Infinite-Dimensional DIC for Heterogeneous Material Properties
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Solution Overview
Problem
Existing non-destructive evaluation methods for heterogeneous materials face challenges in breadth, reliability, and speed due to high sensitivity to boundary data errors and limitations to well-posed problems, requiring long durations for mechanical testing.
Innovation Solution
An inverse problem analysis system using an ∞-dim IDIC approach that integrates image registration and physics-based modeling to determine spatially varying mechanical parameters, employing adjoint methods and Hessian actions for efficient gradient computation, allowing for rapid and accurate detection of material defects.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If conventional mechanical testing is used to measure material properties, then measurement precision can be achieved, but the testing duration becomes very long and the process becomes complex
Solution Approach 1:
The patent replaces conventional mechanical testing with a computational inverse problem solving approach. Instead of physically testing materials through mechanical loading and deformation, the system uses digital image correlation to capture surface patterns and feeds this data into an inverse problem solver that reconstructs material properties through mathematical optimization, thereby eliminating the need for lengthy mechanical testing procedures
Solution Approach 2:
The patent creates a virtual copy of the material behavior through computational modeling. By capturing the deformation field through image correlation and creating a corresponding computational model that replicates the same deformation under controlled conditions, the system can analyze material properties without physically subjecting the material to destructive mechanical testing
2Reliability
If Digital Image Correlation (DIC) is used for parameter identification, then non-destructive evaluation is achieved, but the approach is highly sensitive to boundary data errors and limited to well-posed problems
Solution Approach 1:
The patent implements an iterative inverse problem solving process that uses feedback from the computational model to refine material property estimates. The system continuously compares model predictions with actual image correlation data and adjusts the inferred material properties accordingly, allowing the system to compensate for boundary data errors and converge on accurate material parameters even when input data contains noise or uncertainties
Solution Approach 2:
The patent transforms the problem from directly measuring material parameters to inferring them through a change in approach. Instead of directly measuring properties that are sensitive to boundary conditions, the system changes the measurement approach to capture deformation fields and then invert these to obtain material properties, thereby changing the parameter space in which the solution is sought to one that is more robust to measurement errors
3Measurement precision
If high-resolution analysis is performed to understand heterogeneous material behavior, then measurement precision improves, but the computational time and complexity increase significantly
Solution Approach 1:
The patent segments the material analysis into distinct spatial scales through the use of digital image correlation that can resolve features at different resolutions. By capturing deformation fields at the micro-scale through high-resolution images and then using computational modeling to connect these to macro-scale material properties, the system achieves multi-scale analysis without requiring computationally intensive simulations at every scale simultaneously
Data Source
AI summary
An exemplary system and method that employ inverse-problem analysis that can determine spatially-varying mechanical parameters in a spatially-varying field of a heterogeneous material. Mathematically, the computation simultaneously poses the inversion program and an image registration problem in a continuum limit function space setting to derive a discretization dimension-independent algorithm for the robust inference of heterogeneous material properties. The algorithm can operate using two or more images of a speckled pattern or other non-uniform patterns applied to, or observable of, the surface of the material in a first state and a second state different from the first state. The difference can be used to assess, via a Newtonian-based operator, the infinite-dimensional spatial fields as state variables that are regularized via a regularization model to constrain the inherent ill-posed nature of inverse problems.