Application of radial basis neural network to transform viscoelastic to elastic properties for materials with multiple thermal transitions

• Published in: Journal of materials science 2019-06, Vol.54 (11), p.8401-8413
• Main Authors: Xu, Xianbo, Gupta, Nikhil
• Format: Article
• Language: English
• Subjects: Back propagation; Back propagation networks; Characterization and Evaluation of Materials; Chemistry and Materials Science; Classical Mechanics; Computation and Theory; Crystallography and Scattering Methods; Dynamic mechanical analysis; Elastic properties; Elastomers; Ethylene vinyl acetates; Loss modulus; Materials Science; Mechanical engineering; Modulus of elasticity; Neural networks; Polymer Sciences; Room temperature; Solid Mechanics; Storage modulus; Strain; Stress relaxation; Superposition (mathematics); Temperature; Tensile tests; Time domain analysis; Transformations (mathematics); Viscoelasticity
• ISSN: 0022-2461; 1573-4803
• DOI: 10.1007/s10853-019-03481-0

Dynamic mechanical analysis is a method to characterize the frequency domain viscoelastic properties including storage and loss moduli. Methods have been developed to transform these properties to time domain and extract elastic modulus over strain rates, which is useful in mechanical design. However, application of these methods becomes increasingly complex for materials containing multiple thermal transitions. Neural networks can provide advantages in solving such problems. As the form of radial basis neural network satisfies the form obtained from time–temperature superposition principle, it is used in the present work with back-propagation to establish the master relation of loss modulus. The influence of regulation factor and neuron number is investigated to find the best parameter set. Then, storage modulus is divided into frequency-dependent and frequency-independent part. Both parts are individually calculated from loss modulus using Kramers–Kronig relation. The linear integral relation of viscoelasticity can transform the storage modulus into time-domain relaxation modulus, which can predict the stress response with specific strain history and temperature. The transformation is tested on ethylene–vinyl acetate. The time-domain elastic properties are extracted and compared with those from tensile tests at room temperature. The transformation achieves an average root mean square error of 3.3% and a maximum error 4.9% between strain rates 10 −6 to 10 −2  s −1 . This process can predict the properties at a wide range of temperatures and frequencies from a single specimen and can be implemented using parallel computing, which is promising for complex material systems.