameters and so finding the matching preferential directions of keloid scars growth.

The 2011-2019 Long Valley Caldera inflation: New insights from separation of superimposed geodetic signals and 3D modeling

Increasingly accurate, and spatio-temporally dense, measurements of Earth surface movements enable us to identify multiple deformation patterns and highlight the need to properly characterize the related source processes. This is particularly important in tectonically active areas, where deformation measurement is crucial for monitoring ongoing processes and assessing future hazard. Long Valley Caldera, California, USA, is a volcanic area where frequent episodes of unrest involve inflation and increased seismicity. Ground- and satellite-based instruments show that volcanic inflation renewed in 2011, and is continuing as of early 2021. Additionally, Long Valley Caldera is affected by the large, but spatially and temporally variable, amounts of precipitation falling on the adjacent Sierra Nevada Range.The density and long duration of deformation measurements at Long Valley Caldera provide an excellent collection of data to decompose time-series and separate multiple superimposed deformation sources. We analyze Global Navigation Satellite System (GNSS) time-series and apply variational Bayesian Independent Component Analysis (vbICA) decomposition method to isolate inflation-related signals from other processes. We show that hydrological forcing causes significant horizontal and vertical deformation at different temporal (seasonal and multiyear) and spatial (few to hundreds of km) scales that cannot be ignored while analyzing and modeling the tectonic signal. Focusing on the last inflation episode, we then improve on prior simplistic models of the inflation reservoir by including heterogeneous subsurface material properties and topography. Our results suggest the persistence and stability of the reservoir (prolate ellipsoid at about 8 km beneath the resurgent dome) and indicate a 40-50% reduction of the inflation rate after about 3 years from the inflation onset. The onset of the reduced inflation rate corresponded in time with the occurrence of a strong seismic swarm in the Caldera, but also to the temporal variation of climatic conditions in the area.

Machine learning for high-fidelity prediction of cement hydration kinetics in blended systems

The production of ordinary Portland cement (OPC), the most broadly utilized man-made material, has been scrutinized due to its contributions to global anthropogenic CO2 emissions. Thus — to mitigate CO2 emissions — mineral additives have been promulgated as partial replacements for OPC. However, additives — depending on their physiochemical characteristics — can exert varying effects on OPC’s hydration kinetics. Therefore — in regards to more complex systems — it is infeasible for semi-empirical kinetic models to reveal the underlying nonlinear composition-property (i.e., reactivity) relationships. In the past decade or so, machine learning (ML) has arisen as a promising, holistic approach to predict the properties of heterogeneous materials, even without an across-the-board comprehension of the underlying composition-properties correlations. This paper describes the use of a Random Forests (RF) model to enable high-fidelity predictions of time-dependent hydration kinetics of OPC-based systems — more specifically [OPC + mineral additive(s)] systems — using the system’s physiochemical attributes as inputs. Results show that the RF model can also be used to formulate mixture designs that satisfy user-imposed kinetics-related criteria. Lastly, the presented results can be expanded to formulate mixture designs that satisfy target kinetic criteria, even without knowledge of the underlying kinetic mechanisms.

Efficient prediction of the effective nonlinear properties of porous material by FEM-Cluster based Analysis (FCA)

The present paper extends the FEM-Cluster based Analysis (FCA) method to the efficient prediction of effective properties of porous materials in the nonlinear range. Different from the traditional methods of homogenization or mean field theory, this new approach does not fill the pore with low modulus materials which causes numerical inaccuracy and convergence difficulties as reported in several literature. With no material filling in pores, the average strain theorem and the Hill–Mandel condition which is the basis of the Representative Volume Element (RVE) method for the prediction of effective properties of heterogeneous materials is almost impossible to implement. Furthermore, because of the lack of pore strain information, the compatibility condition of cluster strains cannot be applied in the incremental analysis of reduced order model in the nonlinear stage. In the present study we have overcome these difficulties by several approaches. First, it is found that the energy equivalence principle provides a more suitable basis for effective properties prediction of porous materials. Second, the self-equilibrium cluster stress field obtained from the interaction matrix and the cluster-based minimum complementary energy in FCA can be successfully applied to the incremental analysis of reduced order model in the nonlinear stage instead of the strain compatibility condition. However, due to the errors introduced by averaging stress and strain over each cluster, the interaction matrix becomes non-singular and the self-equilibrium properties of the cluster stress field generated from the interaction matrix become very poor. Fortunately, the most exciting discovery of the present study is that we have found a way to recover the singularity of the interaction matrix by minimizing its rank on the premise that the elastic energy norm of RVE remains unchanged within the given tolerance. Several numerical examples are presented to demonstrate the effectiveness and efficiency of the proposed approach.

Finite-volume flux reconstruction and semi-analytical particle tracking on triangular prisms for finite-element-type models of variably-saturated flow

Consistent particle tracking relies on conforming velocity fields that ensure local mass conservation on elements. Cell-centered finite-volume and mixed finite-element methods result in conforming velocity fields but this is not the case for continuous Galerkin methods, such as the standard finite element method (FEM). Nonetheless standard FEM is often used for subsurface flow modeling because it yields a continuous approximation of hydraulic heads, and it naturally handles unstructured grids and full material tensors. Acknowledging these advantages and the wide-spread use of finite-element-type simulations, we present a postprocessing method that reconstructs a cell-centered finite-volume solution from a finite-element-type solution of the variably-saturated subsurface flow equation to obtain conforming, mass-conservative fluxes. Using the linear average velocity field derived from these fluid fluxes, we employ element-wise analytical solutions for triangular prisms to compute particle trajectories and associated travel times. As a result, we can compute consistent particle trajectories for variably-saturated flow solutions generated by node-centered methods, such as finite element or finite difference methods, that do not yield conforming velocity fields. Our flux reconstruction solves a linear elliptic problem whose size is on the order of the number of elements, which is computationally much faster than solving the initial, non-linear transient variably-saturated flow equation. Compared to other postprocessing schemes, our flux reconstruction is numerically stable, fast to compute, and does not induce severe numerical artifacts when applied to heterogeneous domains with strongly varying velocities. However, these advantages come with a comparably high coding effort and the necessity of solving a global system of equations. We show that the results of our flux reconstruction are close to the node-centered primal solution for variably saturated three-dimensional flow with heterogeneous material properties.

A Finite Element Analysis of Transtrochanteric Curved Varus Osteotomy Combined with Compression Hip Screw System

Background: Complications such as Nonunion, Metal failure and Periprosthetic fracture were found after the TCVO surgery accounting for the mechanical reasons mainly, moreover. There was no any research for simulating TCVO model by using the finite element analysis from the literature. Methods: A TCVO model with 25° fixed with compression hip screw system, which assigned an isotropic heterogeneous material property for the femur was estimated and simulated initial post-operative stage and bone-healing stage, in which the mechanical parameters were compared. Results: (1) The Max displacement in non-friction condition was 9.695 mm. And a strong decrease with the Max displacement of 3.456 mm in condition of bonding for the interfaces. (2) The concentration of von Mises stress on the interfaces were present at the area of lag tunnel with the Max values: 122.0MPa in shaft and 84.20MPa in head, comparing the bone-healing stage, the concentration of von Mises stress in the infero-medial area of contact of the shaft with the Max values: 80.95MPa. (3) The concentration of von Mises stress was both displaced in the junction of osteotomy for the CHS system with the Max von Mises stress values: 1765MPa and 334MPa in two conditions. Conclusions: It was conformed that there was higher instability and fracture risk in the initial post-operative period with more displacement and higher stress in the concentrated point, it was indicated that the load-constrained activities and strong fixation were benefit to decrease the complication and improve the success rate for clinical practice.

Mechanical fatigue of whole rabbit-tibiae under combined compression-torsional loading is better explained by strained volume than peak strain magnitude

The mechanical fatigue behavior of whole bone is poorly defined, particularly for the combined loading modes that occur in vivo. The purpose of this study was to quantify the fatigue life of whole rabbit-tibiae under cyclic uniaxial compression and biaxial (compression and torsion) loading, and to explore the relationship between fatigue life and specimen-specific finite element (FE) predictions of stress/strain. Twelve tibiae were tested cyclically until failure across a range of uniaxial-compressive loads. Another twenty-two tibiae were separated into three groups and loaded biaxially; peak compressive load was constant in all three groups (50% ultimate force) but torsion was varied (0%, 25%, or 50% of ultimate torque). FE models with heterogeneous linear-elastic material properties were developed from computed tomography. We assessed peak stress/strain and stressed/strained volume based on principal stress/strain, as well as von Mises and pressure modified von Mises criteria. A logarithmic (r2 = 0.68; p < 0.001) relationship was observed between uniaxial-compressive load and fatigue life. Biaxial tests demonstrated that fatigue life decreased with superposed torsion (p = 0.034). Strained volume, based on a maximum principal strain or pressure modified von Mises strain criteria, were strong predictors of fatigue life under both uniaxial (r2 = 0.73–0.82) and biaxial (r2 = 0.59–0.60) loads, and these outperformed equivalent peak stress- and strain-based measures. Our findings highlight the importance of evaluating strain distributions, rather than peak stress or strain, to predict the fatigue behavior or whole bone, which has important implications for the study of stress fracture.

Reconstruction of Three-Dimensional Microstructures of Two-Phase Membrane and Phase Property Estimation Through Combination of Experiment and Simulation

In this study, a multiscale property evaluation framework for heterogeneous materials with complex microstructures on a sub-micro scale has been proposed. A detailed investigation of the three-dimensional (3D) microstructural features is necessary for the evaluation of the properties of heterogeneous materials with complex microstructures. However, for heterogeneous materials with microstructures on a sub-micro scale, it is difficult to observe the 3D microstructural features owing to the limit of resolution. In this study, virtual 3D samples were reconstructed based on two-dimensional images, and tensile simulations were performed using the reconstructed 3D samples instead of the real 3D microstructures. The input parameters for the tensile-property simulations were measured via atomic force microscopy, which is used to measure the phase stiffness on a sub-micro scale. The results from these simulations were then compared with those of the experiment on a macro scale to confirm the correlation between the mechanical properties measured on the sub-micron and macro scales.

Investigating the accuracy of ultrasound viscoelastic creep imaging for measuring the viscoelastic properties of a single-inclusion phantom

Ultrasound viscoelastic creep imaging is a noninvasive technique that has potential to measure the internal spatial distribution of viscoelastic properties of materials, based on inducing the creep response of the material and using a viscoelastic mechanical model to analyze the creep response. Since how viscoelastic creep imaging can be applied to accurately measure the viscoelastic properties of heterogeneous materials is still unclear, the purpose of this study is to use finite element computer simulation to quantitatively investigate the accuracy of compressional viscoelastography (viscoelastic creep imaging using external mechanical compression as the source of excitation) on measuring the viscoelastic properties of a single-inclusion phantom. The study intends to answer a question: can compressional viscoelastography accurately measure the viscoelastic properties of the inclusion as well as the background material within a single-inclusion phantom? Based on the simulation results, compressional viscoelastography could not accurately measure the viscoelastic properties of the inclusion. The measurement of a viscoelastic property (modulus of elasticity or relaxation time constant) of the inclusion is accurate if and only if the difference in that property between the inclusion and background material is very small, less than around 10%. On the other hand, compressional viscoelastography can accurately measure the viscoelastic properties of the background material regardless of the difference in the viscoelastic properties between the inclusion and background material. In a real biological tissue, the mechanical behaviors are much more complicated and unpredictable than those in a single-inclusion phantom like the one used in the present study. Hence, based on the simulation results of the present study, it could be more challenging to apply compressional viscoelastography to accurately measure the viscoelastic properties of a mass or a target tissue within a real biological tissue. The findings of the present study based on compressional viscoelastography may also be applicable to acoustic-radiation-force-based viscoelastic creep imaging. In the future, experiments are needed to justify the simulation results found in the present study.

Elliptic functions and lattice sums for effective properties of heterogeneous materials

Effective properties of fiber-reinforced composites can be estimated by applying the asymptotic homogenization method. Analytical solutions are possible for infinite long circular fibers based on the elliptic quasi-periodic Weierstrass Zeta function. This process leads to numerical convergences issues related to lattice sums calculations. The lattice sums original series converge slowly, which make the calculation difficult. This problem needs to be addressed because effective properties are highly sensitive to these values. Therefore, a systematic review and analysis for the lattice sums are a necessity. In the present work, the Eisenstein–Rayleigh lattices sums are reviewed and numerically implemented for fiber-reinforced composites with parallelogram unit periodic cell whose fibers are centered, or not, at the coordinate origin. Numerical values are reported and compared with available data in the literature obtaining good agreements. In this work, new Eisenstein–Rayleigh lattice sums are obtained that are easy to implement and a set of tables with numerical values are given.

Effective Permittivity of a Multi-Phase System: Nanoparticle-Doped Polymer-Dispersed Liquid Crystal Films.

This paper studies the effective dielectric properties of heterogeneous materials of the type particle inclusions in a host medium, using the Maxwell Garnet and the Bruggeman theory. The results of the theories are applied at polymer-dispersed liquid crystal (PDLC) films, nanoparticles (NP)-doped LCs, and developed for NP-doped PDLC films. The effective permittivity of the composite was simulated at sufficiently high frequency, where the permittivity is constant, obtaining results on its dependency on the constituents’ permittivity and concentrations. The two models are compared and discussed. The method used for simulating the doped PDLC retains its general character and can be applied for other similar multiphase composites. The methods can be used to calculate the effective permittivity of a LC composite, or, in the case of a composite in which one of the phases has an unknown permittivity, to extract it from the measured composite permittivity. The obtained data are necessary in the design of the electrical circuits.

Computational Evaluation of Thermal Response of Open-Cell Foam With Circular Pore

Abstract The evaluation of effective material properties in heterogeneous materials (e.g., composites or multicomponent structures) is critically relevant to a wide spectrum of applications, including nuclear power, electronic packaging, flame retardants, hypersonics, and gas turbine power. The work described in this paper is centered around the numerical assessment of the thermal behavior of porous materials obtained from finite element thermal modeling and simulation. Two-dimensional, steady-state analyses were performed on unit cells with centered, circular pores using a second-order accurate Galerkin finite element method (FEM). The effective thermal conductivities of the porous systems were examined, encompassing a range of porosities from 4.9% to 60.1%. The geometries of the models were generated based on ordered circular pores for each modeled porosity level. The system response quantity (SRQ) under investigation was the dimensionless effective thermal conductivity across the unit cell. The dimensionless effective thermal conductivity was compared across all simulated cases, producing a trend between porosity and effective thermal conductivity. In the presented investigation, the method of manufactured solutions (MMS) was used to perform code verification, and the grid convergence index (GCI) was employed to estimate discretization uncertainty as solution verification. Code verification concluded an approximately second order accurate Galerkin FEM solver. It was found that the introduction of porosity to the unit cell material structure reduces effective thermal conductivity, as anticipated. Numerical results obtained in this study are compared to an analytical solution and to a sample of empirical data. This approach can be readily generalized to study a wide variety of porous solids from ranging from structures at the nanoscale—such as nanocarbon tubes—to structures at macrolevel scales—such as geological features.

Non-invasive prediction of the mouse tibia mechanical properties from microCT images: comparison between different finite element models

New treatments for bone diseases require testing in animal models before clinical translation, and the mouse tibia is among the most common models. In vivo micro-Computed Tomography (microCT)-based micro-Finite Element (microFE) models can be used for predicting the bone strength non-invasively, after proper validation against experimental data. Different modelling techniques can be used to estimate the bone properties, and the accuracy associated with each is unclear. The aim of this study was to evaluate the ability of different microCT-based microFE models to predict the mechanical properties of the mouse tibia under compressive load. Twenty tibiae were microCT scanned at 10.4 µm voxel size and subsequently compressed at 0.03 mm/s until failure. Stiffness and failure load were measured from the load–displacement curves. Different microFE models were generated from each microCT image, with hexahedral or tetrahedral mesh, and homogeneous or heterogeneous material properties. Prediction accuracy was comparable among models. The best correlations between experimental and predicted mechanical properties, as well as lower errors, were obtained for hexahedral models with homogeneous material properties. Experimental stiffness and predicted stiffness were reasonably well correlated (R2 = 0.53–0.65, average error of 13–17%). A lower correlation was found for failure load (R2 = 0.21–0.48, average error of 9–15%). Experimental and predicted mechanical properties normalized by the total bone mass were strongly correlated (R2 = 0.75–0.80 for stiffness, R2 = 0.55–0.81 for failure load). In conclusion, hexahedral models with homogeneous material properties based on in vivo microCT images were shown to best predict the mechanical properties of the mouse tibia.

Bulk chemical composition contrast from attractive forces in AFM force spectroscopy.

A key application of atomic force microscopy (AFM) is the measurement of physical properties at sub-micrometer resolution. Methods such as force–distance curves (FDCs) or dynamic variants (such as intermodulation AFM (ImAFM)) are able to measure mechanical properties (such as the local stiffness, kr) of nanoscopic heterogeneous materials. For a complete structure–property correlation, these mechanical measurements are considered to lack the ability to identify the chemical structure of the materials. In this study, the measured attractive force, Fattr, acting between the AFM tip and the sample is shown to be an independent measurement for the local chemical composition and hence a complete structure–property correlation can be obtained. A proof of concept is provided by two model samples comprised of (1) epoxy/polycarbonate and (2) epoxy/boehmite. The preparation of the model samples allowed for the assignment of material phases based on AFM topography. Additional chemical characterization on the nanoscale is performed by an AFM/infrared-spectroscopy hybrid method. Mechanical properties (kr) and attractive forces (Fattr) are calculated and a structure–property correlation is obtained by a manual principle component analysis (mPCA) from a kr/Fattr diagram. A third sample comprised of (3) epoxy/polycarbonate/boehmite is measured by ImAFM. The measurement of a 2 × 2 µm cross section yields 128 × 128 force curves which are successfully evaluated by a kr/Fattr diagram and the nanoscopic heterogeneity of the sample is determined.

Modal Analysis of Beam Structures with Random Field Models at Multiple Scales

Structure material properties are heterogeneous in nature and would be characterized with different statistics at different length scales due to the spatially averaging effects. This work develops a framework for the modal analysis of beam structures with random field models at multiple scales. In this framework, the random field theory is adopted to model heterogeneous material properties, and the cross‐correlations between material properties are explicitly considered. The modal parameters of a structure are then evaluated using the finite element (FE) method with the simulated heterogeneous material properties taken as input. With the aid of Monte Carlo simulation, the modal parameters are analyzed in a probabilistic manner. In addition, to accommodate the necessity of different mesh sizes in FE models, an approach of evaluating random field parameters and generating random field material properties at different length scales is developed. The performance of the proposed framework is demonstrated through the modal analysis of a simply supported beam, where the formulation of the multiscale random field approach is validated and the effects of heterogeneous material properties on modal parameters are analyzed. Parametric studies on the random field parameters, including the coefficient of variation and the scale of fluctuation, are also conducted to further investigate the relations between the random field parameters at different scales.

A Numerical Approach to Analyze Detail Mechanical Characteristic at the Crack Tip of SCC in Dissimilar Metal Welded Joints

The mechanical characteristic at the crack tip is one of the main factors affecting the stress corrosion cracking (SCC) in dissimilar metal welded joints (DMWJs). In this research, to evaluate the effect of heterogeneous material properties on the mechanical characteristic at the crack tip of DMWJs accurately, a heterogeneous material model of the SA508 Cl.3‐Alloy 52M DMWJ was established based on USDFLD subroutine in ABAQUS. The comparison of the traditional “Sandwich” material model with the heterogeneous material properties, stress‐strain conditions, and the plastic zone around the crack tip at the interference zone has been analyzed by the finite element method (FEM). The results indicated that the heterogeneous material model could characterize the mechanical properties of the SA508 Cl.3‐Alloy 52M DMWJs accurately. In addition, the crack at the interface zone between materials will deflect along with the weld metal in two material models.

Stress Wave Propagation and Energy Absorption Properties of Heterogeneous Lattice Materials under Impact Load

A heterogeneous lattice material composed of different cells is proposed to improve the energy absorption capacity. The heterogeneous structure is formed by setting layers of body‐centered XY rods (BCCxy) cells as the reinforcement in the body‐centered cubic (GBCC) uniform lattice material. The heterogeneous lattice samples are designed and processed by additive manufacturing technology. The stress wave propagation and energy absorption properties of heterogeneous lattice materials under impact load are analyzed by finite element simulation (FES) and Hopkinson pressure bar (SHPB) experiments. The results show that, compared with the GBCC uniform lattice material, the spreading velocity of the stress of the (GBCC)3(BCCxy)2 heterogeneous lattice material is reduced by 18.1%, the impact time is prolonged 27.9%, the stress peak of the transmitted bar is reduced by 34.8%, and the strain energy peak is reduced by 29.7%. It indicates that the heterogeneous lattice materials are able to reduce the spreading velocity of stress and improve the energy absorption capacity. In addition, the number of layers of reinforcement is an important factor affecting the stress wave propagation and energy absorption properties.

Nanoscale Effect Investigation for Effective Bulk Modulus of Particulate Polymer Nanocomposites Using Micromechanical Framework

This paper investigates the nanoscale effect on the effective bulk modulus of nanoparticle‐reinforced polymer. An interface‐based model is introduced in this work to study the nanoscale effects on the effective properties of heterogeneous materials. That interface model is able to capture discontinuity of mechanical fields across the surface between the nanoparticle and matrix. A generalized self‐consistent scheme is then employed to determine the effective bulk modulus. It has been seen from the results that, in a certain range of limits, the influence of nanoscale effects on effective properties of heterogeneous materials is significant and needs to be taken into account. In particular, when the nanoparticle radius is smaller than 10 nm, the value of effective bulk modulus significantly increases when the characteristic size of nanofillers decreases. Besides, it is seen that the harder the inclusion, the smaller the nanoscale influence effects on the overall behaviors of composite materials. Finally, parametric studies in terms of surface strength and filler’s volume fractions are investigated and discussed, together with a comparison between the proposed model and other contributions in the literature.

Numerical and experimental investigation of concrete with various dosages of fly ash

<abstract> The nonlinear behavior of reinforced fly ash concrete (RFAC) beams until the ultimate failure is highly a multifaceted phenomenon due to the contention of heterogeneous material properties and the cracking behavior of concrete. This paper represents an exploration of nonlinear finite element analysis of reinforced concrete beams with the inclusion of fly ash under flexural loading. Finite element modelling of RFAC beams is carried out using a distinct reinforcement modelling method. The capability of the model to capture the critical crack regions, loads and deflections for various loadings in RFAC beams has been evaluated. Comparison is made between experimental results and finite element modelling with respect to crack formation and the ultimate capacity for flexural loading and mid-span deflection. The achieved results in the present study indicate acceptable approximation with those in the previous investigations. </abstract>

Evaluation of Slope Stability of Reservoir Considering Heterogeneous Soil Properties

The slope stability evaluation of reservoirs is required because of the aging of reservoirs. Reservoir levees are designed to achieve homogeneous construction, but the spatial heterogeneity of the material properties of reservoirs is unavoidable. Because the existing method for evaluating reservoir stability is limited in terms of considering the spatial heterogeneity of material properties, the stability evaluation was conducted in this study, in which the spatial heterogeneity and uncertainty of the material properties of the reservoir levee were considered. In addition, the results for the existing and proposed methods were compared and analyzed, and the variability of the entire material properties of the reservoir levee, instead of spatial heterogeneity, was reflected. The evaluation results confirmed that the probability of failure obtained using the proposed method was lower than that for the existing stability evaluation method, considering the variations in material properties because the levee did not reach the critical state, owing to changes in local properties. Therefore, the proposed method is useful for the cost-effect repair and reinforcement of reservoir slopes, compared to the existing slope stability evaluation method.