A D V A N C E D M A T E R I A L S & P R O C E S S E S | O C T O B E R 2 0 2 2 3 9 9 (a) FEATURE NiTi material is shown in Fig. 2a and the six material property inputs for the superelastic model in Abaqus—austenite and martensite loading slopes (EA and EM), tensile plateau stresses (σUPS and σLPS), compressive plateau stress (σCPS), and transformation strain (εt)—are annotated in the stress-strain curve. A standard diamond specimen geometry is used. When a diamond specimen is loaded in the deformation sequence shown in Fig. 2b, its struts are subject to bending, and the specimen thus exhibits both tensile and compressive strains as reflected in the shear strains shown in Fig. 2c. The surface strains are experimentally measured using a single-camera DIC setup. A computational model of the dia- mond geometry shown in Fig. 2a is built in Abaqus, and the superelas- tic constitutive material model and the loading path shown in Fig. 2b are applied. A simulation library is constructed by instantiating the model 544 times with varied material parameter inputs. Specifically, the six material parameters are varied such that they span the typical range of values observed in commercially relevant NiTi. From each simulation result, a quantity of interest (QoI) is defined based on: (1) the local strain values at points 1 to 4 shown in Fig. 2c and (2) the global load values in the loading direction at 22 equidistant points on the loading path A-B-C shown in Fig. 2b. A regression model is fitted using the support vector machine (SVM) machine learning (ML) method that takes a set of six material parameters as inputs and furnishes the QoI values. Given an experimental dataset consisting of QoIs listed above and the trained SVM model that estimates the simulated QoIs, the optimum material parameters are determined using the BI method, which is a statistical method of determining probability of a hypothesis based on available data. The numerical determination of the Abaqus material parameter probability distributions is performed using Markov Chain Monte Carlo (MCMC) sampling[5]. In summary, given an experimental dataset consisting of local surface strain and global load data from a tensile test and a simulation library built from a model of the experimental protocol, the method furnishes the probability distributions for the six key material parameters for the superelastic constitutive model in Abaqus. The uncertainty in the determined material properties can be quantified from the width of the probability distribution and is expressed in terms of credibility intervals. CALIBRATION RESULTS USING GLOBAL LOAD AND LOCAL STRAIN DATA Sample results for material parameter determination using the BI method are shown in Fig. 3. The probability distributions for the six material parameters are given in Fig. 3a, where the median parameters (dashed lines) and the 95% credibility intervals (gray highlights) are annotated. A comparison of the simulated load-displacement curve obtained from the median material parameters and the experimental input data is provided in Fig. 3b. A comparison between the simulated surface strain distribution in the diamond specimen model using the median material parameters and the DICmeasurement of the surface strains at peak load is shown in Fig. 3c. The qualitative agreement between the simulated curve from the calibrated model and the experimental input is reasonable. Quantitatively, the error between the simulation and the experiment is 17.3% when calculated in terms of the mean absolute percent error (MAPE). Fig. 2 — A summary of the test protocol: (a) diamond specimen geometry and a schematic of the superelastic stress-strain response; Y is the sheet rolling direction; (b) schematic of the loading sequence used in the test protocol; and (c) surface strain map of diamond at peak load measured using DIC. Adapted from Paranjape et al.[3]. Fig. 3 — Sample results of the calibration method. (a) Probability distribution of determined material parameters. (b) Comparison of experimental load-displacement data and simulation results from the determined parameters. (c) A comparison of experimental and simulation data for surface shear strain. Adapted from Paranjape et al.[3]. (a) (b) (c) (a) (c) (b) 0 1 1
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