Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

Strongly singular and hypersingular integrals for aeroacoustic incident fields

Using the Burton and Miller formulation to predict the scattering of flow‐induced noise by a body immersed in the flow requires the near‐field pressure and pressure gradient incident on the body. In this paper, Lighthill's acoustic analogy is used to derive formulations for the near‐field pressure and pressure gradient at any point within the flow noise source region, including points on the body. These near‐field formulations involve strongly singular and hypersingular volume and surface integrals. To evaluate these singular integrals, an effective singularity regularization technique is derived. An analytical source distribution is used to demonstrate the accuracy of the method. A cell‐averaged representation of this analytical source distribution, similar to the data stored by computational fluid dynamics solvers, is also created. A piecewise linear, continuous source distribution is generated from these cell‐average values, producing a C⁰ distribution. A k‐exact reconstruction technique is then used to create high‐order polynomials of the solution variables for each volume cell. These high‐order polynomials are constructed from its cell average value and the average values of the nearby cells. The source distribution created using the k‐exact reconstruction is discontinuous across cell boundaries but exhibits a smooth polynomial distribution within each cell. The near‐field pressure and pressure gradient predicted using these reconstructed source distributions are compared with the results obtained using the analytical distribution. Copyright © 2014 John Wiley & Sons, Ltd.     

面载荷识别的TSVD正则化方法

线性系统的响应可以表示为单位脉冲响应函数与动态载荷的卷积分,经离散后得到载荷识别反问题。引入TSVD正则化方法处理反问题的不适定性,对不同噪声的实测响应进行了面载荷的反演求解,并对识别精度做出了分析。算例表明,TSVD正则化方法对响应误差的适应性强,识别精度高。     

Scattering of harmonic antiplane shear waves by an arc-shaped interfacial crack in functionally graded annular bi-material guide rail

Abstract

The dynamic behavior of an arc-shaped interfacial crack in an orthotropic functionally graded annular bi-material structure is investigated. In order for the analysis to be executable, the material properties are assumed to vary with the power function of the radial coordinates. By applying the separation variable method, the boundary value problem of the partial differential equation describing the fracture problem of this article can be transformed into a Cauchy kernel singular integral equation with the unknown jump of displacements across the crack surfaces. The obtained integral equation is solved numerically by Lobatto–Chebyshev collocation method to show the effects of the geometric and physical parameters upon the dynamic stress field near the crack tips.

Communicated by Kuang-Hua Chang.     

Residually Stressed Bimaterial Beam Specimen for Measuring Environmentally Assisted Crack Growth

Background:

Subcritical crack growth can occur in a brittle material when the stress intensity factor is smaller than the fracture toughness if an oxidizing agent (such as water) is present at the crack tip.

Objective:

We present a novel bi-material beam specimen which can measure environmentally assisted crack growth rates. The specimen is “self-loaded” by residual stress and requires no external loading.

Methods:

Two materials with different coefficient of thermal expansion are diffusion bonded at high temperature. After cooling to room temperature a subcritical crack is driven by thermal residual stresses. A finite element model is used to design the specimen geometry in terms of material properties in order to achieve the desired crack tip driving force.

Results:

The specimen is designed so that the crack driving force decreases as the crack extends, thus enabling the measurement of the crack velocity versus driving force relationship with a single test. The method is demonstrated by measuring slow crack growth data in soda lime silicate glass and validated by comparison to previously published data.

Conclusions:

The self-loaded nature of the specimen makes it ideal for measuring the very low crack velocities needed to predict brittle failure at long lifetimes.

     

An accurate interface reconstruction method using piecewise circular arcs

A novel piecewise circular interface construction (PCIC) method for accurate reconstruction of interface in a two‐phase flow problem is proposed. This is under the framework of a fixed grid, volume of fluid approach applied on a two‐dimensional semistaggered structured grid. Fluid interface in each mixed cell is represented using a geometric template of piecewise circular arc. Data corresponding to arc center coordinates and radius are first predicted using curve fitting methods and corrected with the help of volume fraction constraints. Further corrections are carried out to achieve function (c0) continuity at cell boundaries. The proposed method does not require additional calculations for the determination of curvature (for calculation of surface tension force), since it is obtained as part of reconstruction process itself. For dynamic interface construction, simple analytical expressions are derived to construct edge matched flux polygons. Area of intersection of flux polygons with area covered by primary fluid is determined to effect geometric advection across a PCIC interface. Accuracy of this method is demonstrated by the reconstruction of standard static and dynamically evolving interface problems. Accuracy levels superior to most interface reconstruction methods using PLIC and schemes using higher order curves are established. Finally, the capability to handle a complex two‐phase flow problem simulation viz the four‐vortex flow field, where interface undergoes breakage and coalescence, is also demonstrated.     

Sensor attack reconstruction for mobile robots via a switching Kalman fusion mechanism

Due to the poor security level in current industrial network, the control performance of robots may be severely affected by cyber attacks. This paper studies the sensor attack reconstruction problem of mobile robots, where a switching Kalman fusion mechanism is proposed to reconstruct the sensor attacks online. It is shown that the proposed mechanism is better than the existing extended state observer and event-triggered sensor attack reconstruction strategy. The experiment test demonstrates the effectiveness and superiority of the proposed method.

     

A new positive‐definite regularization of incompressible Navier–Stokes equations discretized with Q1/P0 finite element

A new regularization method is proposed for the Galerkin approximation of the incompressible Navier–Stokes equations with Q1/P0 element, by newly introducing a square‐type linear form into the variational divergence‐free constraint regularized with the global pressure jump (GPJ) method. The addition of the square‐type linear form is intended to eliminate the hydrostatic pressure mode appearing in confined flows, and to make the discretized matrix positive definite and then non‐singular without the pressure pegging trick. Effects of the free parameters for the regularization on the solutions are numerically examined with a 2‐D driven cavity flow problem. Furthermore, the convergences in the conjugate gradient iteration for the solution of the pressure Poisson equation are compared among the mixed method, the GPJ method and the present method for both leaky and non‐leaky 3‐D driven cavity flows. Finally, the non‐leaky 3‐D cavity flows at different Re numbers are solved to compare with the literature data and to demonstrate the accuracy of the proposed method. Copyright © 2003 John Wiley & Sons, Ltd.     

Synchronization and Non-Smooth Dynamical Systems

In this article we establish an interaction between non-smooth systems, geometric singular perturbation theory and synchronization phenomena. We find conditions for a non-smooth vector fields be locally synchronized. Moreover its regularization provide a singular perturbation problem with attracting critical manifold. We also state a result about the synchronization which occurs in the regularization of the fold-fold case. We restrict ourselves to the 3-dimensional systems (ℓ = 3) and consider the case known as a T-singularity.     

Numerical simulation of impact forces by a falling sphere in air using ALE finite element method

ABSTRACT

A numerical method is developed to simulate the process that a falling rigid sphere hits rigid ground and bounces back in air. The problem is treated as fluid-structure interaction problem based on the ALE finite element flow analysis. In order to introduce the numerical process of impact into the present staggered fluid-structure time marching algorithm, the impact force is applied to the equation of motion of the sphere. The magnitude of the impact force is determined by iteration so that the velocity of the sphere after impact converges to zero. Application of the impact force at a single time instant causes unphysical pressure oscillation. This has been suppressed by applying the impact force smoothly over multiple short time steps. In the present method impulse is evaluated instead of impact force. Computations with different density ratio of the sphere to air showed effect of the air on the sphere motion.     

Regularization of Discontinuous Vector Fields on $${\mathbb{R}^3}$$ via Singular Perturbation

Singular perturbations problems in dimension three which are approximations of discontinuous vector fields are studied in this paper. The main result states that the regularization process developed by Sotomayor and Teixeira produces a singular problem for which the discontinuous set is a center manifold. Moreover, the definition of sliding vector field coincides with the reduced problem of the corresponding singular problem for a class of vector fields.      

Videometrics Measurement for Dynamic Topography of Large Flexible Cable Net Based on Tiny Light Spot Markers

Background:

Traditional videometric method can not be used in the measurement of large flexible cable-net structure for its large overall size and small partial size.

Objective

A videometrics technique was proposed in this work to measure the topography and deformation of a large cable net structure.

Methods

Tiny spots with high brightness (and large gray gradient) are used to mark the cable net nodes. By arranging the imaging light path properly, the light spot markers can be enlarged and accurately identified in the captured images.

Results

The relationship between the imaging parameters and the gray distribution of the light spot markers were derived and verified. And a topographical measurement experiment of a cable net structure was carried out with the proposed videometrics technique.

Conclusions

The topography/deformation of the cable net can be measured with tiny-light spot markers, and the effectiveness and robustness of the technique on topography and deformation measurement of large cable-net structures are demonstrated.

     

Tikhonov regularization with Incremental Hole-Drilling and the Integral Method in Cross-Ply Composite Laminates

Background: Incremental hole-drilling with the integral method has been extensively used in composite laminates but is sensitive to small measurement errors. Error sensitivity can be reduced by limiting the number of depth increments used in the calculation procedure. This approach is limited if a rapidly varying residual stress distribution exists since the calculated stress in each incremental depth is considered constant. Distortion of stress results can consequently occur due to averaging effects if the depth increments become too large. Tikhonov regularization is usually applied in isotropic materials to smooth the resulting residual stress distribution and reduce stress uncertainties, but has only been applied to composite laminates using the slitting technique. Objective: The intention of this work is to extend the use of Tikhonov regularization to incremental hole-drilling of composite laminates using the integral method. Methods: Finite element modelling is used to calculate the necessary calibration coefficients for unit pulses of uniform stress. Monte Carlo simulation is used to the determine uncertainties in the calculated residual stress distributions. Tikhonov regularization is optimised to reduce the stress uncertainty, while ensuring that the stress solution is not distorted. Results: The method is demonstrated on a GFRP (Glass fibre reinforced plastic) laminate of [0₂/90₂]_s construction and the calculated residual stress field is compared with those obtained by the standard integral method and series expansion. Conclusions: It is found that Tikhonov regularization significantly improves the accuracy of the standard integral method in composite laminates and shows good agreement with the series expansion method.

     

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 1. A Theoretical Analysis

Background

This paper deals with the possible field of application of ultrasonic Surface Reflection Method (SRM) to achieve the mechanical characteristics of isotropic materials. This method is based on the measurement of the amplitude of the reflected wave at the interface between reference material and the material to be characterised. Objective: The purpose of Part 1 of this paper is to establish the theoretical conditions for the applicability of SRM.

Methods

First, the theoretical formulas necessary to obtain the mechanical properties of the material to be tested will be established. Then, on the basis of these analytical formulas, the validity of the results for the material to be studied will be discussed according to the choice of the mechanical properties of the reference material through uncertainty calculations. The measurand error of SRM is then compared to that of traditional methods (transmission, transmission in water bath, pulse-echo).

Results

The analytical solution to the inverse problem (the mechanical characteristics of the tested medium based on those of the reference medium and the waves’ amplitude) will be given. From this analytical solution, an analysis of the measurand error will be performed and a method for choosing the reference material will be proposed.

Conclusions

It appears that SRM is better suited than traditional methods in two specific cases: measurement of small deviations of mechanical properties from a reference material or characterisation of high damping materials. In Part 2 of this paper, the practical conditions of applicability of the method are described and then applied to different kinds of materials.

     

An analytic and application to state space reconstruction about chaotic time series

The state space reconstruction is the major important quantitative index for describing non-linear chaotic time series. Based on the work of many scholars, such as: N.H.Packard, F.Takens, M. Casdagli, J.F.Gibson, CHEN Yu-shu et al, the state space was reconstructed using the method of Legendre coordinate. Several different scaling regimes for lag time τ were identified. The influence for state space reconstruction of lag time τ was discussed. The result tells us that is a good practical method for state space reconstruction.     

New Methodologies for Fracture Detection of Automotive Steels in Tight Radius Bending: Application to the VDA 238–100 V-Bend Test

Background

The VDA 238–100 tight radius V-bend test can be used to efficiently characterize the bendability and fracture limits of sheet metals in severe plane strain bending. Material performance in plane strain bending is critical for the selection of advanced high strength steels for energy absorbing structural components.

Objective

The detection of failure based upon a reduction in the punch force can lead to erroneous predictions of failure for ductile or thin gage alloys in the VDA 238–100 test. New failure criteria were proposed and evaluated across a range of automotive steels.

Methods

Four detection methods in the V-bend test were evaluated based upon the load drop, bending moment, novel stress metric and the strain rate for seven steels with strength levels from 270 to 1500 MPa. The appropriate failure threshold was identified from visual inspection of the surface during bending.

Results

The vertical punch force will decrease as a consequence of the mechanics in the V-bend test at intermediate bend angles even without fracture. The novel stress-based metric accounts for sheet thinning and could successfully identify “false positives” and punch lift-off when considering the strain-rate evolution.

Conclusions

Failure detection using the VDA load threshold method may significantly under-report the bend performance of alloys with intermediate-to-high bendability or thin gauges. The proposed stress-based metric can reliably detect fracture for bend angles in excess of 160° and be readily calculated using the existing data. The VDA load threshold for failure can work well for materials that exhibit significant cracking.

     

Scanning-Digital Image Correlation for Moving and Temporally Deformed Surfaces in Scanning Imaging Mode

Background

Images from scanning electron microscopes, transmission electron microscopes and atomic force microscopes have been widely used in digital image correlation methods to obtain accurate full-field deformation profiles of tested objects and investigate the object’s deformation mechanism. However, because of the raster-scanning imaging mode used in microscopic observation equipment, the images obtained from these instruments can only be used for quasi-static displacement measurements; otherwise, spurious displacements and strains may be introduced into the deformation results if these scanning microscopic images are used directly in general digital image correlation calculations for moving and temporally deformed surfaces.

Objective

Realizing kinematic parameter and dynamic deformation measurements on a scanning electron microscope platform.

Methods

Establishing a scanning imaging model of moving and temporally deformed objects that contains motion and deformation equations, a scanning equation and an intensity invariance assumption for small deformations. Then proposing a scanning-digital image correlation (S-DIC) method based on combing the characteristics of the scanning imaging mode with digital image correlation.

Results

Quantitatively investigating the effects of the spurious displacements and strains introduced when using scanning images to represent moving and temporally deformed surfaces in the measurement results. Numerical simulations verify that the accuracy of the S-DIC method is 10^?2pix for the displacement, 10^?4 for the strain, 10^?4pix/s for the velocity and 10^?6s^?1 for the strain rate. Experiments also show that the proposed S-DIC method is effective. Conclusions: The results of this work demonstrate the utility of S-DIC on the field of microscopic dynamic measurement.

     

The Potential Scope of the Ultrasonic Surface Reflection Method Towards Mechanical Characterisation of Isotropic Materials. Part 2. Experimental Results

Background

This paper is Part 2 of a study on the scope of the ultrasonic Surface Reflection Method (SRM). Part 1 deals with the theoretical conditions for a satisfactory usage of this method.

Objective

This second part validates the practical feasibility and reliability of the SRM method by comparison with the conventional Transmission Method (TM) in cases where the latter is applicable.

Methods

Two experimental devices (one for SRM and one for TM) are developed and measurements of shear and bulk moduli are carried out at ultrasonic frequency (610 kHz) and at room temperature.

Results

The experimental conditions in terms of sample geometry, pulse characteristics and interfacial transmission required to obtain a given accuracy on the measurement are stated. The SRM is then validated against other experimental methods and is used to determine the shear modulus of a carbon black filled neoprene at ambient temperature (T?=?21 °C) and ultrasonic frequency.

Conclusions

The benefit brought by this method is well demonstrated: a unique measurement allows the determination of all the moduli of a highly damping isotropic material (carbon black filled neoprene) not achievable by other methods.