This isDigital Image Correlation assignment, fill in question.I simply want to evaluate how well you understood some of the main concepts we explored during the class. Please briefly answer the following questions, bringing in figures and equations from course documents as needed. Simply put answers after the questions in this document. I have also collected documents on attached. These and the lab assignments will be useful for you.
OREGON STATE UNIVERSITY Term assignment Note: I simply want to evaluate how well you understood some of the main concepts we explored during the class. Please briefly answer the following questions, bringing in figures and equations from course documents as needed. Simply put answers after the questions in this document. I have also collected documents on attached. These and the lab assignments will be useful for you. 1. The most common type of digital image correlation uses a two-camera stereo-vision method. Describe briefly the simplified mathematical basis for depth measurement that stereo-vision provides, and the role of camera calibration. 2. Describe the image correlation steps that are required to analyze a set of stereo-image pairs, and how this generates “full-field” displacement data. 3. Describe how we used an Ordinary Least Squares method to calculate the displacement gradient tensor, and how the displacement gradient relates to strain. How is Lagrangian strain different from engineering strain, and what are the advantages of Lagrangian strain? 4. Both Ordinary and Nonlinear Least Squares methods determine the parameter values of a model. What distinguishes models suitable for Ordinary from those that require Nonlinear approaches? Give examples of each. 5. There are two key assumptions made in the development of the Nonlinear Least Squares method. What are they? 6. How is a “noise floor” established when conducting a digital image correlation analysis? 7. How does subregion size relate to the accuracy and spatial resolution of a digital image correlation measurement? 8. Describe the objective function that we used to do parameter identification for the disc diametric compression analysis. What parameters did we identify? 9. Why do you have to have a good starting estimate of translation parameter values when using Nonlinear Least Squares for image correlation? Use a figure to illustrate. 10. What is the role of image data interpolation in digital image correlation, and why is it needed? 1 files/01-what-to-measure-and-why-3soxvdx2.pptx Experimental Mechanics What to measure, and why Expanding roles of Digital Image Correlation Term Project: getting started The term project (this year) is: The development of a proposal for and experimental project Focused on a well-defined objective (make product lighter <-> save the world) Grounded in technical background research Incorporating Digital Image Correlation as a primary tool Details justified through alignment with the iDICs Good Practices Guide Objectives for today: Introduction to companies that provide measurement products Examples to motivate a project topic Digital Image Correlation “thinking”: understanding scope and possibilities Digital Image Correlation reference points (partial list) https://www.idics.org https://www.correlatedsolutions.com https://trilion.com https://www.matchid.eu http://www.lavision.de/en/ https://www.gom.com Professional Society: General Metrology: Digital Image Correlation specialists: This popped up in my browser after lecture … Digital Image Correlation “thinking” If you can cover the surface of an object with suitable speckle Calibrate the measurement space through measurement of target images And collect images of suitable quality while the object is under motion/load Then you can achieve dense point-based full-field measurements of surface: Shape With subsequent calculation of: Motion Deformation (strain) Stress (if we have material property information) Quantitative model comparisons * Everything highlighted becomes a topic for technical understanding and assessment. Discrete Surface Characterization Shape Motion Deformation (strain) Continuous Information Much of basic Engineering Mechanics (and advanced topics such as Theory of Elasticity and Continuum Mechanics) are based on continuously defined functions e.g. The basic beam bending stress equation, s = My/I, defines stress at all locations over the beam cross-section Theory of Elasticity Starts from the differential (infinitesimal) perspective Define strain, stress, and material behavior at every point within an object … Stress Strain Material Properties … Generating Three Sets of Equations These equations are simplified forms that embody the symmetry of the stress and strain tensors. They are also a 2D versions of the full 3D equation set. Body forces are assumed zero in the equilibrium equations. Hooke’s Law Engineering Strain Stress Equilibrium The displacement vector is symbolized as disp = {u,v,w} in 3D, {u,v} in 2d. u = x component of displacement, v = the y component of displacement. Strain is built from the spatial derivatives of displacement. The Problem with Complex Shapes But there is a problem in generalizing this approach to objects with complex shapes: It may be difficult, or even impossible, to define equations representing the basic quantities of interest (displacements, strains, stresses) over a region of complex geometry That is why traditional mechanics approaches are limited to objects of simple shape (prismatic bars, rectangular and circular plates, cylinders) Discretization The solution to the dilemma is discretization … break the object up into small chunks of simpler geometry … that is the basis of Finite Element Analysis Nodes and Elements Look closely and you can see the small pieces (elements) and connection points (nodes) that define the geometry Each individual piece has a simple geometry with simple equations that describe problem variables (displacements, strains, stresses) within that region The nodes connect the individual pieces together and provide “sharing” of information between the elements Taken together, the nodes and elements define the behavior of the entire component Displacement Now the very important point that helps connect Finite Element Analysis with Digital Image Correlation .. And by extension to solid mechanics in general The information that is shared at the nodes (in most FEA formulations) is displacement In fact, the FEA solution is the displacement of the nodes Strain and stress are subsequently calculated from the the nodal displacements Displacements Measured at Discrete Points Wait … that looks familiar! Biomedical example from Correlated Solutions Digital image correlation was used to directly measure the displacements of discrete points over the surface of a test sample This is analogous to the calculation of nodal displacements by finite element analysis Simulation of artery deformation during stent installation … displacements shown as vectors, colors indicate the radial component of displacement. Next time … Data Workflow Shape Motion (displacement) Deformation (strain) Stress Analysis Comparisons (validation, identification) σ xx σ yy τ xy ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ ⎫ ⎬ ⎪⎪ ⎭ ⎪ ⎪ = Exx Exy Exz Exy Eyy Eyz Exz Eyz Ezz ⎡ ⎣ ⎢ ⎢ ⎢ ⎢ ⎤ ⎦ ⎥ ⎥ ⎥ ⎥ ε xx ε yy γ xy ⎧ ⎨ ⎪⎪ ⎩ ⎪ ⎪ ⎫ ⎬ ⎪⎪ ⎭ ⎪ ⎪ s xx s yy t xy ì í ï ï î ï ï ü ý ï ï þ ï ï = E xx E xy E xz E xy E yy E yz E xz E yz E zz é ë ê ê ê ê ù û ú ú ú ú e xx e yy g xy ì í ï ï î ï ï ü ý ï ï þ ï ï files/02-data-workflow-jeflhnzy.pptx Data Workflow Shape Motion (displacement) Deformation (strain) Stress Analysis Comparisons (validation, identification) From Shape to Stress Stress is often the goal of a mechanics analysis Most closely related to common failure criteria (max normal stress, von Mises stress, etc.) A common language for comparing results to prior work in a field But fundamentally DIC just measures object shape Points on the surface of an object located within a 3D coordinate system How do we get from discrete shape information to full field stress patterns? What is Stereo-Imaging? Use two imaging system separated by a distance to interpret a scene With knowledge of the system geometry you can calculate distances The is an old method used for navigation and surveying Digital Image Correlation is the method pushed to the extremes: Conduct high-precision surface shape measurements Measure displacement of objects as they rotate and translate within 3D space Measure strain on object surfaces as they deform under load Triangulation: Distance to an object Aim telescopes at locations A and B (known distance apart) at an object, measure a and b angles. Obviously, both telescopes have to have line-of-sight to the object. Basic Digital Image Correlation set-up Camera, Sensor, and World Coordinate Systems Better to have cameras in a fixed position and identify points within each image, working out the distance through a more complex coordinate transformation process … that is image correlation. Aluminum beverage can A standard Aluminum beverage can Nearly 20 mm of depth About 90o of the surface covered by the image pair Out of plane distance (z-height) Student Project 1 – Can Buckling Example shows very precise 3D shape measurement over a highly curved region with very large depth excursion (~ 20 mm). Project Workflow Equipment and Imaging set-up Target Images and Calibration Test Images and Correlation Post-processing (Data Workflow) 1. Calibration Prepares images and establishes the geometric context for stereo-imaging Intrinsic camera parameters Lens effective focal length Lens distortion correction parameters Options available for various distortion characteristics Extrinsic stereo system parameters Geometry of the stereo set-up Distance between and orientation of cameras Coordinate system of the virtual working volume This information supports very precise triangulation 2. Correlation Convert a ROI point cloud into x,y,z point positions in the volume coordinate system Point cloud is defined as a set of positions on the object surface in the Ref-Left camera image Location of each point in the Ref-Right camera image allows calculation of 3D positions Connect ROI point clouds between in situ experimental steps Correlation between Ref-Left and Step1-Left moves the points with the object (as opposed to a new set of locations on the surface) Convert point cloud at the first load step into x,y,z point positions Correlation between Step1-Left and Step1-Right This completes a load step and provides information for displacement and strain post-processing Ref Step1 Step2 • • • (a) (b) (c) Left Camera Right Camera Stereo Pair 1 Stereo Pair 2 Stereo Pair 3 + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 3. Post-Processing Calculate displacements from point positions This is simple. For each of the n points in the cloud, at each load step, subtract the reference position: u = (x1 – x0), v = (y1 – yo), w = (z1 – z0) This establishes a “total Lagrangian” perspective, with the initial configuration used as the basis for analysis Calculate the displacement gradient tensor Not so easy for irregularly spaced points Often involves a filtering or local fitting approach to control noise Method influences the effective spatial resolution of the result Calculate strain tensor from the displacement gradient Interpret the strain tensor We are now done with correlation, no more image processing. Post-processing operates purely from the x,y,z point positions established during the correlation step. Step 1 displacements Step 2 displacements etc. for the remaining steps Correlated Solutions output file shows the progression A flat surface seems relatively simple X Y How do we manage a curved surface? files/03-strain-vob35r3q.pptx Data Workflow Shape Displacement Strain Stress From Shape to Stress Stress is often the goal of a mechanics analysis Most closely related to common failure criteria (max normal stress, von Mises stress, etc.) A common language for comparing results to prior work in a field But fundamentally DIC just measures object shape Points on the surface of an object located within a 3D coordinate system How do we get from