Stochastic identification of elastic constants for anisotropic materials

Abstract

SUMMARYThis paper presents an energy-based characterization technique that stochastically identifies the elastic constants of anisotropic materials by modeling the measurement noise and removing its effect unlike conventional deterministic techniques, which deterministically identify the elastic constants directly from noisy measurements. The technique recursively estimates the elastic constants at every acquisition of measurements using Kalman Filter. Owing to the non-linear expression of the measurement model, a Kalman gain has been newly derived and achieves optimal estimation. Since the variances in addition to the means are computed, the proposed technique can not only identify the elastic constants but also describe their certainty as an additional advantage. The validity of the proposed technique and its superiority to the conventional technique were first demonstrated via parametric studies of low-dimensional problems. The proposed technique was then successfully applied to the identification of elastic constants of an anisotropic material.

Inverse characterization of composite materials via surrogate modeling

“…Nonparametric constitutive models of anisotropic materials have also been used to identify elastic constants. The use of stochastic corrections to parameter estimates using Kalman filtering is shown in [30]. Another approach based on the use of artificial neural networks [31] is presented in [32] and further demonstrated in [33].…”

“…of x i , at each of which the model of Equations(30)(31)(32)(33) was evaluated at 25 combinations of constitutive parameter values, the constitutive model was evaluated 40,000 times in total. The experimental procedure of the previous section was applied, both the generation of the surrogate models and the subsequent optimization were performed on a computer with a quad-core Intel i7 processor and 16 GB of memory.A simulated annealing optimizer, built into the Mathematica computer algebra system, was used to recover the constitutive parameters.…”

Stochastic identification of defects under sensor uncertainties

“…Despite this continuous effort, defect identification still remains as a challenging problem with limited success. This is largely due to the ill‐posedness of the identification problem with considerable measurement uncertainties as the defect can be too small to be detected by an available sensor or, even if large, located significantly away from a sensor or beyond its field of view . This has given rise to the need for an approach that can handle uncertainties and identifies the detects in a structure as reliably and efficiently as possible .…”

Neural network constitutive modelling for non‐linear characterization of anisotropic materials

“…The technique estimates the elastic parameters at every acquisition of a set of measurements by equating the variation of the external work, derived from the surface displacement/force measurements, with that of the induced strain energy, derived from the fullfield strain measurements, and stochastically correcting the estimation using Kalman filter. This technique can be applied without expensive computation or extensive formulations that the other techniques required, and has been proven to identify the elastic parameters of anisotropic materials even under the presence of considerable noise in the measurements [16], although the successful formulations so far are limited to elastic identification.The conventional continuum techniques have all demonstrated the ability to characterize the anisotropic materials while having their strengths in different features [10,13,15]. However, when the material behaviour is non-linear, the problem that the techniques commonly face is the model error inevitably existing in the resulting constitutive model.…”

“…The technique estimates the elastic parameters at every acquisition of a set of measurements by equating the variation of the external work, derived from the surface displacement/force measurements, with that of the induced strain energy, derived from the fullfield strain measurements, and stochastically correcting the estimation using Kalman filter. This technique can be applied without expensive computation or extensive formulations that the other techniques required, and has been proven to identify the elastic parameters of anisotropic materials even under the presence of considerable noise in the measurements [16], although the successful formulations so far are limited to elastic identification.…”