Paper focuses on the development of an uncertain constitutive model for the analysis of hyperelastic behavior of rubber-like materials. One of the main obstacles in constitutive models is that they are deterministic and cannot show us the error and uncertainty in material behavior. It is hard to manufacture elastomers with identical mechanical properties. Intrestingly, even specimens made from the same batch shows different strain-stress behavior. It is axiomatic that this error may affect their real-world applications. There are several reasons for the variability of the response of elastomeric materials, which each of them depends on many unknown factors. Some of these factors can be controlled in the production process. Deterministic approaches are used to predict the mechanical behavior and properties of the material. Material parameters related to deterministic models can have different values due to different outcomes of experiments. From a mathematical point of view, probabilistic modeling can improve this problem. It means that parameters in constitutive models can be characterized by probability distributions.   
To address this problem, we propose an uncertainty quantification(UQ) approach to be omlemented on constitutive models of rubber-like materials. UQ reduces uncertainties in both computational and real-world applications. There are two types of uncertainty. Aleatory which naturally, occurs randomly and we cannot (or do not know how to) reduce, and epistemic which is because of lack of knowledge and we can reduce it by paying a price. Constitutive models in elastomers play a crucial role in both science and industry due to their unique hyperelastic behavior under different loading conditions (uniaxial extension, biaxial, or pure shear). Here our goal is to model the uncertainty in constitutive models of elastomers, and accordingly, identify senstitive paramters that we highly contribute to model uncertainty and error. Modern UQ models can be implemented to use the physics of the problem compared to balck-box machine learning approaches that uses data only . In this research, we propagate uncertainty through the model, characterize sensitivity to inputs to show the importance of each parameter for uncertainty reduction. To this end, we utilized Bayesian rules to develop a model considering uncertainty in the mechanical properties of elastomers. As an important assumption, we believe that our measurements are around the model prediction, but it is contaminated by Gaussian noise. We can make the noise by maximizing the posterior. The uniaxial extension experimental data set is used to calibrate the model and propagate uncertainty in this research.  
 


Uncertainty Quantification in Predicting Behaviour of Rubber-Like Materials in Uni-Axial Loading

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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